Análisis de la Inflación: Modelado de Series Temporales del Precio del IPC (2000-2024)
Introducción
Este proyecto se centra en el análisis de las tendencias de la inflación global mediante técnicas de modelado de series temporales. El conjunto de datos, procedente del Banco Mundial de Datos, abarca el período 2000-2024 y contiene una amplia gama de indicadores macroeconómicos, como el PIB, la población y diversos indicadores económicos. Sin embargo, el alcance de este proyecto se limita a las variables relacionadas con la inflación, en concreto:
IPC subyacente, sin desestacionalizar
IPC subyacente, desestacionalizado
Precio del IPC (% interanual, ponderado por la mediana, desestacionalizado)
Entre estas variables, el enfoque principal se centra en el precio del IPC (% interanual, ponderado por la mediana, desestacionalizado) para realizar el modelado de series temporales.
Objetivos del Proyecto
El objetivo principal de este proyecto es comprender la dinámica de la inflación global y continental durante las últimas tres décadas y pronosticar tendencias futuras. Para lograrlo:
Exploramos tendencias históricas: Analizamos datos de inflación a nivel mundial y por continente para identificar patrones y anomalías.
Aplicamos modelos de series temporales: Utilizamos modelos ARIMA para analizar y pronosticar el IPC en diferentes continentes.
Generamos información: Obtuvimos información práctica sobre las presiones inflacionarias y sus implicaciones para las economías globales.
Preparación de los datos.
Librerías que se utilizarán en este informe.
library(readr)
library(tidyverse)
library(zoo)
library(naniar)
library(janitor)
library(tseries)
library(forecast)
library(VIM)
library(mice)Los datos fueron extraídos de la base de datos Global Economic Monitor (GEM) que hace parte del Banco Mundial.
Global <- read_csv("~/R/Proyectos/inflacion/0cd27072-2afd-43d6-8837-6eb4fdf2c0b8_Data.csv")
sample_n(Global, 20)## # A tibble: 20 × 129
## Country `Country Code` Series `Series Code` `2000 [2000]` `2000Q1 [2000Q1]`
## <chr> <chr> <chr> <chr> <chr> <chr>
## 1 Central … CAF Excha… DPANUSSPB 711.77879120… ..
## 2 Kenya KEN Core … CORESA .. ..
## 3 Cote d'I… CIV Expor… DXGSRMRCHSAXD .. ..
## 4 Namibia NAM Terms… TOT .. ..
## 5 Mongolia MNG Excha… DPANUSSPB 1073.6650119… ..
## 6 Algeria DZA Expor… DXGSRMRCHSAXD .. ..
## 7 Sao Tome… STP Offic… DPANUSLCU 7.97816666667 ..
## 8 Gambia T… GMB Impor… DMGSRMRCHSACD .. 76.76913887153
## 9 Croatia HRV Core … CORESA .. ..
## 10 Belgium BEL GDP,c… NYGDPMKTPSAKN 362586 89725
## 11 Guatemala GTM Expor… DXGSRMRCHSAXD .. ..
## 12 Greenland GRL Offic… DPANUSLCU 8.08314416667 ..
## 13 Swaziland SWZ Expor… DXGSRMRCHNSKD .. ..
## 14 Slovenia SVN Expor… DXGSRMRCHNSXD .. ..
## 15 Latvia LVA Expor… DXGSRMRCHSAKD .. ..
## 16 Armenia ARM CPI P… CPTOTSAXNZGY -0.739175342… ..
## 17 Kenya KEN Indus… IPTOTSAKD .. ..
## 18 Bahamas … BHS Core … CORESA .. ..
## 19 Netherla… NLD Impor… DMGSRMRCHNSXD 0.64287085423 0.66393601904
## 20 Botswana BWA Month… IMPCOV 2.77050366357 ..
## # ℹ 123 more variables: `2000Q2 [2000Q2]` <chr>, `2000Q3 [2000Q3]` <chr>,
## # `2000Q4 [2000Q4]` <chr>, `2001 [2001]` <chr>, `2001Q1 [2001Q1]` <chr>,
## # `2001Q2 [2001Q2]` <chr>, `2001Q3 [2001Q3]` <chr>, `2001Q4 [2001Q4]` <chr>,
## # `2002 [2002]` <chr>, `2002Q1 [2002Q1]` <chr>, `2002Q2 [2002Q2]` <chr>,
## # `2002Q3 [2002Q3]` <chr>, `2002Q4 [2002Q4]` <chr>, `2003 [2003]` <chr>,
## # `2003Q1 [2003Q1]` <chr>, `2003Q2 [2003Q2]` <chr>, `2003Q3 [2003Q3]` <chr>,
## # `2003Q4 [2003Q4]` <chr>, `2004 [2004]` <chr>, `2004Q1 [2004Q1]` <chr>, …head(Global, 20)## # A tibble: 20 × 129
## Country `Country Code` Series `Series Code` `2000 [2000]` `2000Q1 [2000Q1]`
## <chr> <chr> <chr> <chr> <chr> <chr>
## 1 Afghanis… AFG Core … CORENS .. ..
## 2 Afghanis… AFG Core … CORESA .. ..
## 3 Afghanis… AFG CPI P… CPTOTSAXMZGY .. ..
## 4 Afghanis… AFG CPI P… CPTOTSAXNZGY .. ..
## 5 Afghanis… AFG CPI P… CPTOTSAXN .. ..
## 6 Afghanis… AFG CPI P… CPTOTNSXN .. ..
## 7 Afghanis… AFG Excha… DPANUSSPB 47.356666666… ..
## 8 Afghanis… AFG Excha… DPANUSSPF 47.356666666… ..
## 9 Afghanis… AFG Expor… DXGSRMRCHNSKD .. ..
## 10 Afghanis… AFG Expor… DXGSRMRCHSAKD .. ..
## 11 Afghanis… AFG Expor… DXGSRMRCHNSCD .. ..
## 12 Afghanis… AFG Expor… DXGSRMRCHSACD .. ..
## 13 Afghanis… AFG Expor… DXGSRMRCHNSXD .. ..
## 14 Afghanis… AFG Expor… DXGSRMRCHSAXD .. ..
## 15 Afghanis… AFG GDP,c… NYGDPMKTPSAKN .. ..
## 16 Afghanis… AFG GDP,c… NYGDPMKTPSAKD .. ..
## 17 Afghanis… AFG GDP,c… NYGDPMKTPSACN .. ..
## 18 Afghanis… AFG GDP,c… NYGDPMKTPSACD .. ..
## 19 Afghanis… AFG Impor… DMGSRMRCHNSKD .. ..
## 20 Afghanis… AFG Impor… DMGSRMRCHSAKD .. ..
## # ℹ 123 more variables: `2000Q2 [2000Q2]` <chr>, `2000Q3 [2000Q3]` <chr>,
## # `2000Q4 [2000Q4]` <chr>, `2001 [2001]` <chr>, `2001Q1 [2001Q1]` <chr>,
## # `2001Q2 [2001Q2]` <chr>, `2001Q3 [2001Q3]` <chr>, `2001Q4 [2001Q4]` <chr>,
## # `2002 [2002]` <chr>, `2002Q1 [2002Q1]` <chr>, `2002Q2 [2002Q2]` <chr>,
## # `2002Q3 [2002Q3]` <chr>, `2002Q4 [2002Q4]` <chr>, `2003 [2003]` <chr>,
## # `2003Q1 [2003Q1]` <chr>, `2003Q2 [2003Q2]` <chr>, `2003Q3 [2003Q3]` <chr>,
## # `2003Q4 [2003Q4]` <chr>, `2004 [2004]` <chr>, `2004Q1 [2004Q1]` <chr>, …tail(Global,20)## # A tibble: 20 × 129
## Country `Country Code` Series `Series Code` `2000 [2000]` `2000Q1 [2000Q1]`
## <chr> <chr> <chr> <chr> <chr> <chr>
## 1 Zimbabwe ZWE Impor… DMGSRMRCHSACD .. ..
## 2 Zimbabwe ZWE Impor… DMGSRMRCHNSXD .. 0.74071867439
## 3 Zimbabwe ZWE Impor… DMGSRMRCHSAXD .. 0.74071867439
## 4 Zimbabwe ZWE Indus… IPTOTSAKD .. ..
## 5 Zimbabwe ZWE Indus… IPTOTNSKD .. ..
## 6 Zimbabwe ZWE Month… IMPCOV .. ..
## 7 Zimbabwe ZWE Nomin… NEER .. ..
## 8 Zimbabwe ZWE Offic… DPANUSLCU 2.152E-08 ..
## 9 Zimbabwe ZWE Real … REER .. ..
## 10 Zimbabwe ZWE Retai… RETSALESSA .. ..
## 11 Zimbabwe ZWE Stock… DSTKMKTXN .. ..
## 12 Zimbabwe ZWE Stock… DSTKMKTXD .. ..
## 13 Zimbabwe ZWE Terms… TOT .. ..
## 14 Zimbabwe ZWE Total… TOTRESV 214.42984777… ..
## 15 Zimbabwe ZWE Unemp… UNEMPSA_ .. ..
## 16 <NA> <NA> <NA> <NA> <NA> <NA>
## 17 <NA> <NA> <NA> <NA> <NA> <NA>
## 18 <NA> <NA> <NA> <NA> <NA> <NA>
## 19 Data fro… <NA> <NA> <NA> <NA> <NA>
## 20 Last Upd… <NA> <NA> <NA> <NA> <NA>
## # ℹ 123 more variables: `2000Q2 [2000Q2]` <chr>, `2000Q3 [2000Q3]` <chr>,
## # `2000Q4 [2000Q4]` <chr>, `2001 [2001]` <chr>, `2001Q1 [2001Q1]` <chr>,
## # `2001Q2 [2001Q2]` <chr>, `2001Q3 [2001Q3]` <chr>, `2001Q4 [2001Q4]` <chr>,
## # `2002 [2002]` <chr>, `2002Q1 [2002Q1]` <chr>, `2002Q2 [2002Q2]` <chr>,
## # `2002Q3 [2002Q3]` <chr>, `2002Q4 [2002Q4]` <chr>, `2003 [2003]` <chr>,
## # `2003Q1 [2003Q1]` <chr>, `2003Q2 [2003Q2]` <chr>, `2003Q3 [2003Q3]` <chr>,
## # `2003Q4 [2003Q4]` <chr>, `2004 [2004]` <chr>, `2004Q1 [2004Q1]` <chr>, …Se extraen las filas que contienen indicadores macroeconómicos en la columna “País” y se crea un conjunto de datos de indicadores macroeconómicos.
macroeconomics_indicator <- Global %>%
filter(Country %in% unique(Global$Country)[grep("EMDE|Countries|Income|developing|Emerging Market|High Income|World|Advanced Economies|Commodity", unique(Global$Country))])
#Elimine estas filas de los datos originales para conservar solo las filas con nombres de países
Global <- Global %>%
filter(!Country %in% macroeconomics_indicator$Country)A continuación, se eliminan los duplicados y se visualizan variables y linea de tiempo que hacen parte del archivo de datos.
distinct(Global)## # A tibble: 7,059 × 129
## Country `Country Code` Series `Series Code` `2000 [2000]` `2000Q1 [2000Q1]`
## <chr> <chr> <chr> <chr> <chr> <chr>
## 1 Afghanis… AFG Core … CORENS .. ..
## 2 Afghanis… AFG Core … CORESA .. ..
## 3 Afghanis… AFG CPI P… CPTOTSAXMZGY .. ..
## 4 Afghanis… AFG CPI P… CPTOTSAXNZGY .. ..
## 5 Afghanis… AFG CPI P… CPTOTSAXN .. ..
## 6 Afghanis… AFG CPI P… CPTOTNSXN .. ..
## 7 Afghanis… AFG Excha… DPANUSSPB 47.356666666… ..
## 8 Afghanis… AFG Excha… DPANUSSPF 47.356666666… ..
## 9 Afghanis… AFG Expor… DXGSRMRCHNSKD .. ..
## 10 Afghanis… AFG Expor… DXGSRMRCHSAKD .. ..
## # ℹ 7,049 more rows
## # ℹ 123 more variables: `2000Q2 [2000Q2]` <chr>, `2000Q3 [2000Q3]` <chr>,
## # `2000Q4 [2000Q4]` <chr>, `2001 [2001]` <chr>, `2001Q1 [2001Q1]` <chr>,
## # `2001Q2 [2001Q2]` <chr>, `2001Q3 [2001Q3]` <chr>, `2001Q4 [2001Q4]` <chr>,
## # `2002 [2002]` <chr>, `2002Q1 [2002Q1]` <chr>, `2002Q2 [2002Q2]` <chr>,
## # `2002Q3 [2002Q3]` <chr>, `2002Q4 [2002Q4]` <chr>, `2003 [2003]` <chr>,
## # `2003Q1 [2003Q1]` <chr>, `2003Q2 [2003Q2]` <chr>, …unique(Global$Series)## [1] "Core CPI,not seas.adj,,,"
## [2] "Core CPI,seas.adj,,,"
## [3] "CPI Price, % y-o-y, median weighted, seas. adj.,"
## [4] "CPI Price, % y-o-y, not seas. adj.,,"
## [5] "CPI Price, seas. adj.,,,"
## [6] "CPI Price,not seas.adj,,,"
## [7] "Exchange rate, new LCU per USD extended backward, period average,,"
## [8] "Exchange rate, old LCU per USD extended forward, period average,,"
## [9] "Exports Merchandise, Customs, constant US$, millions, not seas. adj."
## [10] "Exports Merchandise, Customs, constant US$, millions, seas. adj."
## [11] "Exports Merchandise, Customs, current US$, millions, not seas. adj."
## [12] "Exports Merchandise, Customs, current US$, millions, seas. adj."
## [13] "Exports Merchandise, Customs, Price, US$, not seas. adj."
## [14] "Exports Merchandise, Customs, Price, US$, seas. adj."
## [15] "GDP,constant 2010 LCU,millions,seas. adj.,"
## [16] "GDP,constant 2010 US$,millions,seas. adj.,"
## [17] "GDP,current LCU,millions,seas. adj.,"
## [18] "GDP,current US$,millions,seas. adj.,"
## [19] "Imports Merchandise, Customs, constant US$, millions, not seas. adj."
## [20] "Imports Merchandise, Customs, constant US$, millions, seas. adj."
## [21] "Imports Merchandise, Customs, current US$, millions, not seas. adj."
## [22] "Imports Merchandise, Customs, current US$, millions, seas. adj."
## [23] "Imports Merchandise, Customs, Price, US$, not seas. adj."
## [24] "Imports Merchandise, Customs, Price, US$, seas. adj."
## [25] "Industrial Production, constant US$, seas. adj.,,"
## [26] "Industrial Production, constant US$,,,"
## [27] "Months Import Cover of Foreign Reserves,,,,"
## [28] "Nominal Effective Exchange Rate,,,,"
## [29] "Official exchange rate, LCU per USD, period average,,"
## [30] "Real Effective Exchange Rate,,,,"
## [31] "Retail Sales Volume,Index,,,"
## [32] "Stock Markets, LCU,,,"
## [33] "Stock Markets, US$,,,"
## [34] "Terms of Trade,,,,"
## [35] "Total Reserves,,,,"
## [36] "Unemployment rate,Percent,,,"
## [37] NAstr(Global)## spc_tbl_ [7,061 × 129] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
## $ Country : chr [1:7061] "Afghanistan" "Afghanistan" "Afghanistan" "Afghanistan" ...
## $ Country Code : chr [1:7061] "AFG" "AFG" "AFG" "AFG" ...
## $ Series : chr [1:7061] "Core CPI,not seas.adj,,," "Core CPI,seas.adj,,," "CPI Price, % y-o-y, median weighted, seas. adj.," "CPI Price, % y-o-y, not seas. adj.,," ...
## $ Series Code : chr [1:7061] "CORENS" "CORESA" "CPTOTSAXMZGY" "CPTOTSAXNZGY" ...
## $ 2000 [2000] : chr [1:7061] ".." ".." ".." ".." ...
## $ 2000Q1 [2000Q1]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2000Q2 [2000Q2]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2000Q3 [2000Q3]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2000Q4 [2000Q4]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2001 [2001] : chr [1:7061] ".." ".." ".." ".." ...
## $ 2001Q1 [2001Q1]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2001Q2 [2001Q2]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2001Q3 [2001Q3]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2001Q4 [2001Q4]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2002 [2002] : chr [1:7061] ".." ".." ".." ".." ...
## $ 2002Q1 [2002Q1]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2002Q2 [2002Q2]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2002Q3 [2002Q3]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2002Q4 [2002Q4]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2003 [2003] : chr [1:7061] ".." ".." ".." ".." ...
## $ 2003Q1 [2003Q1]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2003Q2 [2003Q2]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2003Q3 [2003Q3]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2003Q4 [2003Q4]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2004 [2004] : chr [1:7061] ".." ".." ".." ".." ...
## $ 2004Q1 [2004Q1]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2004Q2 [2004Q2]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2004Q3 [2004Q3]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2004Q4 [2004Q4]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2005 [2005] : chr [1:7061] ".." ".." ".." "10.24715592289" ...
## $ 2005Q1 [2005Q1]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2005Q2 [2005Q2]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2005Q3 [2005Q3]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2005Q4 [2005Q4]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2006 [2006] : chr [1:7061] ".." ".." ".." "6.76652570958" ...
## $ 2006Q1 [2006Q1]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2006Q2 [2006Q2]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2006Q3 [2006Q3]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2006Q4 [2006Q4]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2007 [2007] : chr [1:7061] ".." ".." ".." "8.66675778504" ...
## $ 2007Q1 [2007Q1]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2007Q2 [2007Q2]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2007Q3 [2007Q3]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2007Q4 [2007Q4]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2008 [2008] : chr [1:7061] ".." ".." ".." "26.44383832063" ...
## $ 2008Q1 [2008Q1]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2008Q2 [2008Q2]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2008Q3 [2008Q3]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2008Q4 [2008Q4]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2009 [2009] : chr [1:7061] ".." ".." ".." "-6.79140946808" ...
## $ 2009Q1 [2009Q1]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2009Q2 [2009Q2]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2009Q3 [2009Q3]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2009Q4 [2009Q4]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2010 [2010] : chr [1:7061] ".." ".." ".." "2.18628234597" ...
## $ 2010Q1 [2010Q1]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2010Q2 [2010Q2]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2010Q3 [2010Q3]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2010Q4 [2010Q4]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2011 [2011] : chr [1:7061] ".." ".." ".." "11.82724209156" ...
## $ 2011Q1 [2011Q1]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2011Q2 [2011Q2]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2011Q3 [2011Q3]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2011Q4 [2011Q4]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2012 [2012] : chr [1:7061] ".." ".." ".." "6.44138171658" ...
## $ 2012Q1 [2012Q1]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2012Q2 [2012Q2]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2012Q3 [2012Q3]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2012Q4 [2012Q4]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2013 [2013] : chr [1:7061] ".." ".." ".." "7.38136116922" ...
## $ 2013Q1 [2013Q1]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2013Q2 [2013Q2]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2013Q3 [2013Q3]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2013Q4 [2013Q4]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2014 [2014] : chr [1:7061] ".." ".." ".." "4.66945580562" ...
## $ 2014Q1 [2014Q1]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2014Q2 [2014Q2]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2014Q3 [2014Q3]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2014Q4 [2014Q4]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2015 [2015] : chr [1:7061] ".." ".." ".." "-0.6701681989" ...
## $ 2015Q1 [2015Q1]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2015Q2 [2015Q2]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2015Q3 [2015Q3]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2015Q4 [2015Q4]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2016 [2016] : chr [1:7061] ".." ".." ".." "4.39026872486" ...
## $ 2016Q1 [2016Q1]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2016Q2 [2016Q2]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2016Q3 [2016Q3]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2016Q4 [2016Q4]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2017 [2017] : chr [1:7061] ".." ".." ".." "4.97948067594" ...
## $ 2017Q1 [2017Q1]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2017Q2 [2017Q2]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2017Q3 [2017Q3]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2017Q4 [2017Q4]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2018 [2018] : chr [1:7061] ".." ".." ".." "0.62169546733" ...
## $ 2018Q1 [2018Q1]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2018Q2 [2018Q2]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2018Q3 [2018Q3]: chr [1:7061] ".." ".." ".." ".." ...
## $ 2018Q4 [2018Q4]: chr [1:7061] ".." ".." ".." ".." ...
## [list output truncated]
## - attr(*, "spec")=
## .. cols(
## .. Country = col_character(),
## .. `Country Code` = col_character(),
## .. Series = col_character(),
## .. `Series Code` = col_character(),
## .. `2000 [2000]` = col_character(),
## .. `2000Q1 [2000Q1]` = col_character(),
## .. `2000Q2 [2000Q2]` = col_character(),
## .. `2000Q3 [2000Q3]` = col_character(),
## .. `2000Q4 [2000Q4]` = col_character(),
## .. `2001 [2001]` = col_character(),
## .. `2001Q1 [2001Q1]` = col_character(),
## .. `2001Q2 [2001Q2]` = col_character(),
## .. `2001Q3 [2001Q3]` = col_character(),
## .. `2001Q4 [2001Q4]` = col_character(),
## .. `2002 [2002]` = col_character(),
## .. `2002Q1 [2002Q1]` = col_character(),
## .. `2002Q2 [2002Q2]` = col_character(),
## .. `2002Q3 [2002Q3]` = col_character(),
## .. `2002Q4 [2002Q4]` = col_character(),
## .. `2003 [2003]` = col_character(),
## .. `2003Q1 [2003Q1]` = col_character(),
## .. `2003Q2 [2003Q2]` = col_character(),
## .. `2003Q3 [2003Q3]` = col_character(),
## .. `2003Q4 [2003Q4]` = col_character(),
## .. `2004 [2004]` = col_character(),
## .. `2004Q1 [2004Q1]` = col_character(),
## .. `2004Q2 [2004Q2]` = col_character(),
## .. `2004Q3 [2004Q3]` = col_character(),
## .. `2004Q4 [2004Q4]` = col_character(),
## .. `2005 [2005]` = col_character(),
## .. `2005Q1 [2005Q1]` = col_character(),
## .. `2005Q2 [2005Q2]` = col_character(),
## .. `2005Q3 [2005Q3]` = col_character(),
## .. `2005Q4 [2005Q4]` = col_character(),
## .. `2006 [2006]` = col_character(),
## .. `2006Q1 [2006Q1]` = col_character(),
## .. `2006Q2 [2006Q2]` = col_character(),
## .. `2006Q3 [2006Q3]` = col_character(),
## .. `2006Q4 [2006Q4]` = col_character(),
## .. `2007 [2007]` = col_character(),
## .. `2007Q1 [2007Q1]` = col_character(),
## .. `2007Q2 [2007Q2]` = col_character(),
## .. `2007Q3 [2007Q3]` = col_character(),
## .. `2007Q4 [2007Q4]` = col_character(),
## .. `2008 [2008]` = col_character(),
## .. `2008Q1 [2008Q1]` = col_character(),
## .. `2008Q2 [2008Q2]` = col_character(),
## .. `2008Q3 [2008Q3]` = col_character(),
## .. `2008Q4 [2008Q4]` = col_character(),
## .. `2009 [2009]` = col_character(),
## .. `2009Q1 [2009Q1]` = col_character(),
## .. `2009Q2 [2009Q2]` = col_character(),
## .. `2009Q3 [2009Q3]` = col_character(),
## .. `2009Q4 [2009Q4]` = col_character(),
## .. `2010 [2010]` = col_character(),
## .. `2010Q1 [2010Q1]` = col_character(),
## .. `2010Q2 [2010Q2]` = col_character(),
## .. `2010Q3 [2010Q3]` = col_character(),
## .. `2010Q4 [2010Q4]` = col_character(),
## .. `2011 [2011]` = col_character(),
## .. `2011Q1 [2011Q1]` = col_character(),
## .. `2011Q2 [2011Q2]` = col_character(),
## .. `2011Q3 [2011Q3]` = col_character(),
## .. `2011Q4 [2011Q4]` = col_character(),
## .. `2012 [2012]` = col_character(),
## .. `2012Q1 [2012Q1]` = col_character(),
## .. `2012Q2 [2012Q2]` = col_character(),
## .. `2012Q3 [2012Q3]` = col_character(),
## .. `2012Q4 [2012Q4]` = col_character(),
## .. `2013 [2013]` = col_character(),
## .. `2013Q1 [2013Q1]` = col_character(),
## .. `2013Q2 [2013Q2]` = col_character(),
## .. `2013Q3 [2013Q3]` = col_character(),
## .. `2013Q4 [2013Q4]` = col_character(),
## .. `2014 [2014]` = col_character(),
## .. `2014Q1 [2014Q1]` = col_character(),
## .. `2014Q2 [2014Q2]` = col_character(),
## .. `2014Q3 [2014Q3]` = col_character(),
## .. `2014Q4 [2014Q4]` = col_character(),
## .. `2015 [2015]` = col_character(),
## .. `2015Q1 [2015Q1]` = col_character(),
## .. `2015Q2 [2015Q2]` = col_character(),
## .. `2015Q3 [2015Q3]` = col_character(),
## .. `2015Q4 [2015Q4]` = col_character(),
## .. `2016 [2016]` = col_character(),
## .. `2016Q1 [2016Q1]` = col_character(),
## .. `2016Q2 [2016Q2]` = col_character(),
## .. `2016Q3 [2016Q3]` = col_character(),
## .. `2016Q4 [2016Q4]` = col_character(),
## .. `2017 [2017]` = col_character(),
## .. `2017Q1 [2017Q1]` = col_character(),
## .. `2017Q2 [2017Q2]` = col_character(),
## .. `2017Q3 [2017Q3]` = col_character(),
## .. `2017Q4 [2017Q4]` = col_character(),
## .. `2018 [2018]` = col_character(),
## .. `2018Q1 [2018Q1]` = col_character(),
## .. `2018Q2 [2018Q2]` = col_character(),
## .. `2018Q3 [2018Q3]` = col_character(),
## .. `2018Q4 [2018Q4]` = col_character(),
## .. `2019 [2019]` = col_character(),
## .. `2019Q1 [2019Q1]` = col_character(),
## .. `2019Q2 [2019Q2]` = col_character(),
## .. `2019Q3 [2019Q3]` = col_character(),
## .. `2019Q4 [2019Q4]` = col_character(),
## .. `2020 [2020]` = col_character(),
## .. `2020Q1 [2020Q1]` = col_character(),
## .. `2020Q2 [2020Q2]` = col_character(),
## .. `2020Q3 [2020Q3]` = col_character(),
## .. `2020Q4 [2020Q4]` = col_character(),
## .. `2021 [2021]` = col_character(),
## .. `2021Q1 [2021Q1]` = col_character(),
## .. `2021Q2 [2021Q2]` = col_character(),
## .. `2021Q3 [2021Q3]` = col_character(),
## .. `2021Q4 [2021Q4]` = col_character(),
## .. `2022 [2022]` = col_character(),
## .. `2022Q1 [2022Q1]` = col_character(),
## .. `2022Q2 [2022Q2]` = col_character(),
## .. `2022Q3 [2022Q3]` = col_character(),
## .. `2022Q4 [2022Q4]` = col_character(),
## .. `2023 [2023]` = col_character(),
## .. `2023Q1 [2023Q1]` = col_character(),
## .. `2023Q2 [2023Q2]` = col_character(),
## .. `2023Q3 [2023Q3]` = col_character(),
## .. `2023Q4 [2023Q4]` = col_character(),
## .. `2024 [2024]` = col_character(),
## .. `2024Q1 [2024Q1]` = col_character(),
## .. `2024Q2 [2024Q2]` = col_character(),
## .. `2024Q3 [2024Q3]` = col_character(),
## .. `2024Q4 [2024Q4]` = col_character()
## .. )
## - attr(*, "problems")=<externalptr>Reforma los datos de formato ancho a largo.
Global_long <- Global %>%
pivot_longer(
cols = matches("^200\\d|^201\\d|^202\\d"),
names_to = "Year",
values_to = "Value"
)
Global <- Global_long
rm(Global_long)Limpia la columna “año” eliminando la parte entre corchetes (p. ej., “[2000]” o “[2000Q1]”).
Global <- Global %>%
mutate(
Year = gsub("\\[.*\\]", "", Year), # Elimina todo lo que esté dentro de los corchetes
Year = gsub("Q", "-Q", Year), # Reemplace 'Q' con '-Q' para una mejor legibilidad
Year = trimws(Year) # Elimina cualquier espacio inicial o final
)
sample_n(Global, 10)## # A tibble: 10 × 6
## Country `Country Code` Series `Series Code` Year Value
## <chr> <chr> <chr> <chr> <chr> <chr>
## 1 United Arab Emirates ARE Exports Mercha… DXGSRMRCHNSCD 2000… 9937…
## 2 Belgium BEL GDP,current LC… NYGDPMKTPSACN 2017… 1108…
## 3 Brunei BRN Months Import … IMPCOV 2013… ..
## 4 Kiribati KIR GDP,current US… NYGDPMKTPSACD 2015… ..
## 5 San Marino SMR Industrial Pro… IPTOTSAKD 2000… ..
## 6 Ukraine UKR Exports Mercha… DXGSRMRCHSACD 2008 6662…
## 7 Mexico MEX GDP,current LC… NYGDPMKTPSACN 2024… 8594…
## 8 Bermuda BMU Unemployment r… UNEMPSA_ 2012… ..
## 9 Burkina Faso BFA Exports Mercha… DXGSRMRCHNSKD 2009… ..
## 10 Uganda UGA Retail Sales V… RETSALESSA 2021… ..Se define el continente de cada país. Se crea el dataframe y se adjunta al conjunto de datos.
countries <- c(
"Afghanistan", "Algeria", "Antigua and Barbuda", "Armenia", "Albania",
"Angola", "Argentina", "Australia", "Azerbaijan", "Aruba",
"Austria", "Bahamas The", "Bahrain", "Barbados", "Bangladesh",
"Belarus", "Belize", "Belgium", "Benin", "Bermuda",
"Bhutan", "Bosnia and Herzegovina", "Brazil", "Bulgaria", "Burundi",
"Cameroon", "Cape Verde", "Central African Republic", "Chile", "Colombia",
"Bolivia", "Botswana", "Brunei", "Burkina Faso", "Cambodia",
"Canada", "Cayman Islands", "Chad", "China", "Comoros",
"Congo Rep.", "Congo Dem. Rep.", "Costa Rica", "Croatia", "Cyprus",
"Cote d'Ivoire", "Cuba", "Denmark", "Djibouti", "Dominican Republic",
"Czech Republic", "Dominica", "El Salvador", "Ecuador", "Egypt Arab Rep.",
"Equatorial Guinea", "Eritrea", "Ethiopia", "Faeroe Islands", "Fiji",
"France", "Gabon", "Georgia", "Ghana", "Estonia",
"Finland", "French Polynesia", "Gambia The", "Germany", "Greece",
"Grenada", "Guinea", "Guyana", "Hong Kong China", "Iceland",
"Indonesia", "Iraq", "Isle of Man", "Greenland", "Guatemala",
"Guinea-Bissau", "Haiti", "Honduras", "Hungary", "India",
"Iran Islamic Rep.", "Ireland", "Israel", "Jamaica", "Jordan",
"Kenya", "Korea Rep.", "Kyrgyz Republic", "Lebanon", "Liberia",
"Lithuania", "Libya", "Lesotho", "Latvia", "Lao PDR",
"Kuwait", "Kiribati", "Japan", "Italy", "Kazakhstan",
"Luxembourg", "Macedonia FYR", "Malawi", "Maldives", "Malta",
"Mauritius", "Micronesia Fed. Sts.", "Mongolia", "Moldova", "Mexico",
"Mauritania", "Malaysia", "Madagascar", "Macao China", "Mali",
"Morocco", "Myanmar", "Nepal", "Netherlands Antilles", "New Zealand",
"Niger", "Norway", "Pakistan", "Papua New Guinea", "Peru",
"Mozambique", "Namibia", "Netherlands", "New Caledonia", "Nicaragua",
"Nigeria", "Oman", "Panama", "Paraguay", "Philippines",
"Somalia", "Slovenia", "Singapore", "Seychelles", "Senegal",
"Sao Tome and Principe", "Samoa", "Russian Federation", "Poland", "Qatar",
"Portugal", "Romania", "Rwanda", "San Marino", "Saudi Arabia",
"Serbia and Montenegro", "Sierra Leone", "Slovak Republic", "Solomon Islands", "South Africa",
"Spain", "St. Kitts and Nevis", "St. Vincent and the Grenadines", "Sudan", "Suriname",
"Sweden", "Syrian Arab Republic", "Tajikistan", "Thailand", "Togo",
"Timor-Leste", "Tanzania", "Taiwan China", "Switzerland", "Swaziland",
"St. Lucia", "Sri Lanka", "Tonga", "Tunisia", "Turkmenistan",
"Ukraine", "United Kingdom", "Vanuatu", "Vietnam", "Trinidad and Tobago",
"Turkey", "Uganda", "United Arab Emirates", "United States", "Uruguay",
"Uzbekistan", "Venezuela RB", "Virgin Islands (U.S.)", "Yemen Rep.", "Zimbabwe",
"Zambia"
)
continents <- c(
"Asia", "Africa", "North America", "Asia", "Europe",
"Africa", "South America", "Oceania", "Asia", "North America",
"Europe", "North America", "Asia", "North America", "Asia",
"Europe", "North America", "Europe", "Africa", "North America",
"Asia", "Europe", "South America", "Europe", "Africa",
"Africa", "Africa", "Africa", "South America", "South America",
"South America", "Africa", "Asia", "Africa", "Asia",
"North America", "North America", "Africa", "Asia", "Africa",
"Africa", "Africa", "North America", "Europe", "Europe",
"Africa", "North America", "Europe", "Africa", "North America",
"Europe", "North America", "North America", "South America", "Africa",
"Africa", "Africa", "Africa", "Europe", "Oceania",
"Europe", "Africa", "Asia", "Africa", "Europe",
"Europe", "Oceania", "Africa", "Europe", "Europe",
"North America", "Africa", "South America", "Asia", "Europe",
"Asia", "Asia", "Europe", "North America", "North America",
"Africa", "North America", "North America", "Europe", "Asia",
"Asia", "Europe", "Asia", "North America", "Asia",
"Africa", "Asia", "Asia", "Asia", "Africa",
"Europe", "Africa", "Europe", "Asia", "Africa", "Asia", "Oceania", "Asia", "Europe", "Asia",
"Europe", "Europe", "Africa", "Asia", "Europe",
"Africa", "Oceania", "Asia", "Europe", "North America",
"Africa", "Asia", "Africa", "Asia", "Africa",
"Africa", "Asia", "Asia", "North America", "Oceania",
"Africa", "Europe", "Asia", "Oceania", "South America",
"Africa", "Africa", "Europe", "Oceania", "North America",
"Africa", "Asia", "North America", "South America", "Asia",
"Africa", "Europe", "Asia", "Africa", "Africa",
"Africa", "Oceania", "Europe", "Europe", "Asia",
"Europe", "Europe", "Africa", "Europe", "Asia",
"Europe", "Africa", "Europe", "Oceania", "Africa",
"Europe", "North America", "North America", "Africa", "South America",
"Europe", "Asia", "Asia", "Asia", "Africa",
"Asia", "Africa", "Asia", "Europe", "Africa",
"North America", "Asia", "Oceania", "Africa", "Asia",
"Europe", "Europe", "Oceania", "Asia", "North America",
"Asia", "Africa", "Asia", "North America", "South America",
"Asia", "South America", "Oceania", "Asia", "Africa",
"Africa")
countries_continents <- data.frame(Country = countries, Continent = continents)
Global <- Global %>%
left_join(countries_continents, by = "Country")
sample_n(Global, 10)## # A tibble: 10 × 7
## Country `Country Code` Series `Series Code` Year Value Continent
## <chr> <chr> <chr> <chr> <chr> <chr> <chr>
## 1 Malaysia MYS Indus… IPTOTNSKD 2011… .. Asia
## 2 St. Vincent and th… VCT Month… IMPCOV 2004 .. North Am…
## 3 Turkmenistan TKM Terms… TOT 2016… .. Asia
## 4 Hungary HUN Total… TOTRESV 2013… .. Europe
## 5 Korea Rep. KOR CPI P… CPTOTSAXN 2007… .. Asia
## 6 French Polynesia PYF Excha… DPANUSSPF 2014… .. Oceania
## 7 Swaziland SWZ Expor… DXGSRMRCHSAXD 2011… .. Africa
## 8 Senegal SEN Unemp… UNEMPSA_ 2011… .. Africa
## 9 Israel ISR Indus… IPTOTSAKD 2004… .. Asia
## 10 Haiti HTI GDP,c… NYGDPMKTPSACD 2018 .. North Am…Convierte la columna ‘Valor’ a numérica, reemplazando ‘..’ con NA.
Global <- Global %>%
mutate(Value = ifelse(Value == "..", NA, as.numeric(Value)))Extraer solo los datos de inflación del conjunto de datos y crear un conjunto de datos de inflación.
inflation_data <- Global %>%
filter(Series %in% c(
"Core CPI,seas.adj,,,",
"Core CPI,not seas.adj,,,",
"CPI Price, % y-o-y, median weighted, seas. adj.,",
"CPI Price, % y-o-y, not seas. adj.,"
)) %>%
mutate(
DataType = if_else(grepl("-Q", Year), "Quarterly", "Annual"),
Date = if_else(
grepl("-Q", Year),
as.Date(as.yearqtr(Year, format = "%Y-Q%q")),
as.Date(paste0(Year, "-01-01"))
),
Year = if_else(DataType == "Quarterly", substr(Year, 1, 4), Year),
Quarter = if_else(DataType == "Quarterly", substr(Year, 6, 7), NA_character_),
Decade = paste0(substr(Year, 1, 3), "0s")
)
inflation_data <- inflation_data %>%
mutate(
Quarter = if_else(
is.na(Quarter) & DataType == "Annual",
"Annual",
Quarter
)
)
sample_n(inflation_data, 10)## # A tibble: 10 × 11
## Country `Country Code` Series `Series Code` Year Value Continent DataType
## <chr> <chr> <chr> <chr> <chr> <dbl> <chr> <chr>
## 1 Somalia SOM CPI P… CPTOTSAXMZGY 2021 NA Africa Quarter…
## 2 Swaziland SWZ Core … CORENS 2023 NA Africa Quarter…
## 3 Estonia EST Core … CORENS 2024 NA Europe Quarter…
## 4 Bermuda BMU Core … CORESA 2007 NA North Am… Annual
## 5 Armenia ARM Core … CORESA 2023 NA Asia Quarter…
## 6 Sierra Le… SLE CPI P… CPTOTSAXMZGY 2005 NA Africa Quarter…
## 7 Cambodia KHM CPI P… CPTOTSAXMZGY 2001 NA Asia Quarter…
## 8 Sudan SDN CPI P… CPTOTSAXMZGY 2020 NA Africa Annual
## 9 Germany DEU Core … CORESA 2022 NA Europe Quarter…
## 10 Maldives MDV Core … CORENS 2010 NA Asia Quarter…
## # ℹ 3 more variables: Date <date>, Quarter <chr>, Decade <chr>Comprobar valores únicos en las columnas clave.
sapply(inflation_data, function(x) length(unique(x)))## Country Country Code Series Series Code Year Value
## 196 196 3 3 25 3006
## Continent DataType Date Quarter Decade
## 6 2 100 2 3Comprobar valores faltantes.
colSums(is.na(inflation_data))## Country Country Code Series Series Code Year Value
## 0 0 0 0 0 70481
## Continent DataType Date Quarter Decade
## 0 0 0 0 0Comprobar valores únicos en columnas específicas.
unique(inflation_data$Series)## [1] "Core CPI,not seas.adj,,,"
## [2] "Core CPI,seas.adj,,,"
## [3] "CPI Price, % y-o-y, median weighted, seas. adj.,"unique(inflation_data$Continent)## [1] "Asia" "Europe" "Africa" "North America"
## [5] "South America" "Oceania"Datos anuales y trimestrales separados.
annual_data <- inflation_data %>% filter(DataType == "Annual")
quarterly_data <- inflation_data %>% filter(DataType == "Quarterly")
annual_data <- annual_data %>%
rename("Annualy" = "Quarter") %>%
select(-DataType) %>%
select(-Date)
inflation_annual_data <- annual_data
quarterly_data <- quarterly_data %>%
rename("Quarterly" = "Quarter") %>%
select(-DataType) %>%
select(-Date)
inflation_quarterly_data <- quarterly_dataAnálisis de datos exploratorios para datos anuales de inflación.
Visualizar lo que falta en el conjunto de datos.
gg_miss_var(inflation_annual_data)
La variable Valor parece tener muchos valores faltantes.
Utilice una prueba de chi-cuadrado para comprobar si los valores faltantes dependen de otras variables.
chisq.test(table(is.na(inflation_annual_data$Value), inflation_annual_data$Country))##
## Pearson's Chi-squared test
##
## data: table(is.na(inflation_annual_data$Value), inflation_annual_data$Country)
## X-squared = 7461.6, df = 195, p-value < 2.2e-16\(H_0\): La falta de la variable Valor es independiente de la variable País.
\(H_1\): La falta de la variable Valor depende de la variable País.
Dado que el valor p es mucho menor que el nivel de significancia común (p. ej., 0,05), rechazamos la hipótesis nula. Esto implica que existe una asociación estadísticamente significativa entre la ausencia de valores de Valor y la variable País.
Comprueba qué país tiene una mayor proporción de valores faltantes.
prop.table(table(is.na(inflation_annual_data$Value), inflation_annual_data$Country),
margin = 2)##
## Afghanistan Albania Algeria Angola Antigua and Barbuda Argentina
## FALSE 0.0000000 0.4533333 0.0000000 0.0000000 0.0000000 0.0000000
## TRUE 1.0000000 0.5466667 1.0000000 1.0000000 1.0000000 1.0000000
##
## Armenia Aruba Australia Austria Azerbaijan Bahamas The
## FALSE 0.5066667 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## TRUE 0.4933333 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
##
## Bahrain Bangladesh Barbados Belarus Belgium Belize Benin
## FALSE 0.0000000 0.0000000 0.0000000 0.6133333 0.6666667 0.0000000 0.0000000
## TRUE 1.0000000 1.0000000 1.0000000 0.3866667 0.3333333 1.0000000 1.0000000
##
## Bermuda Bhutan Bolivia Bosnia and Herzegovina Botswana
## FALSE 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## TRUE 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
##
## Brazil Brunei Bulgaria Burkina Faso Burundi Cambodia
## FALSE 0.6666667 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## TRUE 0.3333333 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
##
## Cameroon Canada Cape Verde Cayman Islands Central African Republic
## FALSE 0.0000000 0.6666667 0.0000000 0.0000000 0.0000000
## TRUE 1.0000000 0.3333333 1.0000000 1.0000000 1.0000000
##
## Chad Chile China Colombia Comoros Congo Dem. Rep.
## FALSE 0.0000000 0.4266667 0.5333333 0.6666667 0.0000000 0.0000000
## TRUE 1.0000000 0.5733333 0.4666667 0.3333333 1.0000000 1.0000000
##
## Congo Rep. Costa Rica Cote d'Ivoire Croatia Cuba Cyprus
## FALSE 0.0000000 0.5066667 0.0000000 0.5600000 0.0000000 0.6666667
## TRUE 1.0000000 0.4933333 1.0000000 0.4400000 1.0000000 0.3333333
##
## Czech Republic Denmark Djibouti Dominica Dominican Republic
## FALSE 0.6666667 0.6666667 0.0000000 0.0000000 0.6666667
## TRUE 0.3333333 0.3333333 1.0000000 1.0000000 0.3333333
##
## Ecuador Egypt Arab Rep. El Salvador Equatorial Guinea Eritrea
## FALSE 0.0000000 0.5600000 0.4266667 0.0000000 0.0000000
## TRUE 1.0000000 0.4400000 0.5733333 1.0000000 1.0000000
##
## Estonia Ethiopia Faeroe Islands Fiji Finland France
## FALSE 0.0000000 0.0000000 0.0000000 0.2133333 0.0000000 0.6666667
## TRUE 1.0000000 1.0000000 1.0000000 0.7866667 1.0000000 0.3333333
##
## French Polynesia Gabon Gambia The Georgia Germany Ghana
## FALSE 0.0000000 0.0000000 0.0000000 0.2000000 0.6666667 0.0000000
## TRUE 1.0000000 1.0000000 1.0000000 0.8000000 0.3333333 1.0000000
##
## Greece Greenland Grenada Guatemala Guinea Guinea-Bissau
## FALSE 0.6666667 0.0000000 0.0000000 0.6400000 0.0000000 0.0000000
## TRUE 0.3333333 1.0000000 1.0000000 0.3600000 1.0000000 1.0000000
##
## Guyana Haiti Honduras Hong Kong China Hungary Iceland
## FALSE 0.0000000 0.0000000 0.6666667 0.5600000 0.6666667 0.6666667
## TRUE 1.0000000 1.0000000 0.3333333 0.4400000 0.3333333 0.3333333
##
## India Indonesia Iran Islamic Rep. Iraq Ireland Isle of Man
## FALSE 0.0000000 0.4800000 0.0000000 0.0000000 0.6666667 0.0000000
## TRUE 1.0000000 0.5200000 1.0000000 1.0000000 0.3333333 1.0000000
##
## Israel Italy Jamaica Japan Jordan Kazakhstan Kenya
## FALSE 0.6666667 0.6666667 0.0000000 0.6666667 0.5066667 0.2400000 0.0000000
## TRUE 0.3333333 0.3333333 1.0000000 0.3333333 0.4933333 0.7600000 1.0000000
##
## Kiribati Korea Rep. Kuwait Kyrgyz Republic Lao PDR Latvia
## FALSE 0.0000000 0.6666667 0.0000000 0.2000000 0.0000000 0.3333333
## TRUE 1.0000000 0.3333333 1.0000000 0.8000000 1.0000000 0.6666667
##
## Lebanon Lesotho Liberia Libya Lithuania Luxembourg
## FALSE 0.0000000 0.0000000 0.0000000 0.0000000 0.6666667 0.6666667
## TRUE 1.0000000 1.0000000 1.0000000 1.0000000 0.3333333 0.3333333
##
## Macao China Macedonia FYR Madagascar Malawi Malaysia Maldives
## FALSE 0.0000000 0.5333333 0.0000000 0.0000000 0.5333333 0.0000000
## TRUE 1.0000000 0.4666667 1.0000000 1.0000000 0.4666667 1.0000000
##
## Mali Malta Mauritania Mauritius Mexico Micronesia Fed. Sts.
## FALSE 0.0000000 0.6666667 0.0000000 0.4800000 0.6666667 0.0000000
## TRUE 1.0000000 0.3333333 1.0000000 0.5200000 0.3333333 1.0000000
##
## Moldova Mongolia Morocco Mozambique Myanmar Namibia Nepal
## FALSE 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## TRUE 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
##
## Netherlands Netherlands Antilles New Caledonia New Zealand Nicaragua
## FALSE 0.6666667 0.0000000 0.0000000 0.0000000 0.0000000
## TRUE 0.3333333 1.0000000 1.0000000 1.0000000 1.0000000
##
## Niger Nigeria Norway Oman Pakistan Panama
## FALSE 0.0000000 0.6666667 0.6666667 0.0000000 0.2000000 0.0000000
## TRUE 1.0000000 0.3333333 0.3333333 1.0000000 0.8000000 1.0000000
##
## Papua New Guinea Paraguay Peru Philippines Poland Portugal
## FALSE 0.0000000 0.6666667 0.6666667 0.0000000 0.6666667 0.6666667
## TRUE 1.0000000 0.3333333 0.3333333 1.0000000 0.3333333 0.3333333
##
## Qatar Romania Russian Federation Rwanda Samoa San Marino
## FALSE 0.0000000 0.5066667 0.6133333 0.0000000 0.0000000 0.0000000
## TRUE 1.0000000 0.4933333 0.3866667 1.0000000 1.0000000 1.0000000
##
## Sao Tome and Principe Saudi Arabia Senegal Serbia and Montenegro
## FALSE 0.0000000 0.0000000 0.3333333 0.0000000
## TRUE 1.0000000 1.0000000 0.6666667 1.0000000
##
## Seychelles Sierra Leone Singapore Slovak Republic Slovenia
## FALSE 0.0000000 0.0000000 0.6666667 0.6133333 0.6666667
## TRUE 1.0000000 1.0000000 0.3333333 0.3866667 0.3333333
##
## Solomon Islands Somalia South Africa Spain Sri Lanka
## FALSE 0.0000000 0.0000000 0.6133333 0.6666667 0.0000000
## TRUE 1.0000000 1.0000000 0.3866667 0.3333333 1.0000000
##
## St. Kitts and Nevis St. Lucia St. Vincent and the Grenadines Sudan
## FALSE 0.0000000 0.0000000 0.0000000 0.0000000
## TRUE 1.0000000 1.0000000 1.0000000 1.0000000
##
## Suriname Swaziland Sweden Switzerland Syrian Arab Republic
## FALSE 0.0000000 0.0000000 0.6666667 0.5333333 0.0000000
## TRUE 1.0000000 1.0000000 0.3333333 0.4666667 1.0000000
##
## Taiwan China Tajikistan Tanzania Thailand Timor-Leste Togo
## FALSE 0.6666667 0.0000000 0.0000000 0.6666667 0.0000000 0.0000000
## TRUE 0.3333333 1.0000000 1.0000000 0.3333333 1.0000000 1.0000000
##
## Tonga Trinidad and Tobago Tunisia Turkey Turkmenistan
## FALSE 0.0000000 0.6666667 0.0000000 0.5866667 0.0000000
## TRUE 1.0000000 0.3333333 1.0000000 0.4133333 1.0000000
##
## Uganda Ukraine United Arab Emirates United Kingdom United States
## FALSE 0.5333333 0.0000000 0.0000000 0.6666667 0.6666667
## TRUE 0.4666667 1.0000000 1.0000000 0.3333333 0.3333333
##
## Uruguay Uzbekistan Vanuatu Venezuela RB Vietnam
## FALSE 0.0000000 0.0000000 0.0000000 0.2133333 0.0000000
## TRUE 1.0000000 1.0000000 1.0000000 0.7866667 1.0000000
##
## Virgin Islands (U.S.) Yemen Rep. Zambia Zimbabwe
## FALSE 0.0000000 0.0000000 0.0000000 0.0000000
## TRUE 1.0000000 1.0000000 1.0000000 1.0000000Visualiza qué país tiene datos completamente faltantes y cuáles tienen datos parcialmente faltantes.
ggplot(inflation_annual_data, aes(x = Country, fill = is.na(Value))) +
geom_bar(position = "fill") +
labs(y = "Proportion", fill = "Missing Value") +
theme_minimal() +
ggtitle("Proportion of Missing Values by Country") + theme(legend.position="bottom") + guides(fill = guide_legend(nrow = 1))
Filtrar los países con un 100% de datos faltantes. Eliminar los países con menos del 100% de datos faltantes y dejar los países con datos faltantes parciales. Convertir “Año” a numérico.
missing_annual_summary <- inflation_annual_data %>%
group_by(Country) %>%
summarize(total_missing = sum(is.na(Value)), total_records = n()) %>%
mutate(missing_percentage = total_missing / total_records)
inflation_annual_data <- inflation_annual_data %>%
filter(Country %in% missing_annual_summary$Country[missing_annual_summary$missing_percentage < 1])
inflation_annual_data$Year <- as.numeric(inflation_annual_data$Year)Limpie los nombres de columna para hacerlos sintácticamente válidos.
inflation_annual_data <- inflation_annual_data %>%
clean_names()Comprueba qué porcentaje de datos faltantes tenemos.
aggr(inflation_annual_data)
Tenemos más del 40 % de valores faltantes en la variable Valor, lo cual representa una gran cantidad de datos. La mejor manera de solucionarlo es imputar los datos en lugar de eliminarlos.
Usemos el método CART para imputar datos.
predictor_matrix_annual <- make.predictorMatrix(inflation_annual_data)
set.seed(123)
annual_imputation_cart <- mice(inflation_annual_data, m = 5, method = "cart")##
## iter imp variable
## 1 1 value
## 1 2 value
## 1 3 value
## 1 4 value
## 1 5 value
## 2 1 value
## 2 2 value
## 2 3 value
## 2 4 value
## 2 5 value
## 3 1 value
## 3 2 value
## 3 3 value
## 3 4 value
## 3 5 value
## 4 1 value
## 4 2 value
## 4 3 value
## 4 4 value
## 4 5 value
## 5 1 value
## 5 2 value
## 5 3 value
## 5 4 value
## 5 5 valueComprobar las imputaciones CART.
annual_imputation_cart$imp$value## 1 2 3 4 5
## 1 48.57916 91.32519 83.45336 41.68769 86.24029
## 2 70.22650 83.06365 103.13131 84.31220 56.17321
## 3 54.27991 90.63433 104.95791 57.40171 90.40317
## 4 76.96679 71.43483 85.38321 63.14192 89.18316
## 5 94.96020 94.70750 93.31005 88.88347 87.73624
## 6 82.74496 69.46001 99.94438 91.72060 97.75885
## 7 93.08193 89.17940 87.31443 70.48718 73.79112
## 8 87.78115 83.30883 88.27120 96.81781 79.76890
## 26 91.95899 91.32519 74.07757 77.73452 87.06722
## 27 82.16888 60.45340 65.23464 79.51359 37.61926
## 28 66.56782 87.90980 90.98065 84.35955 92.01060
## 29 91.33736 85.41806 80.48137 86.46140 91.51116
## 30 89.90957 92.72349 92.15957 86.88603 79.87391
## 31 90.73737 74.55635 87.31443 92.11196 85.98439
## 32 99.46346 99.33319 95.29390 73.59809 97.40585
## 33 93.88938 94.25877 92.98638 101.81818 93.19224
## 51 97.43460 41.68769 87.11384 57.46010 80.07062
## 52 39.64751 91.32519 86.72466 45.30148 97.69924
## 53 89.67846 77.26177 96.08898 81.69164 81.40956
## 54 79.00953 96.08898 65.97222 91.76680 92.43411
## 55 92.43411 71.60730 73.45181 84.62964 93.63593
## 56 92.31872 96.35980 92.98638 99.01258 67.14593
## 57 93.89796 84.65185 97.59867 90.58389 78.96031
## 58 95.35421 90.37662 86.60671 73.98322 81.95826
## 59 80.81964 97.65004 98.67298 97.54853 66.79041
## 60 100.14811 102.07249 105.57289 112.68137 99.62495
## 61 99.41273 100.12346 100.44025 100.48439 100.48408
## 62 102.28962 105.74543 98.22391 104.02852 103.21992
## 63 104.36761 104.32099 109.83401 108.22561 103.62028
## 64 112.78478 108.52239 106.62398 146.43261 120.59903
## 65 124.48441 106.67743 140.96680 102.97737 108.14554
## 66 107.60344 122.52881 107.45477 107.68874 108.60962
## 67 104.05528 123.45281 128.27801 106.18512 98.68517
## 68 120.53017 101.05646 184.33610 114.57763 111.60177
## 69 119.21580 131.30663 109.22285 111.90085 101.10717
## 70 109.52637 102.49460 119.89695 123.12957 127.88706
## 71 110.92679 269.45487 504.61729 111.41676 110.76649
## 72 117.72698 550.46210 121.11605 113.00921 149.56982
## 73 134.67420 148.98291 472.19814 121.75368 133.72371
## 74 298.66443 111.39208 107.64352 140.11829 110.00333
## 75 125.95365 144.93546 123.55923 130.71979 121.38711
## 76 54.07719 77.26177 87.24826 76.38382 55.25180
## 77 60.57741 97.73589 81.13119 60.03765 70.92045
## 78 37.81895 81.88533 88.74066 81.96664 87.24826
## 79 90.11586 96.38065 70.34310 95.53165 84.59334
## 80 75.51253 90.74173 92.35943 88.95131 92.43411
## 81 81.34965 95.06454 85.25340 92.38893 94.16257
## 101 76.63699 87.68738 48.57916 36.79145 48.49429
## 102 79.51430 52.63789 86.72466 89.35444 57.40171
## 103 90.82572 64.04461 50.76923 79.11190 65.10216
## 104 68.22087 73.45181 82.80109 79.31961 93.17554
## 105 89.23611 67.96218 92.43411 92.52781 75.51253
## 106 91.54061 83.40701 95.50927 92.99346 85.25340
## 126 87.20973 91.22254 88.96352 88.93570 86.50740
## 127 82.63836 86.31604 66.61349 84.99905 93.97112
## 128 79.51359 56.17321 98.00046 91.95899 91.23674
## 129 91.43739 81.02063 70.34310 66.86484 92.13118
## 130 70.42076 77.60870 87.78058 53.67943 86.46140
## 131 88.96609 76.94358 94.49291 82.82758 98.92117
## 132 82.82758 92.87515 101.77485 82.74496 96.46720
## 133 96.56863 85.13134 99.46346 79.08784 95.03849
## 134 99.83715 95.08520 97.51408 95.08520 97.76746
## 135 99.65537 97.64965 100.27405 100.31855 100.12346
## 136 101.05028 100.99320 99.12850 102.41009 100.02075
## 137 102.97991 103.12208 111.49880 101.30346 107.55417
## 138 105.71932 102.11598 107.41162 115.19239 101.96463
## 139 115.52511 115.59832 112.37245 104.19667 104.55229
## 140 104.58508 112.52256 107.07546 107.45712 103.07126
## 141 99.26165 108.02726 120.61749 105.34078 113.19995
## 142 115.60556 171.38311 173.66266 107.59443 171.38311
## 143 107.61294 120.53017 107.72305 100.39900 114.57763
## 144 182.62523 117.59139 105.61598 249.03521 114.59080
## 145 103.24642 196.36738 146.06715 254.13701 117.27757
## 146 131.81465 115.01951 115.15690 188.46154 111.87852
## 147 106.35625 114.09905 150.69379 165.47619 111.12244
## 148 118.29243 145.29898 124.46827 131.22664 159.31912
## 149 132.97959 131.58996 127.89808 110.00333 180.75454
## 150 172.84924 219.35145 104.83165 130.54977 161.77992
## 151 49.97188 89.86462 103.54970 85.95653 86.17021
## 152 82.18296 95.66380 48.57916 90.23312 85.57589
## 176 85.03989 87.79150 91.22254 89.45997 89.45997
## 177 79.72385 76.81953 52.63789 54.23814 57.40171
## 201 52.64988 81.69164 84.99905 86.53435 86.30683
## 202 87.19251 54.29599 89.76592 74.10656 86.95843
## 203 91.22254 87.22372 94.37539 68.22153 41.56536
## 204 89.79684 53.96413 93.80144 93.17554 84.62964
## 205 103.24544 76.96679 91.27376 68.72902 91.64965
## 206 81.36691 92.38893 96.46720 57.27377 99.33319
## 207 99.33319 86.65654 91.86796 92.79609 88.75326
## 208 95.36544 96.81781 96.99243 83.40701 57.28155
## 209 92.48857 99.02634 87.92436 91.37769 84.39734
## 210 99.64087 94.57160 99.92843 100.48439 100.83501
## 211 101.27936 101.43557 99.35575 101.53983 100.34017
## 212 120.11251 102.12298 104.30985 104.02852 102.00329
## 213 111.40121 97.65152 111.40121 104.99403 102.47183
## 214 122.96154 106.62398 105.32322 102.48273 106.79214
## 215 105.31331 99.26165 117.47683 150.59021 120.33720
## 216 105.33277 118.92588 103.07126 103.79710 108.36584
## 217 108.01316 166.15643 105.57382 104.92897 108.20026
## 218 115.08633 110.33443 124.45826 160.60608 126.56843
## 219 123.57135 106.78113 111.98145 169.24985 99.61317
## 220 109.74483 134.40526 117.59259 106.28093 118.35876
## 221 117.31404 121.02656 146.31098 105.52984 153.93285
## 222 117.37784 109.58203 169.39628 112.81117 101.07600
## 223 130.73546 124.57749 123.20902 113.56516 126.67551
## 224 107.59809 155.62688 136.71321 155.56938 128.56307
## 225 139.59004 125.24982 1189.82588 118.18972 149.34940
## 276 91.23674 41.62287 41.68769 45.05271 45.05271
## 277 87.19847 84.31220 57.46010 54.29599 90.82572
## 278 86.72466 88.93570 85.58530 70.92045 91.95899
## 279 89.67338 88.66636 53.32295 89.64036 59.41362
## 280 91.33736 82.80109 64.21370 87.79523 73.29890
## 281 91.80362 88.75352 92.11196 78.89058 89.16429
## 282 95.68366 94.04152 75.63255 84.30664 93.60593
## 283 87.31443 93.54731 94.80933 72.44891 83.40701
## 284 92.29034 102.15192 98.59710 96.24320 98.79779
## 285 101.44400 100.44025 98.86147 97.31931 101.53983
## 286 106.21088 97.45585 97.64965 100.24537 100.63553
## 287 102.40763 102.79358 103.27372 102.15226 104.70155
## 288 110.10368 104.01260 106.69773 103.28263 104.25807
## 289 146.43261 102.84426 103.29765 121.87968 115.51272
## 290 144.62638 120.76648 109.96946 104.04960 105.34100
## 291 108.04976 114.52303 111.06992 109.37046 108.22291
## 292 129.20327 117.21355 104.83339 101.05646 422.40814
## 293 104.66835 110.77789 114.81305 116.72342 105.30144
## 294 131.72309 115.95317 109.04433 101.06061 109.22399
## 295 109.04433 117.94491 132.44916 178.26917 116.84813
## 296 145.10697 173.21939 281.71217 99.45656 101.37988
## 297 138.74334 111.59231 120.96510 108.31670 201.07692
## 298 641.17255 171.68656 126.84464 122.30426 116.40820
## 299 156.47831 214.86895 125.77025 118.87561 125.86513
## 300 125.95365 121.42631 124.45213 130.12115 267.05128
## 351 90.82572 37.61926 89.62937 81.69164 85.77597
## 352 70.92045 88.59921 81.13119 88.51961 85.35190
## 353 84.86304 55.46753 84.43896 68.38764 79.62324
## 354 70.11395 72.67259 92.69100 90.48983 93.06302
## 355 92.43411 92.13118 62.68866 53.67943 92.69100
## 356 90.90446 95.50932 87.94957 77.10697 93.60593
## 357 92.43007 91.80362 95.50932 77.22249 68.83437
## 358 69.00003 84.84667 94.31041 94.04443 69.95766
## 359 84.39734 86.57403 99.83715 100.28604 97.25576
## 360 101.52984 101.46492 94.27515 99.62495 102.46154
## 361 99.81995 101.42751 99.65747 100.71676 100.89656
## 362 105.05959 104.99937 102.02099 106.57789 101.41742
## 363 119.89055 103.83656 103.28263 98.87984 98.06457
## 364 251.21835 109.87936 101.23275 105.62299 103.29765
## 365 105.31331 327.17640 133.86898 150.83319 116.28912
## 366 107.31365 107.79080 114.60203 111.04849 127.12370
## 367 143.62356 172.75985 114.07154 108.81487 115.08633
## 368 141.54676 107.03635 156.06017 125.47516 184.33610
## 369 110.33821 154.46581 110.95365 112.23263 109.74483
## 370 110.33369 120.43245 108.84222 132.44916 129.47695
## 371 119.65444 139.10761 161.96111 269.45487 131.76436
## 372 201.07692 120.49509 111.12244 119.47703 125.83242
## 373 116.62220 107.00843 115.92970 117.64437 120.26701
## 374 122.18326 210.95186 110.81273 136.37268 132.34528
## 375 204.04217 142.24827 105.26538 140.27197 121.63895
## 426 87.33405 77.26177 90.62159 97.69924 89.45997
## 427 69.07252 91.95899 95.66380 91.12610 85.95653
## 428 84.98210 63.96155 77.81180 76.38382 84.05367
## 429 65.48751 89.52954 91.64965 79.05238 79.05238
## 430 87.88899 90.96115 93.75936 86.45978 91.87575
## 431 85.60476 81.62223 92.13474 90.38887 94.74468
## 432 82.36210 95.86473 95.36544 95.24474 91.06227
## 433 98.73440 75.63255 86.60671 88.39372 97.79130
## 434 96.28845 83.11151 93.24469 97.45069 102.48466
## 435 100.60284 98.49700 99.38790 99.27417 99.73802
## 436 100.65492 100.27405 100.61728 102.71888 97.34595
## 437 104.64498 164.68155 107.49766 107.49766 111.49880
## 438 103.62028 110.16345 105.03229 105.96625 105.82849
## 439 101.99868 106.79214 109.23746 110.30481 120.16029
## 440 110.34835 99.26165 120.33720 113.19995 109.05125
## 441 124.48441 109.37080 112.55829 118.16721 99.26165
## 442 113.97526 104.37449 100.98039 102.88173 111.05910
## 443 118.79881 123.62344 120.90543 108.45682 108.25397
## 444 107.54896 459.90827 105.41838 110.33821 118.04719
## 445 113.42653 105.65981 155.18207 117.45057 137.21213
## 446 129.18871 116.02424 161.96111 113.25841 126.34928
## 447 120.96510 117.86513 148.02632 147.34885 125.18827
## 448 205.35109 128.50156 369.82714 182.31015 152.44157
## 449 144.57935 111.04844 122.70961 131.41540 446.58161
## 450 159.00152 142.24827 160.38685 125.72791 144.93546
## 451 62.21343 45.05271 90.87033 66.58774 85.58530
## 452 41.62287 60.65947 80.76570 93.92888 98.00046
## 453 70.89381 87.51037 77.34781 95.66380 94.37539
## 454 91.43739 77.44490 89.90957 71.60730 91.72003
## 455 103.24544 64.61268 70.42076 90.14350 77.44490
## 456 86.65654 91.81731 97.36059 97.04058 93.08193
## 457 85.46920 93.19046 88.75326 91.81731 88.29323
## 458 65.86113 97.79130 95.40466 88.62501 69.95766
## 459 95.82734 95.82734 97.53696 91.18015 93.89692
## 476 86.30683 77.73452 87.33405 66.61349 86.69055
## 477 54.23814 60.03765 74.10656 70.22650 87.90980
## 478 62.27695 90.82572 67.53835 84.43896 87.96539
## 479 90.11586 88.88347 94.78517 94.46961 91.71909
## 480 87.74308 95.77954 89.23611 91.76680 65.48751
## 481 97.06502 94.04443 94.80933 69.57160 73.98322
## 482 96.48148 86.07052 88.10025 95.29390 99.33319
## 483 98.64865 97.10315 90.38887 81.65959 88.75326
## 484 93.24388 98.67298 83.11151 98.59710 100.60156
## 501 79.88844 105.36680 87.90980 84.05367 59.27230
## 502 86.84609 85.10968 96.04584 82.24845 88.95706
## 503 86.83467 87.49543 60.57741 54.07719 88.59921
## 504 82.68579 78.03115 51.42515 90.90331 102.22222
## 505 94.70750 91.65131 91.27376 89.64036 64.21370
## 506 96.48671 92.71848 96.46720 92.75237 97.75885
## 507 79.41074 83.82353 92.79609 89.08903 93.54729
## 508 76.71611 94.63581 93.49512 97.10315 98.34261
## 509 96.70003 81.86683 101.52975 91.49750 103.22245
## 510 99.69388 98.53717 100.62028 100.05960 98.35841
## 511 100.89656 94.27515 100.75780 100.12128 99.73802
## 512 107.15872 104.64498 101.82624 102.12298 102.74791
## 513 115.39095 111.54449 105.96625 104.66425 104.23182
## 514 104.55415 104.63845 106.56318 105.64624 100.88040
## 515 111.82715 112.95271 127.27591 108.22291 109.78778
## 516 114.76498 133.63401 102.75253 163.72257 114.76498
## 517 113.60657 111.05910 110.16479 105.46017 112.63187
## 518 103.49693 108.54908 103.64332 158.47743 123.62344
## 519 116.89807 104.77194 105.68832 112.15884 481.19938
## 520 118.41545 108.59125 104.77194 110.85041 117.94491
## 521 114.82032 132.60389 121.11444 123.61111 109.00806
## 522 125.18827 107.26161 111.59231 100.20202 101.07600
## 523 113.56516 118.14756 122.08329 126.44634 104.67082
## 524 298.66443 446.58161 143.62978 111.39208 125.77025
## 525 130.55226 192.70432 162.78949 142.56514 172.82309
## 526 77.84784 87.19251 72.74734 69.00621 92.38744
## 527 77.84784 86.30683 87.11384 36.79145 85.35190
## 528 88.98349 49.78525 79.11190 94.96854 79.47932
## 529 93.33426 86.73150 73.45181 92.92963 94.70750
## 530 83.29147 93.06302 80.57239 86.45978 95.53165
## 551 104.95791 49.97188 57.46010 88.95706 85.65931
## 552 95.61993 90.63433 85.15462 82.63836 89.07701
## 553 41.68769 84.15973 82.76681 76.52190 74.07757
## 554 89.90957 94.78517 93.31005 90.96115 91.76680
## 555 97.01757 91.64965 92.52781 88.15822 59.30769
## 576 88.96352 87.68738 79.51430 65.10216 45.30148
## 577 78.65690 97.69924 66.58774 55.25180 83.04769
## 578 88.97681 57.46010 83.45336 76.52190 66.61349
## 579 79.00953 89.79684 76.00061 84.62964 91.78296
## 580 75.51253 80.66573 92.35943 51.50991 86.61646
## 581 91.54061 98.37955 86.43748 102.22279 91.10648
## 582 83.47741 86.12273 97.49668 70.82698 74.58034
## 583 82.36210 86.43748 98.30169 85.09039 98.45387
## 584 99.64207 97.51408 94.67902 97.65004 96.59170
## 585 101.96489 101.52495 100.54435 100.24116 101.30359
## 586 100.51559 97.93814 100.89656 100.12157 100.66260
## 587 99.97401 164.68155 98.94547 102.74791 104.28966
## 588 113.69048 104.99403 114.10497 103.28263 114.49640
## 589 120.59903 123.20209 130.47818 104.63845 110.08035
## 590 120.56460 103.40420 119.29708 107.19246 100.48315
## 591 120.63251 119.60328 107.68874 110.06902 105.15247
## 592 123.62344 108.20026 110.54372 184.33610 98.76543
## 593 108.81487 160.60608 106.85185 225.66604 158.47743
## 594 105.41838 120.42606 105.65981 149.89209 123.12957
## 595 168.95985 105.61598 136.34087 115.95317 117.02929
## 596 114.83612 139.10761 119.17671 124.30417 133.66675
## 597 101.07600 298.90043 121.48662 148.02632 109.58203
## 598 121.95858 113.79071 131.27959 127.06840 116.51596
## 599 120.97504 127.42447 131.41540 143.27472 155.93496
## 600 158.66038 105.26538 172.82309 135.82040 172.82309
## 651 85.66890 74.82542 82.18981 50.76591 86.59111
## 652 82.24845 104.02357 87.33405 83.04769 91.12610
## 653 63.88756 77.26177 66.62354 70.89381 48.57916
## 654 85.38321 92.64793 76.96679 86.73150 70.42076
## 655 91.78296 87.73624 64.77170 96.04494 94.78517
## 656 85.09039 69.46001 97.62545 94.94681 81.19623
## 657 98.64865 73.98322 93.49512 73.98322 96.90043
## 658 96.35980 92.79609 94.31041 92.93456 94.13769
## 659 97.89099 102.48466 99.64207 97.18961 95.99433
## 660 100.82659 101.49803 101.43779 100.02075 99.01178
## 661 97.46060 100.79759 100.79759 97.46060 97.58014
## 662 102.28962 105.61450 104.69265 100.21886 103.63267
## 663 107.56032 108.28152 260.74334 175.67105 108.28152
## 664 106.16497 98.93909 103.89858 105.32322 109.23746
## 665 106.44959 119.29708 128.61022 120.33720 120.33720
## 666 111.10829 105.34078 114.60203 109.49226 110.88988
## 667 113.17658 112.22418 111.84610 225.66604 124.61969
## 668 111.46081 99.10555 151.70141 113.08183 117.50872
## 669 120.45371 133.08636 134.27037 142.76316 108.84222
## 670 105.60676 198.77153 109.88743 119.33927 118.02153
## 671 110.37718 99.45656 253.72386 109.59436 123.61111
## 672 110.95092 114.09905 127.71320 108.31670 125.53161
## 673 147.99678 115.92970 131.22664 113.61216 126.98589
## 674 448.92817 155.56938 122.70613 143.62978 180.75454
## 675 132.28471 219.60348 132.28471 177.07372 176.97539
## 676 82.24845 76.45865 84.99905 77.84784 77.34781
## 677 77.05714 62.21343 54.23814 86.87865 63.88756
## 678 60.45340 87.51037 57.46010 96.04584 85.03989
## 679 85.84441 94.46961 87.77418 88.16347 92.52781
## 680 95.77954 90.71247 94.46961 88.66636 84.62964
## 681 76.84017 91.27871 91.04108 88.75326 85.51542
## 701 49.97188 36.79145 45.30148 57.40171 89.67846
## 702 79.51359 80.89354 87.90980 97.43460 92.17841
## 703 84.86304 88.51961 74.07757 81.93143 87.11384
## 704 86.77549 91.64965 84.59334 75.91268 79.05238
## 705 53.96413 71.60730 53.67943 76.96679 88.67350
## 706 76.24359 86.43748 73.98322 92.20780 90.73737
## 726 89.62937 103.54970 70.89381 63.12598 74.10656
## 727 85.57589 74.82542 103.13131 81.93143 81.40956
## 728 97.43460 68.86478 36.84186 69.44062 82.18981
## 729 76.00061 91.73298 72.67259 75.74804 91.70420
## 730 91.73298 96.04494 73.29890 68.22087 91.43739
## 731 85.46920 70.60962 92.22074 102.22279 88.96609
## 732 70.48718 85.60476 95.90900 92.98638 85.35279
## 733 92.80954 81.62803 98.94377 88.10025 98.04703
## 734 91.18015 94.08903 95.99433 86.69231 91.33018
## 735 102.66218 98.53717 100.63553 98.98795 87.53341
## 736 99.62495 97.22840 100.63077 100.62028 102.41009
## 737 98.94547 103.63267 104.54117 103.23319 104.51553
## 738 104.04441 108.71738 106.69773 137.77702 108.22561
## 739 113.99777 106.15273 106.44586 141.25711 100.88040
## 740 119.50628 112.13793 118.11594 106.10489 132.21463
## 741 338.64140 119.79731 113.47576 100.70149 114.48351
## 742 115.60556 112.63187 125.54172 110.22047 166.15643
## 743 103.20968 128.12313 116.88010 110.77789 445.05222
## 744 116.94994 183.03809 123.11031 127.88706 109.79184
## 745 119.67466 116.04334 105.65981 132.44916 126.33961
## 746 134.59250 101.37988 131.76436 139.10761 115.01951
## 747 116.98047 318.79224 131.99689 110.76060 112.81117
## 748 132.05508 147.97806 150.27685 122.30426 131.27959
## 749 113.08281 143.27472 111.04844 179.23003 131.78532
## 750 103.71193 219.35145 568.61008 145.77735 132.79757
## 751 87.39805 60.45340 58.63290 79.11190 91.32519
## 752 89.92114 87.79150 80.32086 88.71275 68.22153
## 753 89.62937 97.69212 90.62159 88.93570 81.13119
## 754 75.65387 87.77418 84.59334 92.35943 94.96576
## 776 79.51359 85.10968 86.85072 96.08898 89.62937
## 777 94.96854 89.45997 84.18221 58.84880 83.26203
## 778 87.11384 52.64988 68.38764 80.88184 86.31604
## 779 91.73298 89.18316 65.97222 90.96115 71.43483
## 801 82.63836 89.67846 85.77597 91.12610 95.66380
## 802 89.86462 87.80122 97.99331 88.51961 84.18221
## 803 90.63433 79.51430 86.59730 68.22153 85.35190
## 804 67.96218 92.43986 71.43483 89.18316 92.43986
## 805 73.45181 82.88179 54.27027 72.67259 92.52781
## 806 93.54729 88.10025 93.55041 93.23607 67.45901
## 807 82.13950 98.94377 88.39372 81.44024 90.65794
## 808 78.00297 95.25742 92.71848 100.24863 101.81818
## 809 97.88507 98.73339 88.39189 91.33018 100.77983
## 810 104.09098 99.87192 98.98863 100.65492 102.72571
## 811 100.63553 99.63866 99.11660 100.42929 98.53717
## 812 102.93651 109.08737 103.28508 104.69265 101.81424
## 813 104.13554 101.78633 103.59412 102.94479 103.59412
## 814 111.37424 111.51407 111.22650 110.08035 120.59903
## 815 109.80112 107.45477 109.72657 108.26402 99.68729
## 816 123.31008 117.47683 112.52256 107.45477 113.74127
## 817 125.63590 106.85185 109.39410 106.70624 116.22330
## 818 166.01565 116.12282 163.02863 128.14807 105.36117
## 819 133.08636 105.60676 142.76316 117.02929 136.74200
## 820 113.99420 182.71795 128.46265 113.83465 163.49438
## 821 126.04950 146.31098 121.63101 110.92679 118.45732
## 822 160.98321 131.99689 104.02926 119.47703 113.84924
## 823 162.35652 124.46827 126.98589 130.19223 101.32392
## 824 123.01758 139.77080 744.58839 447.24761 115.24018
## 825 173.22956 132.09207 172.82309 142.24827 161.22399
## 876 81.93143 81.93143 88.96352 60.65947 57.40171
## 877 80.32086 60.03765 80.07062 90.71575 86.84609
## 878 79.88844 82.16888 90.62159 66.61349 89.29480
## 879 91.70420 77.60870 86.40904 86.65280 87.77418
## 880 92.14181 78.61337 94.46961 65.48751 89.67338
## 881 85.13134 95.74852 87.19216 98.34261 95.08598
## 882 96.47162 57.28155 95.40466 95.29390 81.23698
## 883 92.71862 93.23607 75.35918 90.90446 90.73737
## 884 97.53696 97.89099 97.91838 102.69306 100.81566
## 885 102.32023 103.18209 102.32023 100.31855 100.42671
## 886 101.14233 101.24048 100.34017 98.64589 98.87226
## 887 101.98221 105.61450 102.76001 104.18450 107.55417
## 888 110.91829 104.23182 102.92240 104.23182 103.62028
## 889 112.63745 110.08035 100.39438 122.96154 101.44664
## 890 129.12470 112.13793 110.84710 380.88026 127.12370
## 891 122.00069 102.37739 100.70149 112.30907 123.45897
## 892 112.92240 117.82492 105.33872 111.20249 114.09806
## 893 105.33872 111.71435 107.14471 107.14471 110.65562
## 894 121.15220 111.79832 154.46581 110.15822 119.33927
## 895 128.46265 228.18339 113.56368 182.71795 134.27037
## 896 113.59687 119.17671 161.96111 121.33721 113.64010
## 897 112.69286 121.48662 112.81117 116.78040 113.53051
## 898 182.31015 147.79016 108.83590 121.45352 133.72371
## 899 127.04738 162.56055 136.57597 132.78361 210.95186
## 900 128.95963 132.79757 134.82010 130.54977 149.34940
## 951 91.23674 82.24845 97.69924 62.27695 64.04461
## 952 87.68738 85.95653 84.86304 56.17321 37.81895
## 953 81.13119 97.43460 63.12598 91.32519 67.53835
## 954 87.88899 92.40642 85.50989 67.96218 87.60438
## 955 87.73624 76.93336 86.88603 85.95374 85.38321
## 956 73.12163 94.13769 95.82647 85.60476 94.37150
## 957 67.80351 72.44891 94.08517 86.43748 91.29655
## 958 89.16429 65.34469 79.08784 65.23077 91.96508
## 959 100.48347 92.73947 95.08520 101.52975 87.92436
## 960 100.11052 99.73118 100.54435 101.43557 100.44025
## 961 102.77447 99.61333 101.19430 104.30909 102.17427
## 962 103.27372 104.10156 107.41470 101.08255 98.62238
## 963 111.19878 107.76005 105.98155 116.61568 102.92240
## 964 106.62398 112.78478 106.44943 100.39438 103.93445
## 965 105.60826 133.20394 103.37279 111.82715 123.45897
## 966 109.40839 127.75305 140.96680 109.78778 118.11594
## 967 98.34486 445.05222 120.81843 103.20968 106.83120
## 968 162.89176 111.78234 116.46127 123.45281 126.23905
## 969 116.18678 132.79034 116.77544 110.85041 110.33821
## 970 121.43880 105.36249 120.41282 107.93025 111.00068
## 971 113.59687 110.19345 503.42939 131.98531 188.53177
## 972 193.58160 134.17367 114.09905 149.28145 99.41893
## 973 144.79541 146.12892 115.92970 101.32392 205.17426
## 974 136.72926 155.69308 120.74058 166.00129 139.77080
## 975 125.95365 123.69247 121.63895 135.41667 160.75466
## 1026 41.68769 60.45340 41.68769 79.72385 41.68769
## 1027 86.30683 63.96155 87.96539 86.85072 79.11190
## 1028 76.52190 86.59730 83.45336 84.35955 89.67846
## 1029 90.33507 91.87575 79.00953 92.56843 79.07915
## 1030 88.95131 93.31005 92.92963 80.57239 59.41362
## 1031 97.36059 92.03243 92.47394 90.85420 91.96508
## 1032 96.59448 76.31949 83.30883 84.42922 95.90900
## 1033 85.84962 95.03849 96.81781 79.41074 79.41074
## 1034 98.92178 88.39189 87.92436 96.73800 95.99733
## 1035 97.57504 99.64087 100.63077 99.10475 98.27656
## 1036 96.83658 101.74162 101.52495 98.87331 99.67887
## 1037 102.97991 102.02099 104.64498 100.21886 108.96611
## 1038 104.67952 106.30195 117.06788 99.85425 103.14673
## 1039 115.59832 101.44664 106.48477 107.70003 106.44586
## 1040 109.64912 109.72657 108.09263 104.32544 338.64140
## 1041 100.70149 102.94933 106.10489 107.65160 105.33277
## 1042 113.96746 116.12282 135.82276 104.92897 160.60608
## 1043 118.79881 113.17658 108.18084 110.76400 108.32291
## 1044 248.54195 125.82905 123.11031 114.33877 110.72638
## 1045 146.06715 112.23263 104.77194 137.21213 105.36666
## 1046 101.37988 113.59687 146.31098 124.26543 109.59436
## 1047 119.47703 114.28304 118.87545 125.00909 111.05169
## 1048 125.59274 197.99311 157.64839 162.66276 121.62320
## 1049 161.42447 111.39208 447.24761 118.87561 137.93166
## 1050 143.17600 1189.82588 124.63222 121.63895 134.82010
## 1101 88.59921 95.61993 69.00621 93.66601 68.86478
## 1102 54.23814 45.05271 39.64751 79.68953 88.96352
## 1103 80.21945 87.00521 63.88756 85.03989 88.59921
## 1104 85.47067 90.64730 91.33736 75.69345 92.64793
## 1105 90.71247 90.64730 82.80109 93.06302 79.39866
## 1106 94.74468 90.65794 93.41064 84.11676 70.60962
## 1107 89.40975 99.33319 88.90840 85.35279 92.13474
## 1108 93.41064 77.71553 91.27871 82.59775 87.31443
## 1109 94.67902 95.35065 94.67902 89.61493 91.37769
## 1110 102.46154 102.41009 101.52984 98.86147 101.77396
## 1111 100.63553 100.54435 97.54033 103.49682 98.00079
## 1112 110.28205 106.58140 104.51553 102.93651 105.61450
## 1113 104.06422 104.89362 106.30195 110.93115 105.96625
## 1114 100.39438 120.16029 105.97367 121.74289 104.55229
## 1115 108.59177 120.82444 110.05322 108.46440 105.34100
## 1116 117.59082 105.34785 105.31331 123.45897 129.13669
## 1117 114.84015 103.20968 101.05646 111.84610 130.86886
## 1118 98.76543 98.34486 115.48170 113.43226 120.23841
## 1119 110.95365 136.74200 108.83104 112.23263 119.67466
## 1120 111.79832 117.02929 118.56621 138.80017 131.42239
## 1121 101.37988 188.53177 188.53177 110.92679 110.37718
## 1122 111.73959 318.79224 123.59155 123.85819 118.31005
## 1123 108.83590 145.14124 131.27959 205.17426 470.08200
## 1124 210.70998 215.03986 143.27472 140.18034 143.36483
## 1125 1189.82588 219.35145 142.24715 166.25036 104.83165
## 1126 70.89381 86.24029 97.73589 88.97681 39.64751
## 1127 94.43840 86.50740 81.40956 76.81953 93.97112
## 1128 89.67846 90.98065 85.21347 54.23814 55.25180
## 1129 86.61646 91.73298 87.60438 84.59334 63.14192
## 1151 70.89381 84.31220 52.64988 90.71575 91.12610
## 1152 80.88184 79.51430 82.37310 66.56782 81.13119
## 1153 81.69164 52.64988 39.70148 85.54361 82.16888
## 1154 85.95374 79.39866 91.78296 89.12614 79.39866
## 1176 63.12598 79.88844 90.71575 82.38977 87.26977
## 1177 49.78525 85.66890 81.93143 66.61349 41.62287
## 1178 86.50740 76.52190 81.93143 65.23464 81.40956
## 1179 92.56843 53.67943 90.71247 96.04494 81.02063
## 1180 90.64730 91.46595 91.27376 85.47067 86.40904
## 1181 93.19224 92.47394 78.89058 88.80377 93.55041
## 1182 91.04108 89.32484 94.96528 90.19618 79.43407
## 1183 93.54731 94.20244 88.04751 86.59472 82.13950
## 1184 101.01189 97.48328 96.36786 100.79476 97.48328
## 1185 99.83780 98.71030 99.99093 102.01587 102.70549
## 1186 100.05478 100.75329 97.34595 103.18209 101.86862
## 1187 98.62238 101.08255 106.00277 102.48483 100.36611
## 1188 101.96463 105.98155 111.54449 103.88052 102.47183
## 1189 106.62398 105.74991 106.56318 103.29765 105.74991
## 1190 120.33720 99.75145 116.13150 122.00069 99.75145
## 1191 108.16236 129.12470 109.91606 108.59177 110.52339
## 1192 172.75985 136.57143 113.64498 115.08633 112.92240
## 1193 125.93080 105.33872 130.70175 103.62725 173.66266
## 1194 117.56838 108.04980 117.59259 132.44916 132.42378
## 1195 108.83104 148.34249 110.72638 104.29527 106.95759
## 1196 118.49745 113.64695 119.31776 102.82057 117.26462
## 1197 320.44206 114.28304 99.75966 99.75966 148.34604
## 1198 117.70833 122.11990 152.40741 323.44806 152.18813
## 1199 103.33840 215.03986 131.41540 116.66334 748.29994
## 1200 132.28471 267.49050 132.79757 137.19342 121.38711
## 1201 89.67846 93.66601 77.73452 66.58774 92.17841
## 1202 93.66601 60.03765 80.21945 85.46386 85.77597
## 1203 86.26102 91.32519 96.08898 85.66890 82.63836
## 1204 82.68579 91.33736 76.96679 63.88924 70.11395
## 1205 89.67338 86.40904 86.61646 91.65131 65.48751
## 1206 81.95826 88.10025 91.80362 85.84962 96.59448
## 1207 88.08301 92.87515 87.94957 81.34965 90.42765
## 1208 95.40466 92.21051 87.78115 99.33319 86.43748
## 1209 96.30855 92.99363 97.18961 86.84800 93.24469
## 1226 87.80122 60.65947 56.17321 87.19251 76.81953
## 1227 70.89381 79.62324 87.22372 95.61993 80.32086
## 1228 84.18221 86.50740 87.24826 86.31604 82.75869
## 1229 70.85132 73.45181 79.05238 96.04494 93.75936
## 1230 91.76680 79.39866 91.43739 92.52781 93.06302
## 1231 85.09039 94.67286 93.51373 97.99241 91.10648
## 1232 81.62803 96.35391 88.21839 85.09039 94.16257
## 1233 76.31949 95.40466 81.34965 98.92117 75.63255
## 1234 98.70271 101.11111 97.51408 99.79936 97.65543
## 1251 82.37310 81.96664 77.28096 80.42268 79.88844
## 1252 75.67416 105.36680 83.26203 94.96854 84.05367
## 1253 69.44062 57.40171 77.28096 87.90980 80.76570
## 1254 59.30769 73.45181 91.71909 71.43483 83.29147
## 1255 53.67943 93.80379 91.87575 80.57239 93.75936
## 1256 77.71553 93.45691 70.48718 92.20780 93.41064
## 1257 76.24359 98.73440 95.58712 102.22279 97.36059
## 1258 85.46920 88.08301 84.65185 80.22518 84.30664
## 1259 97.25576 98.73339 91.33018 91.18015 97.25576
## 1260 100.54435 100.60284 101.40897 102.42961 97.43528
## 1261 98.71030 100.52245 101.33226 102.42961 99.65747
## 1262 105.05959 103.23319 110.28205 144.11512 102.97991
## 1263 97.65152 107.83794 103.83656 110.32772 110.69491
## 1264 114.26822 118.86091 102.84426 110.08035 111.22650
## 1265 108.22291 103.29518 104.13499 326.24215 107.45477
## 1266 106.44959 102.84663 102.75253 103.29518 105.18351
## 1267 105.39379 114.85910 120.53017 105.04216 144.16979
## 1268 125.93080 105.46017 105.36117 108.18084 112.96915
## 1269 134.40526 111.40073 104.29527 99.61317 116.41392
## 1270 114.59080 119.77823 110.11613 104.77194 127.88706
## 1271 178.65124 126.34928 188.77832 161.96111 112.70218
## 1272 115.23936 147.34885 193.58160 148.02632 99.41893
## 1273 108.93036 134.67420 116.40820 126.33907 127.97053
## 1274 132.01165 155.93496 666.96867 137.93166 157.06224
## 1275 124.21849 144.66941 161.57427 191.15108 168.55762
## 1276 90.82572 82.18296 87.06722 88.74066 91.22254
## 1277 88.96352 86.95843 87.06722 41.91126 83.26203
## 1278 52.63789 86.84609 58.84880 94.96854 86.72466
## 1279 86.00700 79.87391 86.00700 94.38345 91.27376
## 1280 85.95374 53.32295 91.46595 75.65387 79.05238
## 1281 92.21051 101.49594 90.19618 93.82111 93.45691
## 1282 100.75978 93.88938 90.18384 82.13950 95.36544
## 1283 93.32995 94.95988 79.76890 88.11056 98.04703
## 1284 94.97735 88.01447 98.59710 99.02634 97.51408
## 1301 81.13119 87.20973 78.65690 45.05271 90.23312
## 1302 88.98349 50.76591 87.24826 85.21347 76.43678
## 1303 70.92045 97.69212 74.49210 60.57741 86.31604
## 1304 87.73624 80.66573 75.51253 89.67338 59.41362
## 1305 87.74308 88.67350 92.75428 96.08898 53.67943
## 1306 88.21839 93.54731 102.22279 91.14090 91.10648
## 1307 88.96609 101.36364 99.94438 80.21429 88.66208
## 1308 96.28014 81.44024 93.45691 89.16429 75.81067
## 1309 93.89692 98.07092 86.57403 99.83715 99.02634
## 1310 101.31817 98.27656 100.04108 100.44025 102.07249
## 1311 101.14849 99.69388 101.78553 102.41009 100.35603
## 1312 103.33940 104.51553 110.28205 105.57143 105.74543
## 1313 110.07958 115.19239 109.83401 110.10368 101.78633
## 1314 141.25711 104.88907 97.88709 106.44943 297.32487
## 1315 121.63392 104.04960 126.73526 107.06580 151.36925
## 1316 152.66391 100.67826 129.12470 122.76389 109.64912
## 1317 105.50042 141.54676 106.70624 112.92240 156.88157
## 1318 128.12313 100.65657 128.31784 117.50872 225.66604
## 1319 105.55215 149.17460 109.39168 131.30663 109.36204
## 1320 123.57135 169.24985 105.65981 121.92049 111.98145
## 1321 503.42939 146.31098 118.49745 119.21853 117.26462
## 1322 108.58455 131.49077 320.44206 118.87545 127.71320
## 1323 145.60938 642.58180 125.59274 116.62220 113.61216
## 1324 153.78922 121.97617 133.97506 125.77025 448.92817
## 1325 130.12115 143.17600 193.09064 124.21849 113.78304
## 1326 84.35955 36.84186 76.43678 80.88184 74.49210
## 1327 80.89354 63.96155 84.86304 88.96352 50.76923
## 1328 39.70148 87.68738 89.67846 82.38977 82.16888
## 1329 92.75428 90.74173 91.33736 90.41604 92.13118
## 1330 87.78058 81.00761 79.87391 64.61268 79.05238
## 1331 65.23077 97.99241 86.43748 81.23698 74.55635
## 1332 85.35279 92.80954 95.90900 99.94438 82.82758
## 1333 94.04443 81.36691 92.80954 81.93717 77.22249
## 1334 101.01189 96.31460 92.29034 96.36786 96.03599
## 1335 99.36712 102.17427 102.70549 103.84216 98.03175
## 1336 100.51559 100.35603 98.54870 101.71123 100.71676
## 1337 164.68155 100.99355 110.28205 120.11251 105.59849
## 1338 104.99403 175.67105 99.22778 110.10368 109.90148
## 1339 103.54806 101.99868 115.34707 115.51272 105.32322
## 1340 103.40420 105.81129 105.52295 106.52577 107.73630
## 1341 144.62638 162.87960 110.46209 150.83319 104.32544
## 1342 115.48170 105.50042 100.65657 105.36117 107.72305
## 1343 138.15359 106.26756 111.20249 163.02863 101.05646
## 1344 143.06657 115.65876 119.21580 108.59125 136.68277
## 1345 136.34087 110.85041 122.07269 108.26185 116.75754
## 1346 252.70767 106.62682 252.70767 114.24503 209.26474
## 1347 108.31670 298.90043 115.23936 125.55562 121.48662
## 1348 323.38504 641.17255 130.19223 120.22822 104.67082
## 1349 194.98985 117.61831 127.50389 155.62688 116.61761
## 1350 204.79928 125.24982 124.21849 124.21849 103.71193
## 1401 80.80704 81.40956 86.53435 93.92888 81.93143
## 1402 49.78525 76.43678 39.64751 82.18296 69.00621
## 1403 66.58774 84.15973 86.87865 87.68738 86.31604
## 1404 73.45181 86.73150 71.60730 79.00953 95.77954
## 1405 64.61268 91.87575 94.70750 75.91268 75.69345
## 1406 99.01804 94.16257 97.06889 97.55667 97.61660
## 1407 85.46920 92.31872 84.21325 92.98638 98.34261
## 1408 97.95033 90.37662 87.22890 79.43407 85.13210
## 1409 96.21200 94.96702 99.83715 97.00814 97.65543
## 1410 101.05028 99.09051 101.33226 100.65492 98.78481
## 1411 101.02647 101.77396 102.01587 103.84216 98.87331
## 1412 101.19407 103.47246 109.50161 103.54319 103.16092
## 1413 105.86541 108.71738 132.29157 108.28152 111.56361
## 1414 112.78478 105.97367 108.52239 103.89858 105.62299
## 1415 148.10349 106.10489 106.19239 107.32870 152.66391
## 1416 112.55568 110.46209 143.88871 108.46440 108.22291
## 1417 160.60608 111.84610 141.53477 102.88173 114.84006
## 1418 105.30144 111.05910 105.56697 158.47743 103.49693
## 1419 168.95985 134.40526 169.43669 116.42214 99.49455
## 1420 163.49438 102.39567 110.72638 113.82010 119.89695
## 1421 160.58730 119.65444 105.52984 118.49745 188.77832
## 1422 117.86513 108.31670 107.26161 132.31067 168.75973
## 1423 323.44806 140.40671 323.44806 162.66276 121.62320
## 1424 168.40951 161.42447 127.04738 132.44953 111.39208
## 1425 146.56163 117.40587 123.69247 112.93395 150.81380
## 1426 83.45336 77.73452 88.03280 50.76923 87.19251
## 1427 85.66890 87.79150 88.93570 49.78525 72.67589
## 1428 80.76570 41.91126 92.38744 96.04584 68.86478
## 1429 92.13118 92.43411 91.46595 83.29147 91.62935
## 1430 79.39866 63.37863 88.66636 69.59554 97.31578
## 1431 78.89058 94.25877 84.30664 93.32995 97.06502
## 1432 96.56863 97.55667 84.21325 97.48628 75.63255
## 1433 91.27871 88.80377 95.06403 75.63255 97.10315
## 1434 95.81535 66.97690 94.96702 86.84800 100.81566
## 1435 104.30909 102.46154 98.83097 96.69969 112.68137
## 1451 89.45997 88.03280 84.86304 93.97112 97.69212
## 1452 84.16547 85.15462 57.46010 87.00521 96.08898
## 1453 85.58530 69.00621 66.56782 77.81180 82.37310
## 1454 88.67350 75.91268 84.62964 102.63692 53.58974
## 1455 90.90331 88.66636 95.77954 83.29147 90.41604
## 1456 75.51250 93.45691 94.16257 92.99346 94.18004
## 1457 93.54731 95.03849 90.85420 78.89058 101.81818
## 1458 73.31933 81.56341 80.53962 93.41064 91.27871
## 1459 101.01189 98.07092 97.73507 92.99363 102.69306
## 1460 99.10475 100.42671 99.41273 101.25268 100.05960
## 1461 100.50736 98.78481 101.14233 101.05028 103.30935
## 1462 103.21992 143.70360 103.16092 116.80319 98.62238
## 1463 105.98155 104.26913 105.84633 105.88496 105.82849
## 1464 116.98133 296.34216 106.79214 102.74489 112.78478
## 1465 126.73526 107.60344 338.64140 116.28912 106.72359
## 1466 124.49640 107.66647 108.36584 106.44959 128.61022
## 1467 208.23501 105.39379 116.48510 118.71088 135.10290
## 1468 114.65557 123.62344 101.05646 110.65562 110.16206
## 1469 116.89807 109.22399 105.73385 109.52637 110.33821
## 1470 129.81371 125.82905 114.59080 131.13540 120.40397
## 1471 153.93285 99.45656 129.23151 111.87852 115.01951
## 1472 132.31067 126.41812 120.40953 104.02926 117.27221
## 1473 115.43671 120.93341 131.27959 130.73546 113.61216
## 1474 120.93599 111.04844 107.64352 123.73880 247.11846
## 1475 191.15108 187.66109 132.09207 139.45128 125.24982
## 1476 85.58530 75.04270 41.56536 82.75869 94.37539
## 1477 89.92114 74.10656 89.76592 60.67146 86.17021
## 1478 84.98210 90.05968 84.16547 87.26977 87.49543
## 1479 91.35638 90.40701 91.71909 97.33569 88.66636
## 1480 89.23611 71.60730 85.41806 89.23611 93.33426
## 1481 83.14199 88.75352 82.36210 75.63255 73.79112
## 1482 88.21839 88.66208 73.59809 85.13134 75.35918
## 1483 94.95988 82.82758 90.44223 72.84820 91.86796
## 1484 97.51408 98.21780 96.70003 89.81541 91.18015
## 1485 99.62205 101.74416 97.96079 102.42961 96.34616
## 1486 100.12346 100.64034 97.93814 100.56819 101.96489
## 1487 102.48483 104.70155 109.50161 119.98249 105.61450
## 1488 115.39095 106.30195 105.71932 104.20592 103.88052
## 1489 140.53637 100.39438 105.74991 104.97312 111.17116
## 1490 102.94933 113.13935 105.52295 111.06992 102.88066
## 1491 152.66391 120.82444 379.87625 108.02726 106.40525
## 1492 109.17025 171.38311 120.27348 112.93166 110.22047
## 1493 114.57763 118.77751 120.23841 107.05697 121.36237
## 1494 113.42653 115.62426 120.45371 110.85041 175.68796
## 1495 131.30663 108.13831 132.73572 136.74200 109.52637
## 1496 126.65652 117.71484 252.70767 131.98531 139.51296
## 1497 111.53629 140.12399 127.09092 121.48662 118.87545
## 1498 182.98188 120.22822 127.06840 131.22664 120.26701
## 1499 140.18034 132.44953 166.21715 194.98985 113.08281
## 1500 146.13979 191.15108 123.66954 267.49050 192.70432
## 1551 86.30683 90.40317 70.22650 87.19847 70.22650
## 1552 62.27695 80.21945 85.57589 90.05968 39.64751
## 1553 104.02357 86.83467 81.88533 89.62937 74.07757
## 1554 92.35943 83.29147 77.44490 85.47067 94.70750
## 1555 63.88924 91.33736 91.50520 94.46961 96.08898
## 1556 96.81781 91.29655 98.30169 96.59448 94.74468
## 1557 80.21429 80.22518 96.43636 94.80933 88.11056
## 1558 92.72501 101.81818 88.21839 81.93717 99.84694
## 1559 66.97690 94.96702 89.81541 97.18961 101.01189
## 1560 101.93226 100.65492 103.32134 100.79741 99.73802
## 1561 101.74162 101.56744 97.96079 101.46492 101.63367
## 1562 102.00329 103.28508 103.23319 101.82624 101.24287
## 1563 104.38677 109.81562 104.04441 106.16602 105.45455
## 1564 115.34707 106.29270 113.99777 120.59903 104.74776
## 1565 106.44959 120.63251 116.68623 122.20380 121.63392
## 1566 107.03475 155.66885 123.31008 120.82444 106.67743
## 1567 107.14471 138.15359 114.57763 107.13503 208.23501
## 1568 114.25129 445.05222 108.38241 113.94046 162.89176
## 1569 118.56621 119.59454 113.56368 123.60722 169.43669
## 1570 110.38324 120.41282 131.42239 101.06061 117.92879
## 1571 123.80165 178.65124 111.36527 118.49745 133.66675
## 1572 108.31670 127.98187 201.41432 119.71218 136.02601
## 1573 130.19223 126.67551 131.11396 134.36298 173.04556
## 1574 136.72926 118.87561 180.75454 179.39371 132.58687
## 1575 168.55762 166.25036 132.28471 125.95365 105.26538
## 1626 36.84186 76.63699 82.18296 80.88184 97.43460
## 1627 90.05968 86.17021 97.99331 79.88844 54.29599
## 1628 63.96155 86.85072 82.24845 79.47972 54.23814
## 1629 77.44490 89.64036 69.59554 79.00953 91.78296
## 1630 69.59554 61.05559 70.42076 91.70420 61.37006
## 1631 93.89796 93.55041 82.74496 91.10648 82.82758
## 1632 81.36691 94.67286 90.90446 91.81731 88.96747
## 1633 75.81067 92.71848 75.35918 94.63581 95.01535
## 1634 97.29414 96.70003 98.67298 91.25397 94.67902
## 1635 103.32134 100.14407 99.10475 101.95012 96.92005
## 1636 100.89656 100.05478 101.95012 97.96420 101.43557
## 1637 102.48483 101.33319 107.11129 100.81512 106.43074
## 1638 104.01260 106.16602 108.33239 104.97123 104.99403
## 1639 115.34707 137.90473 103.54806 111.37424 107.23509
## 1640 104.27964 105.31331 108.46440 111.65145 107.06580
## 1641 102.94933 116.68623 103.37279 140.79911 103.29518
## 1642 135.82276 162.89176 106.18512 112.92240 173.66266
## 1643 104.95144 117.52555 111.63016 165.59254 116.14203
## 1644 123.41478 120.19411 120.45371 126.30030 146.06715
## 1645 252.84839 119.67466 110.82173 108.83104 132.42378
## 1646 111.23759 113.31907 112.72984 123.54203 105.58526
## 1647 108.27347 168.75973 99.41893 117.86513 112.69286
## 1648 641.17255 100.74375 115.43671 642.58180 133.39248
## 1649 116.61761 166.21715 120.93599 116.61761 138.84010
## 1650 131.01274 130.12115 142.56514 161.00529 131.01274
## 1651 83.26203 49.97188 79.68953 84.43896 77.73452
## 1676 45.05271 80.05830 83.26203 97.99331 97.69924
## 1701 76.43678 87.51037 84.35955 88.59921 80.32086
## 1702 88.52178 70.22650 88.98349 60.65947 70.22650
## 1703 39.70148 70.22650 97.69924 62.27695 79.68953
## 1704 65.97222 91.72003 65.48751 68.22087 70.85132
## 1705 87.78058 68.22087 89.64036 63.88924 91.71909
## 1706 99.94438 94.74468 93.41064 76.84017 88.02860
## 1707 94.94681 92.22074 96.35980 82.13950 88.75876
## 1708 83.30883 77.71553 92.38893 65.72650 76.71611
## 1709 81.86683 97.88507 97.91254 95.98072 96.24320
## 1710 102.66218 97.58014 97.46060 99.36712 100.50736
## 1711 98.03175 101.05372 99.69357 100.48408 99.93156
## 1712 104.28966 111.49880 98.94547 110.47760 110.47760
## 1713 260.74334 108.33239 105.38233 109.83401 103.29265
## 1714 109.23746 102.70067 110.43121 101.96945 120.16029
## 1715 108.26402 116.28912 113.74127 118.21245 133.41503
## 1716 150.83319 123.31008 112.13793 116.13150 107.93066
## 1717 121.52583 109.39410 104.37449 162.89176 109.42068
## 1718 171.38311 105.46017 116.12282 126.23905 207.17797
## 1719 136.40266 99.15638 116.75754 114.13036 129.81371
## 1720 114.13036 109.39168 122.07269 163.49438 110.15822
## 1721 111.00264 173.21939 123.80165 126.04950 123.80165
## 1722 112.31699 112.31699 127.98187 131.49077 147.34885
## 1723 172.63492 172.63492 197.77093 147.79016 108.93036
## 1724 179.23003 122.70613 133.97506 127.21345 136.72926
## 1725 204.79928 172.82309 142.24715 700.68873 134.29708
## 1776 77.84784 93.97112 87.90980 68.86478 84.18221
## 1777 67.53835 104.95791 86.93202 88.51961 82.47773
## 1778 41.62287 86.26102 90.71575 76.81953 74.10656
## 1779 75.91268 86.61646 79.07915 88.67350 89.12614
## 1780 61.37006 86.73150 51.50991 92.03351 96.08898
## 1781 57.27377 96.81781 97.59867 90.44223 85.13134
## 1782 93.63286 95.09096 90.76756 81.95826 89.08083
## 1783 95.70887 93.89796 86.43748 93.44060 90.90446
## 1784 97.48328 93.70331 102.48466 99.50617 101.52975
## 1785 99.27417 100.71676 99.73118 103.30935 99.12850
## 1786 102.64242 95.79865 100.54435 96.34616 101.77396
## 1787 102.97991 103.23319 103.23319 124.71287 106.15999
## 1788 110.69491 113.69048 106.69830 103.46585 114.49640
## 1789 120.16029 104.54255 100.88040 110.08035 110.43121
## 1790 109.05125 108.59177 103.79710 108.26402 110.34835
## 1791 109.49226 110.88988 127.12370 110.06902 150.95828
## 1792 116.22330 128.31784 109.39410 110.54372 103.49693
## 1793 132.25443 109.70550 106.28720 107.90621 126.56843
## 1794 149.15188 118.56621 108.93042 132.79034 112.23263
## 1795 106.49688 117.94491 116.41392 111.00068 108.93042
## 1796 129.23151 141.39107 105.91190 136.66000 139.84188
## 1797 112.31699 125.66132 149.28145 122.96619 193.58160
## 1798 121.45352 100.32828 126.67551 118.29243 229.18128
## 1799 117.61831 137.93166 180.75454 447.23895 123.77131
## 1800 150.61485 131.93130 121.42631 172.82309 129.97848
## 1801 69.07252 54.23814 84.31220 103.54970 91.22254
## 1802 79.54693 50.76591 104.44557 91.29758 86.53435
## 1803 85.21347 81.93143 94.96854 84.16547 87.22372
## 1804 63.14192 76.96679 88.66636 70.47614 90.40701
## 1826 86.59111 87.53040 85.77597 65.10216 72.74734
## 1827 87.33405 87.53040 104.44557 94.96854 80.76570
## 1828 50.76923 87.53040 86.59730 49.78525 87.68738
## 1829 62.68866 86.45978 86.77549 90.96115 80.66573
## 1851 80.89354 79.62324 87.22372 85.21347 85.57589
## 1852 85.54361 36.84186 66.58774 87.53040 94.37539
## 1853 74.49210 87.68738 79.68953 98.00046 63.96155
## 1854 82.88179 75.74804 90.74173 91.27376 89.12743
## 1855 88.95131 97.33569 85.84441 87.79523 85.47067
## 1856 81.34965 99.46346 78.96031 89.08083 88.96609
## 1857 90.45155 96.81781 93.47648 80.22518 92.71848
## 1858 93.25658 90.70701 95.40466 98.45387 91.80362
## 1859 96.61032 98.73339 99.50617 95.08520 91.49750
## 1860 101.96822 102.71888 99.90523 99.04384 101.96489
## 1861 100.05478 101.27936 103.18209 99.65747 100.71676
## 1862 103.89341 101.35203 106.37830 103.63267 104.28966
## 1863 114.83120 105.86541 110.69491 119.89055 111.54449
## 1864 103.89858 102.70067 141.25711 102.84426 104.55229
## 1865 105.34100 112.47647 121.34056 132.29487 132.29487
## 1866 99.68729 99.68729 107.06727 118.92588 107.73630
## 1867 108.38241 126.56843 108.54908 113.08183 166.15643
## 1868 105.46017 125.17527 132.25443 142.28863 114.70431
## 1869 129.13351 120.45371 105.61598 201.13498 230.35639
## 1870 118.02153 168.95985 131.40097 99.61317 117.02929
## 1871 102.82057 110.76649 106.07490 115.59228 139.51296
## 1872 118.31690 551.74786 108.27347 143.70353 134.17367
## 1873 116.40820 100.97366 470.08200 116.40820 113.56516
## 1874 107.64352 121.00863 131.94135 136.57597 136.72926
## 1875 172.62743 222.64729 147.24048 120.39609 115.98005
## 1926 90.71575 77.84784 89.45997 77.81180 52.64988
## 1927 86.69055 87.00521 66.56782 84.43896 50.76591
## 1928 95.66380 94.43840 81.40956 87.22372 103.54970
## 1929 82.80109 88.67350 53.58974 70.42076 70.11395
## 1930 102.63692 86.88603 51.42515 89.67338 93.80144
## 1931 97.18258 97.36059 94.04443 92.80954 69.81468
## 1932 94.74468 90.37662 84.65185 91.54061 98.98092
## 1933 74.58034 98.45387 78.96031 92.30889 92.13474
## 1934 94.08903 92.93899 96.28845 100.77983 98.72624
## 1935 100.24917 101.71123 101.19430 103.99275 98.98795
## 1936 100.31855 101.43557 100.65492 100.65492 99.12850
## 1937 106.15999 119.98249 116.80319 102.76001 107.55417
## 1938 102.47183 104.42528 102.47183 101.78633 117.06788
## 1939 105.62299 109.15415 106.02560 115.34707 138.18694
## 1940 124.48441 120.33720 110.52339 109.91606 113.73976
## 1941 108.02726 105.12161 99.95012 109.80112 103.79710
## 1942 98.34486 158.28246 131.96356 125.47516 119.06632
## 1943 172.70436 126.56843 142.28863 113.17658 117.50872
## 1944 131.58483 110.11613 116.02923 149.90408 105.90435
## 1945 169.43669 117.34339 119.29898 111.97003 116.04334
## 1946 110.44112 188.53177 106.35984 146.31098 119.21853
## 1947 551.74786 160.99520 127.98187 112.31699 119.03563
## 1948 128.50156 129.88004 234.32398 131.26142 120.93341
## 1949 169.95212 179.39371 247.11846 143.27472 113.08281
## 1950 143.17600 107.76487 126.26499 168.55762 122.97546
## 2001 84.31220 83.04769 104.02357 88.96352 79.51430
## 2002 72.67589 86.30683 89.45997 84.13422 104.44557
## 2003 87.19847 94.43840 86.31604 87.20973 83.04769
## 2004 79.05238 92.64793 78.61337 92.14181 87.88899
## 2005 78.61337 93.06302 88.16347 79.07915 94.78517
## 2006 88.11056 91.12778 96.48148 94.95988 68.03409
## 2007 81.56341 85.60476 91.81731 69.00003 94.21084
## 2008 92.21051 89.33854 94.74468 92.79609 93.82111
## 2009 95.81535 101.52975 92.73947 97.45069 97.51408
## 2010 98.71030 94.27515 98.64589 100.72108 98.99128
## 2011 100.05478 102.46154 106.21088 98.87331 99.55544
## 2012 104.24491 99.86831 104.44993 105.59849 106.58140
## 2013 261.53239 104.89362 102.92240 97.65152 105.63446
## 2014 105.58494 104.55415 108.37045 104.55415 109.23746
## 2015 107.93066 144.62638 106.01707 113.14683 106.40525
## 2016 141.68112 106.80057 107.79080 110.52339 103.64675
## 2017 101.13796 98.68517 143.07937 106.47021 136.57143
## 2018 117.21355 142.28863 119.10468 115.02123 104.95144
## 2019 110.82173 136.26939 114.98647 118.15310 113.42653
## 2020 459.90827 100.69865 134.23700 262.84895 107.93025
## 2021 188.36355 252.70767 118.49745 108.07771 131.76436
## 2022 149.28145 131.99689 131.99689 119.71218 120.26187
## 2023 205.35109 134.36298 106.96507 122.30426 147.79016
## 2024 161.07897 125.77025 137.93166 298.66443 120.74058
## 2025 168.55762 161.00529 117.45275 132.13756 135.41667
## 2026 98.00046 86.17021 86.31604 97.69924 86.69055
## 2027 82.38977 86.87865 88.96352 97.73589 39.64751
## 2028 63.88756 86.50740 77.28096 97.69212 85.54361
## 2029 75.69345 94.96576 53.32295 90.14350 75.74804
## 2030 81.19130 94.70750 77.60870 92.14181 79.91193
## 2031 76.24359 91.96508 75.35918 97.40585 74.04314
## 2032 92.79609 93.54731 98.34261 92.43007 88.08301
## 2051 89.76592 41.91126 94.96854 74.10656 84.15973
## 2052 104.44557 88.96352 79.51359 105.36680 86.87865
## 2053 88.96352 93.92888 87.06722 68.86478 36.79145
## 2054 92.35943 94.38345 59.30769 94.96576 53.58974
## 2055 76.00061 54.27027 89.34008 81.00761 92.52781
## 2056 95.74852 78.96031 92.72501 81.34965 94.08517
## 2057 81.44024 89.32484 94.69594 93.56191 85.25340
## 2076 86.59730 41.62287 90.87033 87.39805 76.63699
## 2077 60.57741 60.57741 86.26102 86.30683 83.04769
## 2078 75.04270 74.82542 88.59921 85.21347 54.23814
## 2079 93.31005 85.01780 75.74804 77.60870 85.50989
## 2080 92.56843 91.35638 65.97222 87.79523 85.01096
## 2081 88.29323 91.06227 93.23607 70.48718 92.87515
## 2082 98.98092 68.83437 88.75876 100.72179 70.48718
## 2083 99.01804 94.18004 57.27377 84.00430 90.70701
## 2084 94.67902 102.69306 86.43389 95.99733 102.15192
## 2085 103.84216 112.35484 101.52984 100.50102 103.30935
## 2086 101.95012 100.75329 97.59288 101.84448 103.82921
## 2087 112.42372 110.28205 102.58764 100.99168 101.35203
## 2088 137.64899 119.67320 128.88305 119.67320 102.92240
## 2089 111.37424 105.97255 118.86091 104.19667 140.53637
## 2090 111.82715 124.48441 111.04849 129.64533 102.67333
## 2091 124.48441 158.28096 110.52339 109.40839 112.66109
## 2092 105.30144 102.88173 114.42351 135.17986 132.25443
## 2093 111.20249 126.70203 105.56697 103.62654 112.50254
## 2094 114.03509 137.21213 146.06715 107.97407 116.96535
## 2095 111.88715 114.59080 185.25808 461.00933 185.25808
## 2096 139.84188 126.04950 110.76649 123.61111 105.58526
## 2097 126.41812 116.07684 111.05169 201.41432 121.26949
## 2098 119.08348 104.67082 129.88004 108.93036 126.98589
## 2099 144.57935 128.56307 247.11846 144.57935 215.03986
## 2100 127.20428 128.95963 154.38763 103.71193 147.24048
## 2151 70.92045 80.21945 81.96664 89.92114 104.02357
## 2152 87.00521 67.53835 97.73589 83.06365 84.13422
## 2153 82.16888 88.52178 92.38744 80.07062 96.08898
## 2154 90.20065 73.29890 64.21370 96.08898 93.17554
## 2155 86.73150 75.65387 102.81987 91.72003 81.19130
## 2156 81.19623 81.68889 90.76756 95.52910 76.94358
## 2157 87.76968 100.24863 95.74852 95.25742 101.49594
## 2158 82.13950 84.30664 70.48718 74.04314 93.44060
## 2159 97.94876 93.24388 98.73339 83.11151 91.25397
## 2160 101.50892 99.41273 95.14710 98.64589 101.27295
## 2161 103.49682 99.55544 99.01178 94.57160 102.41009
## 2162 103.21992 103.54319 101.78127 107.41470 104.51553
## 2163 111.56361 109.81562 111.56361 107.83794 105.86541
## 2164 105.21949 106.44943 102.70067 104.82608 110.08035
## 2165 103.64675 107.00910 116.62201 107.03475 118.16721
## 2166 103.01636 122.00069 122.20380 99.29293 105.31331
## 2167 103.64332 120.98189 109.29644 134.81898 136.57143
## 2168 184.33610 104.18835 107.59443 121.48413 111.71435
## 2169 114.03509 116.33617 201.13498 105.73385 99.49455
## 2170 119.77823 116.42214 198.77153 198.77153 123.11031
## 2171 124.28462 269.12711 281.71217 115.01951 252.70767
## 2172 99.75966 143.15570 116.98047 140.12399 116.78040
## 2173 162.66276 131.01205 100.97366 109.17176 120.93341
## 2174 122.70613 214.86895 132.97959 110.00333 132.97959
## 2175 222.64729 146.56163 121.38711 130.12115 150.81380
## 2226 85.10968 72.67589 41.56536 91.29758 62.21343
## 2227 82.37310 54.27991 86.24029 60.45340 82.63836
## 2228 95.66380 103.13131 77.26177 62.21343 87.11384
## 2229 88.67350 93.75936 93.17554 90.96115 85.01096
## 2230 53.58974 78.03115 63.88924 91.71909 61.37006
## 2231 91.27871 87.88031 86.43748 92.31872 90.38887
## 2232 95.35421 88.11056 91.86796 97.69841 94.31004
## 2233 82.70288 82.59775 88.27120 93.25658 93.81893
## 2234 99.79936 98.79779 86.84800 95.98072 99.43150
## 2235 100.16114 102.01587 101.31817 102.29349 97.15385
## 2236 99.35575 101.93226 97.08944 98.64589 102.32023
## 2237 102.76001 104.64498 102.58764 100.21886 104.70155
## 2238 107.83794 104.32099 97.65152 99.85425 110.36126
## 2239 104.97312 121.87968 122.96154 112.63745 97.50000
## 2240 123.31008 109.05125 148.10349 102.37739 117.36111
## 2241 163.72257 117.88453 105.34078 106.01707 107.93066
## 2242 171.10256 113.43226 108.64252 124.92916 101.13796
## 2243 116.75936 103.62654 131.98691 123.02067 114.28594
## 2244 128.64430 136.26939 108.93042 129.47695 109.22399
## 2245 110.11613 110.33821 110.85041 102.49460 117.02929
## 2246 139.84188 101.37988 140.58533 113.64010 101.02694
## 2247 107.47599 110.95092 118.87545 121.48662 99.75966
## 2248 108.83590 115.92970 152.11439 101.32392 113.61216
## 2249 446.58161 117.61831 156.47831 132.01165 156.47831
## 2250 188.82540 142.24715 187.48733 267.49050 193.09064
## 2301 70.92045 86.59730 72.74734 93.97112 87.26977
## 2302 104.95791 80.88184 90.40317 70.89381 74.07757
## 2303 76.43678 87.68738 60.03765 36.79145 79.62324
## 2304 91.64965 63.14192 79.31961 86.00700 88.16347
## 2305 85.84441 92.43986 93.33426 89.12743 51.42515
## 2306 91.54061 91.27871 94.95988 94.31004 77.71553
## 2307 88.02860 101.81818 83.40701 94.20244 95.40466
## 2308 85.98439 93.47648 65.23077 73.79112 74.55635
## 2309 89.61493 98.03552 97.70301 100.77983 97.73507
## 2310 101.82777 96.69969 97.15385 100.93304 94.57160
## 2311 99.35575 103.49682 99.11660 100.18869 100.31855
## 2312 98.22391 103.27481 102.40763 104.99937 104.18450
## 2313 105.82849 101.85783 108.28152 118.19123 103.14673
## 2314 110.40473 105.11212 104.19667 116.14286 100.39438
## 2315 105.35619 107.45712 106.94296 107.07546 129.13669
## 2316 117.41760 103.37279 129.79219 104.58508 112.95271
## 2317 111.46081 158.28246 158.28246 151.51333 126.70203
## 2318 105.46017 116.88010 183.38993 111.60177 104.92897
## 2319 138.61044 111.40073 482.34621 126.30030 119.89695
## 2320 230.35639 128.64430 113.82010 252.84839 148.34249
## 2321 123.00073 123.61111 111.41676 123.80165 110.76649
## 2322 125.00909 147.34885 121.11605 137.72482 109.58203
## 2323 120.22822 115.76302 117.64437 112.60288 116.40820
## 2324 103.33840 117.61831 298.66443 131.37534 180.75454
## 2325 107.76487 131.93130 139.45128 132.09207 1189.82588
## 2376 57.40171 79.54693 87.39805 87.22372 93.97112
## 2377 77.26177 86.24029 74.82542 87.11384 92.01060
## 2378 85.21347 97.69924 86.84609 104.02357 54.23814
## 2379 79.31961 91.02956 75.65387 91.51116 90.41604
## 2380 95.82526 51.50991 92.43411 92.13118 64.77170
## 2381 94.01651 81.62223 92.30889 79.08784 93.56191
## 2382 95.75119 87.88031 70.82698 95.68366 67.14593
## 2383 88.39372 96.46720 70.74005 95.35421 95.01535
## 2384 95.99433 97.91254 94.85522 92.48857 100.36361
## 2385 97.22840 100.31855 101.38662 97.45585 101.38552
## 2386 100.06442 100.41819 99.09122 112.35484 101.25268
## 2387 111.49880 103.23319 112.72664 106.37830 102.76001
## 2388 115.06294 114.65787 114.49640 109.57484 107.76005
## 2389 146.43261 104.85046 107.23509 100.88040 115.07238
## 2390 104.27964 106.38032 133.41503 110.88988 106.66069
## 2391 113.47576 107.06580 106.02534 113.13935 117.87121
## 2392 113.17658 124.45826 104.99605 110.16479 116.75936
## 2393 111.90901 111.71435 105.56697 104.18835 103.49693
## 2394 120.17283 103.24642 105.61598 102.49460 112.23263
## 2395 482.34621 104.77194 130.64683 175.39744 132.44916
## 2396 269.12711 123.61111 110.44112 126.54096 173.21939
## 2397 100.34248 110.95092 144.04249 550.46210 169.39628
## 2398 126.98589 147.80102 234.32398 233.93590 128.97574
## 2399 246.70513 116.61761 127.50389 120.78285 194.98985
## 2400 105.26538 1196.02892 570.80855 160.75466 1189.82588
## 2401 84.98210 79.51359 90.05968 76.52190 82.18296
## 2402 82.63836 90.82572 56.17321 76.43678 90.40317
## 2403 77.84784 45.05271 80.32086 64.04461 69.07252
## 2404 90.71247 81.00761 64.83246 92.52781 87.60438
## 2405 76.96679 89.18316 77.60870 89.12614 81.19130
## 2406 73.98322 93.08193 94.37053 96.92817 81.62223
## 2426 84.86304 93.92888 74.07757 68.22153 87.00521
## 2427 84.98210 79.51359 84.16547 90.71575 90.23312
## 2428 84.99905 82.16888 86.72466 89.20607 87.19251
## 2429 88.16347 71.60730 79.00953 87.79523 73.29890
## 2430 68.71703 90.90331 75.69345 51.50991 97.01757
## 2431 94.31004 74.58034 95.03849 88.66208 94.63581
## 2451 87.96539 72.67589 82.18981 92.01060 91.23674
## 2452 87.53040 89.62937 93.66601 80.88184 81.96664
## 2453 84.18221 82.16888 97.69212 89.20607 41.91126
## 2454 89.16226 87.78058 92.72349 94.46961 86.65280
## 2455 89.12614 94.70750 102.81987 91.76680 92.14181
## 2456 95.24474 96.43636 91.96319 95.50927 92.87515
## 2457 91.27871 94.18004 88.08301 94.04152 93.55041
## 2458 97.62545 85.10674 98.92117 96.46720 73.59809
## 2459 97.73507 97.45069 95.48108 97.76746 93.63993
## 2460 99.01178 100.82659 101.38552 101.40897 97.82476
## 2461 101.52495 99.97309 101.71123 100.92643 99.61333
## 2462 102.59787 99.97401 102.02099 101.81424 102.97991
## 2463 110.07958 131.62010 104.38677 101.95037 106.69773
## 2464 103.35384 120.59903 108.52239 296.34216 111.22650
## 2465 120.63251 153.83333 108.26402 107.65160 102.97737
## 2466 106.52577 112.47647 106.66069 115.41369 127.27591
## 2467 125.93080 124.92916 173.66266 110.16479 114.64604
## 2468 117.21355 112.42533 138.67541 105.57382 108.67903
## 2469 109.40244 154.46581 111.40073 116.89807 122.07269
## 2470 109.29769 136.26939 108.26185 111.88715 116.04334
## 2471 124.26543 123.61111 121.02656 124.28462 124.28462
## 2472 164.56084 119.43852 99.41893 134.12285 120.96510
## 2473 117.25999 105.44614 162.66276 131.01205 132.05508
## 2474 128.56307 131.37534 125.86513 123.73880 132.97959
## 2475 117.45275 113.78304 125.95365 222.82480 135.53362
## 2476 98.00046 83.11619 81.88533 89.86462 89.20607
## 2477 79.54693 92.38744 86.24029 85.03989 85.65931
## 2478 76.52190 94.96854 97.69924 36.84186 58.63290
## 2479 93.75936 92.40642 90.41604 97.01757 87.60438
## 2480 64.77170 53.67943 61.37006 90.11586 80.48137
## 2481 93.82111 88.02860 96.56863 90.70701 90.58389
## 2482 80.22518 86.07052 87.94957 80.21429 98.04703
## 2483 93.41064 92.79609 82.13950 89.17940 93.54729
## 2484 98.06073 97.00814 99.02634 91.03641 93.70331
## 2485 100.75780 101.90641 100.69733 100.65492 102.01587
## 2486 102.59875 101.38662 99.38790 99.10218 100.04916
## 2487 101.30591 107.49766 104.51553 100.81512 101.30346
## 2488 105.03229 108.22561 108.71738 107.63745 102.92240
## 2489 110.08035 105.32322 108.37045 113.20401 105.77540
## 2490 102.75253 110.40044 120.76648 105.62608 110.05322
## 2491 109.37046 153.83333 129.64533 106.15231 106.69451
## 2492 110.54372 109.29644 104.83339 142.28863 114.84006
## 2493 124.92263 100.65657 109.29644 120.96729 103.20968
## 2494 110.36058 108.88442 131.40097 113.83465 254.13701
## 2495 114.59080 116.73749 146.06715 129.81371 128.06191
## 2496 106.62682 114.82032 503.42939 113.25841 118.46197
## 2497 99.41893 116.98047 134.17367 137.90285 149.28145
## 2498 115.18519 157.64839 134.67420 145.60938 105.44614
## 2499 155.49033 140.19862 156.68950 183.06954 127.50389
## 2500 570.80855 132.09207 134.29708 144.66941 124.21849
## 2501 82.18981 76.63699 86.84609 104.02357 84.86304
## 2502 82.16888 90.62159 80.21945 36.84186 67.95676
## 2503 69.07252 60.57741 75.04270 86.31604 98.00046
## 2504 63.88924 87.73624 64.77170 92.35943 90.41604
## 2505 80.48137 97.33569 80.66573 92.35943 82.88179
## 2506 95.58712 84.04155 81.23698 83.40701 79.76890
## 2507 85.13134 94.20244 86.60671 100.75978 86.07052
## 2526 77.84784 41.68769 82.18296 69.07252 89.62937
## 2527 58.63290 89.59827 88.97681 85.54361 54.23814
## 2528 80.76570 50.76591 54.23814 83.06365 85.54361
## 2529 89.16226 93.17554 102.63692 92.13118 92.43411
## 2530 70.47614 75.69345 51.42515 91.71909 70.11395
## 2531 69.81468 57.27377 88.08301 84.65185 95.75119
## 2532 91.04108 65.34469 95.35421 94.31004 93.60593
## 2533 88.96747 97.79130 101.81818 94.25877 81.36691
## 2534 96.03599 92.29034 100.57932 95.35065 98.06073
## 2535 99.74750 99.99093 99.36712 98.87226 101.74162
## 2536 101.43557 101.56744 99.90523 100.54435 96.69969
## 2537 101.30346 103.72201 106.00277 104.51553 100.21886
## 2538 261.53239 104.89362 109.57484 104.04441 102.47183
## 2539 106.04066 109.98478 115.51272 120.74558 111.22650
## 2540 102.72838 107.07546 107.68874 140.79911 107.93877
## 2541 108.16236 106.38032 105.33277 128.61022 380.88026
## 2542 108.18268 143.07937 112.92240 166.15643 101.13796
## 2543 108.25397 130.97942 151.70141 108.54908 127.05009
## 2544 136.42447 116.89807 105.95084 119.29898 133.08636
## 2545 132.79034 126.30030 155.76773 117.89025 116.42214
## 2546 105.52984 141.46732 173.21939 110.44112 129.18871
## 2547 108.31670 148.34604 118.31690 101.07600 119.71218
## 2548 127.97053 131.26142 108.93036 140.40671 125.59274
## 2549 121.31393 155.49033 210.70998 102.96003 144.42358
## 2550 222.82480 121.63895 149.34940 104.83165 165.89263
## 2601 104.95791 81.96664 86.93202 90.82572 104.44557
## 2602 80.42268 95.61993 88.96352 85.95653 88.98349
## 2603 82.63836 50.76591 41.91126 88.74066 54.29599
## 2604 70.34310 59.30769 92.56843 91.02956 89.23611
## 2605 92.43986 70.47614 62.53634 91.27376 81.00761
## 2606 86.65654 94.96528 94.95988 96.48148 93.41064
## 2607 87.94957 93.60593 85.60476 90.58389 86.07052
## 2608 82.36210 92.71862 96.35391 93.20396 87.76968
## 2609 90.75582 98.79779 93.37227 98.34969 98.92178
## 2610 100.44025 98.87331 104.30909 96.69969 100.27405
## 2611 100.92304 101.16487 98.49700 99.50621 112.35484
## 2612 102.93651 102.49331 106.70248 111.49880 101.30346
## 2613 117.06788 107.61418 117.06788 117.06788 110.36126
## 2614 107.70003 120.74558 97.50000 123.98612 104.97312
## 2615 112.13793 104.32544 109.37080 107.93877 116.68623
## 2616 118.16721 109.96946 107.03475 111.06992 105.12161
## 2617 115.02123 106.83120 104.92897 117.52555 126.23905
## 2618 110.22047 114.70431 109.29644 104.99605 125.27704
## 2619 123.11031 125.65309 108.13831 113.82010 129.81371
## 2620 136.42447 113.42653 111.40073 122.56407 117.89025
## 2621 161.35621 118.49745 119.45063 161.96111 145.99686
## 2622 111.12244 117.37784 148.34604 147.34885 199.02722
## 2623 113.56516 124.85976 118.29243 126.42492 182.98188
## 2624 155.93496 123.00804 179.23003 157.06224 136.72926
## 2625 146.56163 162.40041 121.63895 130.14879 160.44585
## 2626 92.38744 80.32086 57.40171 80.80704 82.63836
## 2627 97.69924 54.27991 76.78643 82.75869 84.18221
## 2628 89.86462 90.63433 76.45865 86.26102 85.65931
## 2629 91.64965 70.83933 80.66573 87.57756 93.31005
## 2630 63.37863 71.60730 92.69100 64.83246 91.61554
## 2631 95.90900 77.10697 94.74468 97.10315 72.27934
## 2632 94.94681 81.56341 99.01804 94.67286 87.88031
## 2633 94.69594 78.96031 94.25877 85.09039 91.04108
## 2634 92.48857 95.98072 86.84800 97.32737 97.73507
## 2635 98.86450 101.02647 100.83501 99.69388 101.14849
## 2651 80.89354 94.43840 86.84609 37.61926 84.99905
## 2652 84.35955 82.75869 56.17321 41.68769 80.07062
## 2653 60.45340 87.49543 52.63789 90.23312 86.69055
## 2654 91.70420 86.65280 91.27376 91.51116 91.64965
## 2655 91.72003 70.85132 90.96115 81.02063 77.60870
## 2656 80.73125 78.00297 69.81468 88.90840 95.50932
## 2657 90.58389 87.94957 88.27120 90.65794 99.94438
## 2658 95.58712 93.25658 93.48537 75.63255 96.46720
## 2659 92.63802 100.48347 101.52975 97.70301 84.80091
## 2660 97.73434 97.24605 97.54033 99.76842 103.99275
## 2661 100.83501 97.59288 100.48439 102.01587 101.38662
## 2662 102.62943 103.12208 143.70360 103.47246 111.49880
## 2663 104.32099 111.54449 104.09200 104.01260 111.19878
## 2664 105.00669 104.51977 124.85189 120.74558 97.88709
## 2665 110.34835 104.04960 109.05125 107.45477 108.26402
## 2666 133.86898 110.84710 133.41503 107.06727 107.07546
## 2667 422.40814 105.29585 225.66604 421.37245 106.04627
## 2668 118.71088 103.20968 104.83339 111.84610 105.34664
## 2669 122.18671 262.84895 116.02923 155.33333 123.12957
## 2670 104.77194 113.99420 149.17460 118.52359 120.42606
## 2671 108.07771 113.64010 119.21853 269.12711 114.82032
## 2672 137.72482 133.76551 111.73959 132.31067 118.92416
## 2673 323.44806 371.76418 116.51596 124.46827 131.11396
## 2674 246.70513 194.98985 170.04901 107.59809 132.34528
## 2675 142.24715 172.84924 129.97848 121.63895 161.00529
## 2676 81.13119 82.63836 90.23312 88.74066 60.67146
## 2677 85.03989 86.84609 89.07701 85.95653 77.84784
## 2678 84.15973 68.22153 79.72385 77.84784 86.31604
## 2679 61.05559 90.33507 65.97222 90.11586 93.33426
## 2680 94.46961 73.45181 83.29147 90.40701 76.00061
## 2681 90.82499 93.41064 73.79112 97.84749 99.01804
## 2682 95.52910 89.17940 81.44024 99.90496 93.88938
## 2683 94.21084 96.38773 86.12273 75.35918 84.40052
## 2684 95.81535 95.48108 81.86683 100.60156 94.67902
## 2685 100.64034 100.16114 101.19430 100.79741 100.93304
## 2686 102.42961 94.57160 97.32866 100.60284 99.09122
## 2687 103.96579 101.30346 102.58764 102.35425 108.96611
## 2688 105.96625 105.38233 103.69813 109.90148 102.11598
## 2689 102.74489 111.51407 104.74776 105.73638 297.32487
## 2690 105.34100 105.31331 105.45227 105.18351 157.31993
## 2691 106.40525 106.12299 107.45482 110.88988 112.43048
## 2692 108.45682 110.76400 111.19603 173.10494 112.96915
## 2693 117.21355 130.70175 116.48510 105.57382 143.07937
## 2694 106.51329 168.95985 111.26537 128.06191 134.27037
## 2695 103.24642 118.04719 115.66438 123.57135 123.12957
## 2696 159.69565 132.60389 117.26462 153.93285 101.37988
## 2697 138.74334 106.93167 122.96619 193.58160 318.79224
## 2698 122.30426 140.40671 159.22729 126.67551 121.62320
## 2699 132.78361 136.96747 744.58839 110.81273 120.74058
## 2700 124.63222 191.15108 150.13554 176.97539 130.71979
## 2726 70.92045 86.59111 104.02357 87.96539 87.49543
## 2727 88.95706 90.82572 60.67146 85.77597 81.40956
## 2728 64.04461 84.31220 87.68738 85.95653 87.24826
## 2729 91.73298 90.40701 87.79523 89.34008 92.64793
## 2730 72.67259 89.12743 73.45181 97.01757 94.78517
## 2731 57.28155 96.38773 90.70701 80.22518 95.12441
## 2732 98.92117 73.12163 97.06889 90.58389 93.51373
## 2733 69.57160 92.13474 94.20244 81.93717 87.76968
## 2734 101.52975 87.92436 100.60156 91.18015 83.11151
## 2735 100.56819 101.74416 100.24537 99.69388 100.31855
## 2736 99.38790 101.14849 97.54033 101.00012 98.36124
## 2737 102.79358 102.79358 104.02718 101.88398 102.23617
## 2738 104.26492 103.88052 107.75036 175.67105 107.56032
## 2739 102.31685 100.39438 104.63845 251.94731 140.53637
## 2740 113.14683 103.08793 111.06992 99.10803 107.72406
## 2741 142.48689 123.45897 103.37279 129.64533 117.88453
## 2742 100.58081 124.92916 124.92916 103.32460 125.63590
## 2743 422.40814 104.37449 111.63016 123.45281 226.14411
## 2744 111.26537 131.72309 155.18207 149.15188 263.32021
## 2745 105.04438 196.36738 132.04917 110.35033 146.06715
## 2746 106.62682 123.79254 123.54203 119.17671 101.02694
## 2747 111.12244 99.41893 114.28304 148.00592 281.06088
## 2748 118.14624 127.97053 134.35013 116.51596 126.98589
## 2749 161.42447 120.74058 120.97504 107.64352 136.71321
## 2750 173.22956 166.25036 103.71193 121.63895 176.97539
## 2751 97.69924 91.23674 87.53040 85.57782 37.61926
## 2752 86.31604 55.25180 85.58530 86.69055 76.38382
## 2753 77.05714 89.29480 85.57589 62.21343 69.44062
## 2754 87.88899 91.78296 86.00700 96.04494 75.74804
## 2755 90.71247 82.88179 91.50520 92.40642 86.77549
## 2756 85.60476 90.37662 92.67817 97.36059 65.23077
## 2757 96.46720 101.08586 94.18004 85.09039 87.22890
## 2758 88.80377 92.47394 75.51250 91.12778 90.65794
## 2759 98.21780 100.48347 98.03552 97.54853 99.50617
## 2760 105.57289 100.12346 100.54435 101.86862 102.32023
## 2761 94.57160 100.55374 105.57289 100.14188 100.51559
## 2762 106.00277 102.23617 106.58140 103.23319 106.82694
## 2763 105.71932 127.01718 99.85425 106.92872 105.88496
## 2764 106.15273 99.28725 115.07238 111.17116 130.47818
## 2765 103.64675 105.45227 113.19995 99.75145 105.31331
## 2766 105.18351 110.06902 107.79080 105.18351 123.31008
## 2767 109.70550 113.96746 166.01565 105.50042 172.75985
## 2768 105.72597 116.14203 128.89845 113.96746 101.12136
## 2769 118.04719 116.96535 252.84839 123.41478 108.88442
## 2770 109.04433 136.74200 227.19329 119.21580 112.60621
## 2771 106.35984 173.21939 209.70686 113.64010 119.25556
## 2772 121.04988 147.34885 144.04249 111.59231 225.69219
## 2773 101.32392 113.56516 131.01205 100.74375 126.98589
## 2774 168.40951 127.50389 140.18034 143.62978 136.71321
## 2775 222.64729 268.49932 132.13756 570.80855 268.49932
## 2826 91.12610 82.14150 70.22650 84.43896 41.62287
## 2827 89.67846 90.05968 91.95899 90.40317 86.95843
## 2828 94.43840 52.63789 82.18981 84.57300 88.03280
## 2829 66.86484 87.77418 90.14350 92.92963 91.02956
## 2830 97.01757 82.88179 94.78517 71.43483 90.20065
## 2831 94.21084 99.46346 93.89796 92.67817 87.88031
## 2832 91.86796 81.02273 86.07052 100.24863 94.25877
## 2833 100.24863 91.06227 76.36179 97.95033 90.19618
## 2834 93.37227 98.92178 97.70301 94.08903 100.77983
## 2835 97.78074 97.93814 93.82459 100.65492 99.61333
## 2836 101.05028 98.35841 97.59288 100.41002 98.37455
## 2837 103.33940 107.55417 99.86831 101.41742 103.03193
## 2838 114.83120 100.72350 104.26492 108.28152 109.83401
## 2839 114.77675 105.32322 103.35384 106.04066 104.55415
## 2840 119.82356 132.21463 105.60826 108.22291 104.58508
## 2841 99.95012 119.79731 105.34785 114.60203 157.19087
## 2842 125.88797 121.52583 130.86886 114.70431 117.21355
## 2843 107.05697 110.54372 115.02123 421.37245 108.32291
## 2844 110.95365 106.78113 104.77194 114.03509 230.35639
## 2845 481.19938 137.21213 116.18678 175.39744 117.34339
## 2846 126.04950 113.25841 126.65652 111.36527 269.12711
## 2847 115.23936 119.43852 108.31670 117.11838 165.47619
## 2848 131.27959 117.64437 111.01689 172.63492 152.11439
## 2849 131.41540 136.71321 127.89808 127.21345 107.59809
## 2850 142.56514 146.13979 132.79757 161.57427 123.55923
## 2901 70.89381 77.05714 87.39805 60.45340 85.15462
## 2902 70.22650 86.84609 87.49543 88.51961 82.63836
## 2903 88.71275 50.76591 76.45865 79.11190 80.42268
## 2904 75.69345 75.51253 96.01923 68.22087 64.21370
## 2905 92.56843 95.53165 85.41806 97.63935 85.01780
## 2906 95.24474 93.48537 76.94358 82.25437 88.11056
## 2907 93.82111 101.08586 99.94438 95.50932 81.62223
## 2908 99.94438 92.22074 79.76890 94.04152 92.93456
## 2909 97.29414 86.57403 96.28845 91.29703 86.84800
## 2910 99.09051 101.00012 103.18209 98.53717 102.72571
## 2911 97.31931 100.35603 98.87331 100.95731 97.34595
## 2912 104.44993 109.50161 101.41742 110.77857 109.08737
## 2913 103.08257 104.32099 104.26492 114.65787 110.41270
## 2914 296.34216 118.86091 105.58494 106.16497 108.52239
## 2915 102.88066 109.72657 100.48315 106.44959 108.42459
## 2916 117.47683 107.60344 108.02726 105.52295 106.00929
## 2917 104.37449 110.16206 126.23905 105.41808 105.39379
## 2918 135.82276 151.51333 142.28863 120.53017 113.70289
## 2919 109.89687 118.56621 106.95759 132.73572 125.82905
## 2920 113.56368 109.89687 113.99420 117.34339 131.46900
## 2921 121.91524 134.59250 110.76649 252.70767 109.00806
## 2922 110.95092 106.93167 117.37784 109.87654 127.98187
## 2923 118.14756 116.40820 124.57749 159.31912 144.79541
## 2924 132.97959 158.11991 127.89808 153.78922 254.51475
## 2925 144.93546 129.97848 142.24715 139.45128 137.19342
## 2926 55.25180 86.95843 49.78525 91.95899 79.62324
## 2927 83.45336 87.96539 58.84880 105.36680 79.51359
## 2928 97.69212 82.76681 41.91126 76.52190 82.38977
## 2929 92.15957 68.72902 94.96020 93.63593 82.80109
## 2930 86.77549 88.16347 91.87575 71.60730 93.63593
## 2951 89.62937 82.47773 84.15973 72.74734 79.47972
## 2952 62.21343 86.93202 90.63433 91.29758 50.76923
## 2953 84.99905 89.49587 82.18981 89.76592 104.44557
## 2954 78.03115 76.00061 93.06302 91.72003 91.43739
## 2955 64.21370 73.45181 94.70750 92.03351 70.83933
## 2976 85.03989 91.22254 49.78525 85.46386 87.06722
## 2977 87.49543 84.43896 104.44557 41.91126 49.97188
## 2978 41.68769 63.12598 97.69212 82.18981 62.21343
## 2979 97.01757 81.00761 102.63692 79.05238 93.80379
## 2980 102.81987 70.11395 91.61554 92.03351 68.71703
## 2981 92.38893 99.33319 97.97282 86.60671 97.62545
## 2982 93.45691 93.44060 91.72060 94.67286 85.84962
## 2983 95.01535 91.14090 83.14199 88.62501 96.59448
## 2984 97.65543 91.49750 97.51408 84.39734 91.49750
## 2985 98.93923 98.78481 98.03175 100.69733 99.61333
## 2986 100.26036 100.18869 99.04384 101.43779 101.40897
## 2987 107.11129 100.21886 102.00745 101.30591 100.21886
## 2988 103.59412 103.14673 104.97123 111.19878 119.89055
## 2989 116.83474 111.17116 106.04066 107.97734 115.07238
## 2990 105.34100 106.80057 104.96484 132.51117 117.36111
## 2991 103.01636 104.32544 119.79731 163.72257 129.12470
## 2992 113.60657 110.76400 116.14203 125.93080 172.70436
## 2993 125.88797 100.98039 112.22418 125.47516 103.85802
## 2994 136.74200 117.34339 105.73385 117.63440 118.41545
## 2995 136.42447 109.74483 168.95985 114.13036 110.35033
## 2996 139.28654 117.31404 123.61111 123.79254 116.17452
## 2997 119.03563 108.31670 117.72698 125.97572 125.53161
## 2998 147.79016 127.06840 121.62320 116.40820 112.60288
## 2999 131.37534 121.97617 127.21345 247.11846 143.36483
## 3000 139.14007 135.41667 187.66109 112.93395 107.76487
## 3001 84.16547 69.00621 87.00521 76.63699 76.52190
## 3002 91.22254 82.76681 88.97681 76.63699 75.67416
## 3003 86.30683 86.69055 67.95676 89.76592 70.22650
## 3004 75.65387 82.88179 92.14181 96.38065 75.91268
## 3005 92.03351 82.68579 95.82526 61.37006 89.52954
## 3026 64.04461 80.05830 64.04461 56.17321 79.54693
## 3027 76.63699 82.18296 41.62287 76.63699 87.06722
## 3028 84.98210 82.47773 68.38764 76.63699 94.43840
## 3029 85.50989 90.90331 86.00700 97.63935 65.48751
## 3030 89.18316 92.13118 68.71703 54.27027 85.38321
## 3051 86.95843 77.73452 84.15973 75.67416 83.04769
## 3052 74.07757 81.93143 87.96539 64.04461 84.16547
## 3053 89.07701 89.92114 86.85072 83.06365 60.03765
## 3054 92.69100 86.00700 91.27376 70.11395 79.07915
## 3055 95.82526 89.64036 94.38345 89.12614 53.96413
## 3056 88.90840 88.75352 95.58712 82.70288 82.82758
## 3057 82.74496 94.67286 91.86796 97.06502 93.44638
## 3058 87.88031 83.30883 98.04703 95.74852 92.03243
## 3059 91.37769 87.92436 96.73800 99.83715 99.76656
## 3060 99.67887 100.41002 98.99128 99.38790 96.34616
## 3061 98.87226 102.07249 100.42671 96.92005 101.71123
## 3062 104.69265 107.49766 106.43074 101.32439 107.41470
## 3063 105.03229 110.10368 110.69491 103.28263 116.61568
## 3064 251.94731 107.37269 97.88709 113.99777 105.97367
## 3065 111.06928 103.10562 112.47647 105.34078 124.49640
## 3066 108.59177 105.81129 122.66667 123.45897 114.70735
## 3067 131.96356 111.71435 117.52555 156.06017 107.12818
## 3068 106.70624 108.18268 102.88173 108.32291 135.10290
## 3069 110.26906 109.78836 121.15220 110.36058 109.89687
## 3070 108.88442 148.34249 116.75754 131.13540 130.64683
## 3071 114.83612 113.64695 145.99686 159.69565 117.31404
## 3072 133.76551 125.83242 133.41070 125.00909 106.93167
## 3073 112.60288 127.97053 145.29898 119.08348 121.62320
## 3074 102.60494 161.42447 120.93599 111.04844 120.74058
## 3075 700.68873 121.63895 142.56514 105.26538 173.22956
## 3126 81.93143 72.67589 91.32519 104.95791 80.76570
## 3127 78.65690 86.72466 87.11384 67.53835 57.40171
## 3128 79.47932 88.51961 82.75869 68.38764 83.45336
## 3129 88.16347 82.88179 97.63935 91.61554 90.11586
## 3130 91.71909 90.40701 79.07915 68.72902 91.87575
## 3131 91.96319 99.46346 65.86113 75.35918 99.90496
## 3132 94.80933 57.28155 90.73737 83.40701 81.93717
## 3133 73.12163 89.08083 95.35421 84.84667 94.24815
## 3134 86.43389 97.88507 97.91838 100.81566 84.39734
## 3135 97.22840 98.49700 100.61728 101.43779 102.72571
## 3136 103.49682 100.57566 87.28822 100.05478 97.78074
## 3137 102.94154 104.24491 102.00745 102.35425 109.50161
## 3138 128.88305 105.03229 107.56032 105.96625 103.59412
## 3139 109.87936 102.74489 105.74991 106.48477 106.62398
## 3140 112.74811 110.59961 106.40525 128.61022 111.65145
## 3141 122.20380 105.18351 103.10562 106.44959 112.77835
## 3142 113.08183 108.44376 104.92897 116.48510 105.36117
## 3143 156.88157 112.63187 125.93080 106.47021 110.77789
## 3144 116.18678 105.95084 169.24985 116.73749 116.96535
## 3145 116.42214 120.42606 125.65309 105.83593 131.58483
## 3146 136.83834 123.80165 112.72984 118.26464 161.96111
## 3147 120.96510 164.56084 281.06088 149.28145 99.41893
## 3148 641.17255 106.96507 152.44157 126.30539 148.98291
## 3149 120.93599 121.97617 158.11991 110.81273 132.44953
## 3150 204.79928 142.24827 191.15108 139.59004 132.28471
## 3151 104.02357 77.28096 82.47773 74.82542 84.15973
## 3152 72.74734 39.70148 64.04461 104.02357 60.65947
## 3153 81.40956 66.56782 89.86462 80.80704 87.19251
## 3154 92.14181 89.23611 92.69100 91.46595 90.71247
## 3155 94.96020 79.39866 102.81987 84.62964 85.50989
## 3156 81.68889 100.75978 86.07052 92.71848 83.82353
## 3157 101.30804 88.02860 86.59472 97.62545 81.34965
## 3176 85.35190 45.05271 83.45336 87.06722 87.00521
## 3177 79.54693 84.43896 76.38382 84.15973 77.73452
## 3178 90.62159 66.61349 90.71575 90.40317 89.62937
## 3179 88.67350 85.84441 94.96576 102.63692 88.66636
## 3180 92.72349 86.45978 77.60870 91.73298 91.02956
## 3181 92.71848 95.24474 83.14199 70.48157 90.42765
## 3182 94.04443 95.40466 96.56863 72.84820 65.34469
## 3201 91.22254 88.97681 86.26102 87.12146 88.51961
## 3202 90.40317 70.89381 89.59827 79.54693 74.82542
## 3203 84.18221 89.20607 94.96854 98.00046 77.84784
## 3204 89.90957 81.02063 90.33507 90.74173 89.23611
## 3205 87.74308 93.80144 91.62935 93.75936 53.67943
## 3206 97.18258 94.20244 89.17940 99.33319 83.14199
## 3207 97.84749 101.77485 93.82111 79.43407 76.84017
## 3208 93.30245 93.44060 88.66208 91.96508 79.41074
## 3209 95.81535 100.75586 98.92178 101.52975 89.61493
## 3210 97.82476 99.87192 100.79741 98.54870 99.04384
## 3211 99.62495 102.70549 102.46154 98.35841 101.25268
## 3212 101.24287 100.81512 102.76001 112.94194 101.81424
## 3213 105.88496 261.53239 108.33239 104.25807 114.83120
## 3214 104.90277 107.70003 108.52239 110.83466 115.51272
## 3215 128.61022 106.86974 110.52339 129.31746 143.88871
## 3216 151.36925 127.27591 100.70149 143.88871 109.64912
## 3217 105.33872 101.12136 141.53477 125.63590 120.90543
## 3218 111.05910 106.28720 103.64332 103.32460 138.67541
## 3219 115.13316 169.43669 113.83465 116.77544 112.23263
## 3220 481.19938 117.59139 138.90371 115.66438 118.15310
## 3221 111.94593 132.60389 113.64010 110.19345 121.91524
## 3222 300.11344 551.74786 160.99520 148.00592 193.74717
## 3223 126.42492 146.12892 172.63492 150.27685 115.76302
## 3224 155.93496 136.71321 143.36483 127.16439 143.38537
## 3225 1189.82588 139.14007 1196.02892 267.05128 143.17600
## 3276 80.88184 58.63290 62.27695 66.56782 85.77597
## 3277 63.88756 85.66890 84.05367 84.15973 80.89354
## 3278 87.51037 87.39805 80.88184 80.05830 75.67416
## 3279 91.72003 64.61268 88.88347 59.41362 87.78058
## 3280 79.00953 91.35638 91.73298 88.88347 95.77954
## 3281 88.90840 81.23698 83.40701 95.58712 96.90043
## 3282 93.60593 91.81731 74.55635 83.82353 96.90043
## 3283 99.01804 89.81119 75.35918 92.93456 95.52910
## 3284 95.48108 95.35065 96.70003 83.11151 97.94876
## 3285 100.82826 105.57289 97.43528 100.50736 101.38662
## 3286 100.42929 98.93923 97.08944 100.34017 100.38785
## 3287 102.00745 103.96579 102.35425 106.03844 101.08255
## 3288 104.32099 105.45455 106.11781 106.30195 110.07958
## 3289 297.32487 101.44664 120.59903 101.96257 100.39438
## 3290 105.52295 109.91606 339.67506 114.76498 103.64675
## 3291 111.55464 118.32347 118.92588 105.81129 157.31993
## 3292 103.32460 113.70289 172.75985 125.54172 120.81843
## 3293 115.08633 108.32291 114.84006 116.24810 108.64252
## 3294 119.59454 101.10717 111.90085 110.33369 132.04917
## 3295 227.19329 134.40526 131.40097 132.73572 109.39168
## 3296 121.33721 117.31404 116.81541 145.10697 115.01951
## 3297 160.98321 112.23078 168.75973 120.01017 125.97572
## 3298 134.67420 131.11396 233.93590 157.64839 159.31912
## 3299 448.92817 210.70998 144.57935 136.37268 136.11654
## 3300 131.01274 121.63895 104.07086 1189.82588 142.56514
## 3351 60.03765 56.17321 72.67589 70.22650 85.21347
## 3352 85.21347 84.35955 96.08898 84.99905 79.72385
## 3353 85.57782 83.06365 66.62354 97.73589 88.03280
## 3354 91.76680 86.46140 67.96218 86.40904 70.11395
## 3355 59.30769 91.46595 90.40701 91.50520 93.63593
## 3356 80.22518 101.08586 92.31872 92.71848 91.86796
## 3357 91.96508 88.75352 97.36059 97.61660 92.87873
## 3358 91.72060 98.34261 98.73440 99.80850 95.01535
## 3359 99.37149 81.86683 97.45069 94.67902 98.72624
## 3360 100.24116 100.65492 101.49803 101.78553 101.78553
## 3361 100.03001 99.73635 102.33343 99.55544 101.43779
## 3362 101.08255 104.18450 101.08255 104.02852 106.37830
## 3363 137.64899 114.50839 108.28152 101.63512 105.03229
## 3364 110.83466 138.18694 118.86091 106.15273 97.50000
## 3365 129.79219 109.40839 109.72657 107.45712 98.91687
## 3366 117.59082 100.67826 103.10562 122.52881 106.01707
## 3367 107.69149 111.88506 108.01316 109.39410 106.20255
## 3368 144.16979 111.88506 114.96845 106.47021 128.89845
## 3369 178.26917 119.21580 128.64430 119.29898 105.73385
## 3370 138.90371 109.78836 149.71884 119.29898 105.61598
## 3371 111.94593 146.31098 116.17452 119.65444 139.51296
## 3372 149.56982 193.58160 168.75973 137.90285 281.25637
## 3373 146.18996 472.19814 172.63492 150.27685 124.85976
## 3374 448.92817 131.41540 132.44953 111.04844 136.37268
## 3375 168.55762 204.79928 161.77992 204.79928 146.13979
## 3426 86.83467 85.10968 89.20607 56.17321 89.59827
## 3427 39.64751 36.84186 87.24826 66.56782 85.58530
## 3428 75.04270 88.03280 82.47773 90.71575 87.24826
## 3429 63.14192 70.11395 89.34008 70.85132 84.59334
## 3430 64.77170 75.69345 64.21370 89.18316 85.38321
## 3431 95.58712 73.12163 99.33319 90.45155 95.50932
## 3432 86.43748 95.08598 90.82499 96.46720 75.81067
## 3433 92.21051 90.58389 93.88938 81.34965 93.45691
## 3434 92.93899 91.38998 98.67298 97.53696 88.01447
## 3435 101.78696 99.11660 93.82459 101.24048 105.05805
## 3436 101.27295 100.31597 101.43557 103.49682 93.82459
## 3437 164.65078 103.47246 107.49766 107.55417 101.82865
## 3438 103.59412 104.32099 103.46585 110.07958 105.86541
## 3439 102.31685 104.85046 251.21835 115.07238 146.43261
## 3440 113.13935 103.10562 105.18351 106.40525 122.76389
## 3441 104.39012 106.66069 112.55829 109.80112 107.45712
## 3442 115.48170 115.48170 138.15359 173.10494 108.32291
## 3443 114.85910 183.38993 173.10494 126.23905 105.41808
## 3444 198.77153 185.25808 109.40244 146.06715 117.34339
## 3445 109.79184 119.29898 128.64430 127.92063 138.80017
## 3446 109.73607 119.31776 209.26474 101.43678 123.79254
## 3447 111.53629 118.87545 133.41070 106.35625 160.98321
## 3448 146.18996 127.06840 164.06744 129.88004 205.17426
## 3449 140.11829 131.94135 157.06224 127.50389 131.94135
## 3450 161.00529 112.93395 699.04638 130.71979 132.79757
## 3501 81.69164 55.25180 91.23674 68.38764 41.62287
## 3502 48.57916 93.66601 94.96854 77.05714 59.27230
## 3503 96.08898 68.86478 54.27991 85.58530 85.77597
## 3504 91.64965 68.71703 87.60438 86.00700 92.43411
## 3505 95.82526 97.63935 53.96413 88.67350 75.74804
## 3506 76.71611 101.81818 86.59472 88.75326 94.01651
## 3507 68.03409 94.31004 94.31041 84.84667 93.20396
## 3508 92.93456 96.84995 98.45387 89.08083 90.70701
## 3509 99.54432 96.30855 97.29414 99.02634 96.20178
## 3510 97.43528 100.38785 97.43528 99.87192 101.52984
## 3511 98.71030 98.98538 100.34017 98.98863 100.35603
## 3512 102.00745 110.77857 104.44993 104.28966 107.63287
## 3513 118.19123 104.99403 103.88052 100.72350 107.75036
## 3514 109.30307 122.62570 108.05007 105.77540 104.55229
## 3515 107.65160 108.46440 109.72657 327.17640 105.34100
## 3516 109.40672 120.33720 108.04976 118.32347 118.32347
## 3517 422.40814 135.17986 172.75985 135.82276 151.70141
## 3518 141.54676 104.95144 106.47021 141.54676 113.22591
## 3519 100.69865 128.06191 129.13351 110.26906 105.04438
## 3520 105.95084 116.18678 110.33821 482.34621 461.00933
## 3521 253.72386 173.21939 110.76649 136.66000 116.17452
## 3522 123.85819 118.31005 136.02601 168.75973 148.34604
## 3523 104.67082 152.11439 157.85270 126.42492 116.40820
## 3524 179.23003 448.92817 122.70961 179.23003 103.33840
## 3525 138.78205 130.14879 123.69247 187.48733 123.66954
## 3526 48.57916 81.13119 96.08898 82.18981 98.00046
## 3527 87.12146 54.23814 87.68738 89.86462 91.32519
## 3528 103.13131 54.07719 86.59111 81.13119 62.27695
## 3529 92.52781 92.43986 91.64965 68.22087 92.56843
## 3530 92.69100 92.35943 68.71703 72.67259 81.19130
## 3531 97.95033 81.02273 91.06227 88.62501 81.23698
## 3547 135.68449 121.11605 99.75966 114.09905 147.34885
## 3548 123.15943 147.99678 119.61790 121.63738 147.80102
## 3549 194.26937 155.69308 155.62688 120.78285 447.24761
## 3550 150.61485 117.40587 105.26538 135.41667 137.63779
## 3551 104.02357 80.21945 59.27230 82.14150 84.43896
## 3552 79.11190 86.84609 89.67846 59.27230 87.06722
## 3553 76.63699 79.62324 88.51961 85.57782 81.40956
## 3554 87.57756 75.91268 63.88924 91.71909 82.88179
## 3555 78.03115 64.61268 94.78517 75.74804 70.34310
## 3556 98.94377 96.59448 92.87515 82.82758 94.28239
## 3557 77.22249 88.96747 88.02860 75.35918 79.08784
## 3558 94.74468 91.29655 90.65794 94.69594 93.30245
## 3559 97.76746 91.03641 93.53041 97.76746 89.81541
## 3560 97.32866 101.86862 100.44025 100.54435 97.24605
## 3561 101.14849 101.24048 97.22840 103.82921 97.22840
## 3562 101.19407 116.21552 103.53782 106.43074 104.30985
## 3563 117.06788 110.91829 107.41162 106.69830 103.14673
## 3564 251.94731 122.62570 101.23275 114.26822 130.47818
## 3565 107.68874 100.70149 105.34100 108.02726 112.72938
## 3566 114.76498 108.09263 133.20394 327.17640 129.12470
## 3567 111.78234 128.89845 104.66835 103.85802 100.98039
## 3568 108.25397 107.61294 113.22591 118.77751 165.32051
## 3569 131.46900 115.95317 481.19938 126.30030 101.10717
## 3570 120.45371 134.27037 122.18671 108.83104 118.15310
## 3571 281.71217 114.83612 113.64010 121.11444 139.84188
## 3572 118.87545 143.70353 125.97572 101.07600 112.81117
## 3573 127.97053 470.08200 118.14624 124.85976 130.19223
## 3574 125.83247 128.56307 123.01758 122.70613 102.89562
## 3575 125.71272 128.95963 124.23769 150.13554 124.45213
## 3576 54.07719 86.69055 85.57782 80.07062 85.66890
## 3577 84.98210 97.99331 84.18221 90.05968 79.54693
## 3578 77.28096 82.37310 79.54693 91.12610 39.70148
## 3579 82.88179 91.62935 75.69345 61.05559 62.68866
## 3580 70.42076 93.75936 89.12743 81.19130 86.73150
## 3581 94.94681 101.49594 101.77485 72.84820 82.70288
## 3582 84.11676 89.17940 90.82499 97.62545 96.56863
## 3583 72.44891 96.43636 95.68366 82.13950 85.84962
## 3584 90.75582 95.99433 95.98072 91.37769 97.45069
## 3585 99.09122 100.52245 97.31931 99.00218 100.62028
## 3586 101.93226 99.64087 99.83780 100.38785 102.07249
## 3587 106.37830 102.12298 105.57143 101.34497 103.27481
## 3588 116.41026 103.88052 114.83120 119.67320 115.39095
## 3589 100.88040 104.59839 106.56318 105.77540 106.04066
## 3590 106.40525 338.64140 100.30303 128.61022 120.63251
## 3591 121.34056 129.31746 109.91606 99.75145 150.83319
## 3592 118.01427 99.10555 138.67541 126.56843 172.75985
## 3593 130.70175 151.70141 98.76543 118.77751 116.24810
## 3594 111.88715 110.82173 154.46581 183.03809 113.82010
## 3595 117.52653 112.66447 116.84813 105.68665 107.97407
## 3596 114.46560 132.60389 139.28654 107.85640 159.69565
## 3597 320.44206 281.06088 140.12399 137.72482 114.28304
## 3598 126.48677 131.01205 108.83590 128.50156 134.67420
## 3599 122.70613 126.82551 131.41540 127.42447 194.98985
## 3600 125.61016 132.77700 146.13979 160.44585 130.17448
## 3651 89.35444 89.49587 85.58530 76.45865 88.51961
## 3652 60.57741 87.20973 66.58774 89.76592 85.57782
## 3653 103.13131 87.39805 88.74066 67.95676 88.71275
## 3654 79.00953 91.76680 75.65387 84.59334 64.83246
## 3655 92.15957 91.78669 81.02063 92.15957 81.00761
## 3656 92.99346 65.34469 93.55041 72.27934 91.96319
## 3657 81.23698 94.24815 89.16429 84.34966 81.56341
## 3658 97.84749 65.72650 93.88938 97.69841 93.88938
## 3659 99.54432 100.77983 95.81535 96.03599 92.48857
## 3660 102.01587 95.79865 99.98555 99.63866 101.95012
## 3661 95.71676 101.71123 101.43557 97.34595 101.25268
## 3662 102.49331 104.55716 105.57143 103.27481 102.93651
## 3663 116.41026 105.98155 104.89362 106.16602 107.63745
## 3664 105.32322 107.70003 105.62299 106.29270 106.15273
## 3665 108.80848 150.83319 111.82715 99.10803 113.14683
## 3666 122.66667 112.47647 105.18351 112.95271 112.30907
## 3667 105.36117 125.54172 105.41808 183.38993 125.38679
## 3668 108.32291 173.80710 225.66604 113.17658 128.12313
## 3669 183.98454 106.51329 105.68665 182.62523 136.34087
## 3670 105.68832 125.82905 131.13540 116.65831 137.21213
## 3671 111.94593 123.79254 112.70218 110.19345 112.72984
## 3672 147.34885 106.40294 113.53051 106.35625 125.97572
## 3673 146.18996 140.05752 100.32828 124.57749 126.67551
## 3674 130.86005 181.00000 122.18326 166.00129 118.87561
## 3675 121.42631 161.77992 125.95365 121.63895 113.78304
## 3726 87.19251 86.53435 84.35955 77.28096 66.62354
## 3727 81.93143 93.66601 55.46753 86.31604 84.16547
## 3728 86.50740 89.45997 85.65931 88.51961 41.68769
## 3729 70.47614 89.34008 91.35638 90.96115 51.42515
## 3730 93.80379 75.69345 91.27376 86.40904 97.33569
## 3731 88.62501 91.96319 94.80933 77.71553 100.24863
## 3732 99.46346 91.14090 83.40701 101.49594 85.84962
## 3733 84.84667 97.59867 91.72060 86.43748 94.04443
## 3734 97.55989 97.76746 90.75582 98.70271 97.25576
## 3735 100.54435 100.54435 100.03001 99.10218 101.26409
## 3736 98.98538 101.24048 101.86862 100.65492 101.53983
## 3737 102.00329 102.28962 116.21552 103.03193 106.58140
## 3738 108.28152 115.39095 110.32772 116.61568 98.06457
## 3739 113.99777 101.23275 111.51407 120.59903 99.28725
## 3740 107.06727 116.68623 110.06902 105.34078 117.41760
## 3741 380.88026 106.40525 140.96680 108.26402 109.96946
## 3742 105.41808 108.93434 130.70175 114.65557 110.76400
## 3743 117.50872 134.81898 121.52583 103.49693 108.18084
## 3744 104.29527 133.08636 108.93042 481.19938 108.13831
## 3745 104.29527 123.57135 107.93025 128.06191 105.68832
## 3746 188.53177 269.45487 140.58533 131.81465 106.35984
## 3747 108.58455 108.58455 126.41812 111.05169 119.47703
## 3748 127.06840 323.38504 470.08200 159.22729 171.68656
## 3749 162.56055 127.42447 144.23375 183.04556 132.01165
## 3750 132.83794 161.77992 130.14879 569.08911 139.45128
## 3801 87.79150 85.95653 55.25180 91.12610 87.53040
## 3802 68.86478 90.82572 85.57782 87.90980 88.74066
## 3803 68.22153 87.22372 77.26177 91.29758 72.74734
## 3804 65.97222 102.81987 91.46595 86.65280 93.06302
## 3805 89.12614 87.77418 102.63692 87.60438 64.61268
## 3806 57.27377 67.45901 78.89058 69.57160 81.36691
## 3807 92.13474 98.30169 99.84694 84.04155 93.09747
## 3808 78.00297 94.04152 96.35980 78.00297 83.30883
## 3809 91.25397 103.22245 96.31460 97.65543 98.70271
## 3810 97.35676 101.63367 100.14407 99.10475 100.63553
## 3811 99.55544 99.73118 103.18209 102.59875 99.81995
## 3812 102.76001 110.47760 101.32439 104.10156 103.72201
## 3813 101.95037 108.33239 104.04441 103.46585 104.13530
## 3814 101.96257 115.59832 141.25711 106.23389 97.88709
## 3815 105.15247 109.72657 109.72657 104.58508 152.35816
## 3816 107.03475 132.29487 105.52295 106.19343 102.88066
## 3817 108.18084 107.13503 113.17658 108.38241 107.24831
## 3818 132.25443 109.70550 158.47743 105.34664 102.72149
## 3819 118.52359 134.27037 136.68277 116.75754 116.77544
## 3820 122.18671 249.03521 148.34249 101.47904 120.42606
## 3821 110.76649 105.91190 269.12711 114.46560 121.91524
## 3822 298.90043 149.56982 125.66132 281.06088 112.96036
## 3823 323.38504 159.31912 229.18128 118.14756 121.45352
## 3824 136.71321 166.21715 215.03986 215.03986 446.58161
## 3825 130.54977 135.82040 324.26805 222.82480 130.55226
## 3876 50.76923 82.18296 54.23814 39.64751 79.88844
## 3877 86.83467 95.66380 62.21343 89.29480 87.11384
## 3878 83.45336 79.68953 70.89381 84.31220 55.25180
## 3879 95.82526 53.96413 90.41604 91.46595 86.73150
## 3880 102.22222 87.78058 81.19130 90.33507 68.72902
## 3881 81.62803 88.96609 91.62297 98.34261 79.43407
## 3882 94.20589 92.13474 97.99241 92.22074 88.62501
## 3883 94.37053 82.82758 96.38773 72.44891 67.80351
## 3884 84.39734 95.35065 97.00814 91.49750 97.54853
## 3885 98.03175 101.14233 105.05805 101.52984 99.65537
## 3886 99.98555 97.08944 97.24605 100.16114 101.82777
## 3887 106.43074 106.58140 101.03606 101.30591 107.41470
## 3888 104.03054 106.30195 103.69813 104.20592 101.95037
## 3889 106.16497 130.47818 106.48477 104.82608 104.54255
## 3890 109.37080 102.41684 122.66667 107.45712 151.36925
## 3891 151.36925 110.88988 123.31008 117.87121 105.45227
## 3892 120.90543 105.57382 104.92897 103.49693 125.93080
## 3893 101.05646 117.21355 116.88010 100.98039 116.46127
## 3894 155.76773 110.11771 106.32849 114.33877 108.91640
## 3895 110.11613 120.19411 104.77194 114.03509 118.52359
## 3896 173.21939 115.59228 111.00264 117.31404 139.51296
## 3897 148.34604 137.90285 122.96619 108.27347 121.04988
## 3898 117.25999 117.64437 131.01205 323.38504 259.83518
## 3899 102.60494 155.60288 122.70961 169.95212 214.86895
## 3900 143.72395 107.76487 159.00152 188.82540 132.09207
## 3901 85.54361 57.40171 80.80704 84.98210 74.49210
## 3902 76.81953 86.17021 70.22650 41.68769 90.71575
## 3903 92.01060 79.88844 80.32086 66.56782 97.73589
## 3904 53.45668 73.29890 89.12614 71.60730 85.95374
## 3905 94.78517 85.38321 91.61554 76.93336 87.57756
## 3906 91.96319 68.83437 69.57160 96.84995 100.75978
## 3926 88.96352 76.43678 81.96664 82.75869 50.76923
## 3927 76.78643 83.00664 87.80122 60.45340 84.16547
## 3928 82.16888 88.96352 86.17021 88.95706 49.78525
## 3929 59.30769 82.68579 97.33569 102.63692 51.50991
## 3930 86.88603 92.56843 91.02956 85.50989 75.69345
## 3931 98.45387 79.41074 92.79609 91.81731 87.76968
## 3951 68.22153 85.10968 81.40956 82.47773 76.78643
## 3952 69.07252 84.18221 89.29480 76.52190 87.19251
## 3953 96.08898 86.59111 76.81953 85.46386 70.92045
## 3954 90.40701 92.64793 88.15822 90.48983 53.45668
## 3955 79.91193 91.35638 92.56843 80.57239 75.69345
## 3956 95.03849 90.19618 65.72650 94.74468 92.71848
## 3957 81.19623 98.94377 96.47162 96.81781 91.29655
## 3958 94.16257 93.49512 70.74005 94.04443 87.19216
## 3959 96.24320 97.54853 100.28604 102.69306 93.37227
## 3960 101.82777 99.50621 99.89300 99.69357 100.90765
## 3961 101.30359 99.63866 100.89656 99.09122 100.60284
## 3962 111.52278 104.18608 112.94194 102.48483 103.12208
## 3963 110.32772 111.19878 103.14673 102.47183 114.65787
## 3964 104.51977 116.59730 116.14286 105.62299 107.23509
## 3965 108.04976 119.50628 124.48441 140.79911 111.10829
## 3966 108.14554 133.86898 122.00069 106.40525 116.13150
## 3967 116.48510 226.14411 113.17658 109.17025 110.22047
## 3968 118.71088 113.70289 107.24831 107.24831 114.57763
## 3969 109.89687 99.95210 132.44916 110.36058 106.28093
## 3970 105.55215 201.13498 130.64683 134.23700 130.64683
## 3971 123.79254 116.17452 113.64695 140.58533 131.81465
## 3972 127.09092 117.11838 108.58455 121.26949 147.54034
## 3973 145.60938 100.97366 164.06744 205.35109 119.61790
## 3974 131.58996 298.66443 744.58839 162.56055 111.04844
## 3975 568.61008 115.98005 125.24982 125.95365 114.62269
## 3976 87.68738 82.18296 68.86478 86.72466 88.96352
## 3977 74.49210 103.13131 54.29599 76.43678 84.99905
## 4001 41.91126 86.50740 76.81953 79.68953 86.93202
## 4002 50.76591 83.45336 88.95706 58.63290 37.61926
## 4026 54.23814 90.71575 86.31604 87.24826 97.43460
## 4027 87.33405 86.59111 85.35190 87.53040 91.12610
## 4028 85.57589 81.93143 85.57589 79.54693 82.18981
## 4029 95.82526 71.43483 79.00953 75.51253 88.67350
## 4030 91.65131 82.80109 53.96413 97.33569 92.69100
## 4031 95.06454 89.08903 98.94377 89.40975 85.98439
## 4032 95.36544 90.38887 73.79112 88.39372 78.00297
## 4033 93.88938 80.73125 87.94957 95.75119 88.75876
## 4034 98.59710 95.98072 93.70331 98.59710 94.88037
## 4035 99.87192 99.69357 100.32598 101.19430 99.55544
## 4036 98.98863 104.09098 101.27295 100.64034 100.18869
## 4037 104.54930 104.99937 105.05959 102.00329 109.50161
## 4038 104.13554 109.83401 101.85783 114.83120 104.97123
## 4039 107.37269 97.50000 115.34707 297.32487 105.58494
## 4040 102.84663 106.15231 110.94952 119.60328 119.82356
## 4041 109.85664 112.47647 119.50628 111.06928 107.88385
## 4042 108.62230 108.18084 173.80710 144.16979 108.00357
## 4043 225.66604 174.29516 111.78234 135.17986 226.14411
## 4044 263.32021 118.04719 111.97003 106.28093 117.52653
## 4045 134.44921 198.77153 115.99298 102.82229 116.02923
## 4046 161.35621 113.25841 281.71217 129.23151 159.69565
## 4047 112.69286 148.08932 107.26161 147.54034 147.54034
## 4048 126.15987 121.75368 124.57749 133.39248 116.51596
## 4049 132.34528 113.08281 123.77131 194.26937 125.83247
## 4050 219.35145 267.49050 222.64729 131.01274 123.66954
## 4076 95.61993 41.91126 66.58774 97.43460 86.53435
## 4077 77.28096 58.84880 48.49429 85.57589 79.51359
## 4078 90.63433 36.84186 85.58530 88.97681 67.53835
## 4079 79.00953 86.77549 86.88603 85.50989 89.79684
## 4080 90.33507 90.71247 92.35943 91.46595 86.00700
## 4081 89.81119 98.34261 85.09039 91.04108 97.04058
## 4082 89.08903 100.24863 92.67817 82.13950 94.74468
## 4083 83.14199 97.61660 98.37955 94.49291 89.81119
## 4084 93.63993 94.97735 97.32737 98.70271 97.32737
## 4085 100.11056 103.84216 100.34017 102.07249 98.87331
## 4086 100.75780 100.27405 101.31817 97.49637 100.14811
## 4087 104.98080 102.74791 102.27497 102.79358 110.47760
## 4088 131.62010 105.86541 109.82740 110.10368 98.87984
## 4089 108.37045 111.51407 138.18694 103.29765 108.25918
## 4090 108.04976 133.86898 108.36584 108.36584 157.31993
## 4091 162.87960 100.67826 106.72359 112.74811 113.36324
## 4092 117.50872 126.23905 111.19603 131.98691 114.42351
## 4093 163.02863 104.69508 109.39410 104.83339 128.89845
## 4094 111.98145 163.49438 120.40397 101.47904 110.38324
## 4095 254.13701 134.27037 136.26939 101.47904 262.84895
## 4096 119.04881 281.71217 121.91524 114.83612 115.73388
## 4097 125.18827 117.72698 139.94499 114.09905 225.69219
## 4098 131.01205 122.30426 126.48677 134.67420 121.75368
## 4099 123.00804 122.70613 144.42358 298.66443 183.06954
## 4100 124.62081 143.72395 130.54977 161.22399 267.05128
## 4101 87.90980 84.31220 97.43460 87.26977 77.05714
## 4102 69.44062 66.58774 45.05271 82.76681 90.23312
## 4103 85.10968 55.25180 84.18221 77.81180 90.62159
## 4104 96.04494 87.57756 79.07915 92.92963 90.74173
## 4105 94.70750 72.67259 96.38065 89.90957 71.60730
## 4106 90.45155 85.28735 91.80362 83.30883 90.85420
## 4107 82.13950 90.58389 98.37955 94.18004 87.31443
## 4108 84.65185 95.50932 80.21429 84.84667 84.65185
## 4109 97.48328 97.25576 100.48347 97.29414 98.06073
## 4110 98.27656 102.46154 100.21679 99.50621 100.56819
## 4111 100.66260 102.42961 100.14811 97.15385 99.64087
## 4112 103.28508 101.33319 101.24287 120.11251 101.41742
## 4113 132.29157 98.87984 104.01260 107.75036 101.85783
## 4114 123.98612 104.63845 104.74776 114.26822 120.16029
## 4115 105.52295 114.70735 148.87401 109.40672 112.74811
## 4116 157.19087 122.20380 105.52295 133.20394 153.83333
## 4117 113.94046 207.17797 130.97942 109.81380 117.21355
## 4118 126.63332 123.62344 108.18268 107.61294 126.63332
## 4119 109.04433 110.38324 108.59125 117.34339 120.19411
## 4120 178.26917 110.15822 131.72309 107.54896 102.39567
## 4121 102.11599 119.31776 160.58730 140.58533 123.54203
## 4122 193.74717 100.34248 116.07684 550.46210 111.73959
## 4123 131.11396 130.19223 147.80102 148.98291 131.01205
## 4124 298.66443 121.31393 118.87561 131.58996 127.16439
## 4125 131.01274 135.41667 117.45275 1196.02892 187.48733
## 4176 74.10656 57.40171 91.22254 39.64751 77.28096
## 4177 63.88756 97.73589 85.77597 77.28096 90.05968
## 4178 88.03280 92.38744 74.07757 60.45340 60.65947
## 4179 95.82526 78.03115 71.60730 94.96576 70.85132
## 4180 96.08898 82.68579 63.37863 89.79684 82.80109
## 4181 92.47394 100.75978 96.99243 92.87873 83.30883
## 4182 57.28155 81.34965 90.42765 73.31933 86.65654
## 4183 96.56863 83.14199 99.84694 88.80377 88.90840
## 4184 92.99363 81.86683 101.11111 92.63802 66.79041
## 4185 101.84448 101.05028 100.51559 96.69969 98.53717
## 4186 98.37455 101.82777 99.69357 100.89656 99.10218
## 4187 107.10395 104.69265 105.57143 116.80319 108.96611
## 4188 105.88496 98.06457 105.96625 128.88305 103.08257
## 4189 120.74558 106.44943 114.77675 106.04066 123.98612
## 4190 124.49640 109.40839 113.19995 107.73630 119.29708
## 4191 122.20380 152.35816 117.59082 107.88385 112.95271
## 4192 111.88506 125.54172 114.42351 108.20026 110.22047
## 4193 172.70436 108.05597 208.23501 114.42351 171.38311
## 4194 182.46342 114.59080 133.42357 119.67466 129.47695
## 4195 183.03809 119.59454 105.61598 114.98647 149.89209
## 4196 119.21853 110.37718 115.73388 114.82032 188.77832
## 4197 134.12285 126.41812 113.84924 143.15570 125.97572
## 4198 147.97806 117.70833 172.63492 135.07640 117.70833
## 4199 161.42447 111.04844 125.86513 446.58161 214.86895
## 4200 204.79928 160.75466 142.56514 187.79756 267.49050
## 4201 87.00521 65.23464 84.99905 84.86304 84.57300
## 4202 86.31604 54.23814 85.03989 84.05367 90.62159
## 4226 88.93570 83.11619 87.20973 87.06722 76.43678
## 4227 69.07252 66.56782 70.92045 65.10216 103.54970
## 4251 87.19251 59.27230 66.56782 80.21945 79.51359
## 4252 89.86462 83.45336 87.06722 90.71575 79.88844
## 4253 89.07701 84.18221 76.63699 76.63699 86.84609
## 4254 79.00953 81.00761 71.43483 75.91268 93.80379
## 4255 79.87391 80.66573 91.87575 79.91193 93.31005
## 4256 92.13474 81.34965 96.48148 86.59472 83.14199
## 4257 97.04058 85.13134 94.04152 99.80850 86.65654
## 4258 93.82111 95.90900 97.06889 76.84017 92.30889
## 4259 100.28604 97.54853 102.48466 96.28845 90.75582
## 4260 101.90641 100.31597 101.16487 97.45585 102.64242
## 4261 100.18869 102.32023 99.67887 97.96420 101.84448
## 4262 102.58764 106.37830 102.31760 107.63287 109.50161
## 4263 103.69813 104.25807 103.03594 111.54449 104.01260
## 4264 107.23509 97.50000 105.73638 112.78478 106.15273
## 4265 105.18351 117.36111 132.21463 116.60229 116.13150
## 4266 140.96680 103.35880 103.79710 106.72359 108.59177
## 4267 107.67523 113.70289 111.46081 172.70436 114.57763
## 4268 111.19603 108.54908 104.92897 112.22418 106.20642
## 4269 118.02153 131.42239 131.40097 101.06061 263.32021
## 4270 133.08636 482.34621 248.54195 105.04438 109.36204
## 4271 117.26462 111.41676 99.11934 153.93285 281.71217
## 4272 225.69219 225.69219 120.01017 110.76060 117.11838
## 4273 323.44806 152.26582 116.62220 147.97806 126.42492
## 4274 121.40691 166.00129 143.81742 166.21715 155.69308
## 4275 172.62743 135.41667 219.60348 118.18972 145.77735
## 4326 66.61349 84.13422 85.57782 76.52190 82.18981
## 4327 84.15973 96.04584 52.64988 86.59730 79.51359
## 4328 87.11384 90.82572 85.65931 41.56536 84.99905
## 4329 87.60438 87.73624 93.31005 97.63935 86.61646
## 4330 91.51116 53.67943 73.29890 91.78669 90.64730
## 4331 95.08598 90.65794 94.04152 88.08301 86.65654
## 4332 88.08301 91.12778 101.36364 96.28014 92.31872
## 4333 81.19623 101.77485 93.60593 82.74496 96.59448
## 4334 101.52975 97.32737 86.57403 92.63802 81.86683
## 4335 100.14407 101.26409 101.82777 99.73118 101.93226
## 4336 102.77447 112.68137 100.35603 97.46060 100.51559
## 4337 106.70248 124.71287 104.69265 124.71287 107.11129
## 4338 104.67952 105.84633 104.99403 102.94479 110.93115
## 4339 110.43121 130.72207 110.40473 146.30854 110.83466
## 4340 107.68874 103.95877 115.41369 107.35540 107.45482
## 4341 120.82444 115.26766 107.72406 104.32544 112.72938
## 4342 104.92897 114.28594 107.69149 111.20249 120.81843
## 4343 112.50254 116.75936 101.12136 111.19603 109.17025
## 4344 121.92049 108.04980 109.04433 149.17460 108.93042
## 4345 136.74200 120.42606 130.64683 105.04438 108.91640
## 4346 101.37988 126.04950 123.79254 188.77832 115.59228
## 4347 118.92416 164.56084 120.70979 148.08932 298.90043
## 4348 205.35109 147.80102 234.32398 127.06840 234.32398
## 4349 162.56055 125.82526 183.06954 111.04844 131.58996
## 4350 122.97546 130.14879 125.95365 135.53362 150.81380
## 4351 89.76592 83.00664 70.89381 80.88184 84.16547
## 4352 86.69055 85.57782 88.59921 86.93202 83.45336
## 4376 87.22372 48.49429 91.95899 85.57782 91.95899
## 4377 97.43460 87.96539 80.32086 55.25180 85.15462
## 4401 88.98349 37.81895 79.11190 87.68738 89.76592
## 4402 60.57741 55.25180 80.76570 89.07701 66.56782
## 4403 55.25180 89.49587 83.00664 84.35955 59.27230
## 4404 79.87391 93.31005 93.33426 79.31961 61.37006
## 4405 81.02063 89.12743 91.43739 81.02063 88.88347
## 4406 85.13210 93.19046 81.02273 94.95988 93.44638
## 4407 85.84962 92.13474 91.96508 78.96031 76.94358
## 4408 96.48671 99.46346 98.98092 91.54061 85.98439
## 4409 83.11151 97.45069 89.61493 96.59170 97.94876
## 4410 99.09051 104.30909 112.68137 97.32866 99.87306
## 4411 100.41819 100.35603 100.66260 105.57289 98.64589
## 4412 102.35425 101.41742 105.59849 104.02718 101.69734
## 4413 102.11598 115.39095 104.99403 111.19878 127.01718
## 4414 112.63745 108.05007 108.37045 109.87936 146.43261
## 4415 103.95877 110.05322 110.52339 119.79731 114.70735
## 4416 108.46440 117.59082 108.02726 100.70149 107.45712
## 4417 111.78234 445.05222 104.66835 105.29585 108.05597
## 4418 104.37449 107.24831 108.64252 105.57382 104.95144
## 4419 129.47695 141.37796 141.37796 178.11247 134.40526
## 4420 110.72638 183.98454 163.68244 155.18207 113.91920
## 4421 118.26464 106.03007 116.17452 111.94593 102.82057
## 4422 108.31670 149.56982 119.71218 138.74334 225.69219
## 4423 144.79541 126.84464 323.38504 118.14624 131.26142
## 4424 127.04738 183.06954 123.00804 156.67740 127.16439
## 4425 103.71193 150.81380 132.28471 118.18972 139.45128
## 4476 86.85072 80.42268 82.14150 82.47773 82.18296
## 4477 87.11384 68.86478 89.86462 85.54361 66.58774
## 4478 50.76591 41.68769 84.05367 60.45340 85.54361
## 4479 86.46140 90.74173 97.31578 84.62964 72.67259
## 4480 91.65131 96.08898 64.21370 91.46595 72.67259
## 4481 89.32484 95.50927 69.46001 76.31949 97.69841
## 4482 101.49594 88.96747 89.33854 94.96528 83.30883
## 4483 93.44638 84.34966 94.28239 93.51373 97.40585
## 4484 98.03552 96.70003 94.67902 96.28845 93.70331
## 4485 100.63553 100.71676 99.65747 100.41819 100.14188
## 4486 100.04108 100.14811 99.35575 98.86450 97.96420
## 4487 104.18450 104.28966 106.82694 111.52278 100.99355
## 4488 119.89055 104.39336 110.93115 104.04441 110.93115
## 4489 297.32487 102.18154 109.98478 109.87936 121.74289
## 4490 105.33277 108.42459 109.64912 107.65160 116.68623
## 4491 107.07546 105.35619 114.70735 98.91687 109.40839
## 4492 114.07154 111.60177 105.56697 160.60608 111.05910
## 4493 98.34486 110.77789 125.17527 121.52583 111.63016
## 4494 101.10717 249.03521 111.79832 109.04433 155.76773
## 4495 115.62426 105.65981 123.60722 104.77194 117.63440
## 4496 112.05516 117.71484 121.33721 173.03071 117.71484
## 4497 121.48662 131.49077 116.07684 150.69379 115.23936
## 4498 131.01205 205.35109 124.85976 120.93341 197.77093
## 4499 162.17781 162.56055 116.66334 113.08281 134.46696
## 4500 268.49932 176.97539 204.79928 134.82010 145.77735
## 4551 90.23312 84.18221 80.07062 80.07062 93.92888
## 4552 54.27991 45.30148 36.84186 77.05714 72.74734
## 4553 81.40956 90.87033 81.40956 72.74734 79.47932
## 4554 59.30769 71.60730 80.66573 90.48983 75.51253
## 4555 76.00061 73.29890 91.51116 93.33426 76.00061
## 4556 96.48148 82.25437 91.62297 90.90446 69.81468
## 4557 95.90900 91.81731 90.38887 87.88031 95.31668
## 4558 75.63255 76.84017 93.20396 73.59809 82.74496
## 4559 99.83715 100.48347 98.34969 92.93899 97.76746
## 4560 102.41009 100.79741 97.78074 101.53983 103.99275
## 4561 99.11660 99.62205 99.09122 97.82476 100.14188
## 4562 102.74791 102.58764 103.27481 100.21886 105.74543
## 4563 106.69830 103.40427 102.92240 105.96625 103.28263
## 4564 120.59903 107.80362 116.83474 105.77540 146.30854
## 4565 117.47683 104.39012 102.94933 111.65145 129.79219
## 4566 116.60229 144.62638 143.88871 140.79911 111.55464
## 4567 116.14203 114.65557 120.53017 108.62230 171.60518
## 4568 113.22591 118.71088 107.61294 113.69314 107.03635
## 4569 110.26906 110.35033 126.33961 105.83593 117.02929
## 4570 116.96535 115.95317 109.39168 141.37796 117.59259
## 4571 133.66675 121.11444 99.45656 108.07771 145.99686
## 4572 164.56084 125.66132 134.17367 139.94499 125.53161
## 4573 131.22664 131.27959 121.95858 172.63492 162.35652
## 4574 107.59809 136.37268 110.00333 132.44953 748.29994
## 4575 104.83165 159.00152 124.45213 125.24982 104.83165
## 4576 86.85072 96.04584 96.08898 92.17841 88.71275
## 4577 88.51961 93.66601 86.84609 49.97188 85.57782
## 4578 86.26102 85.95653 77.28096 89.92114 86.31604
## 4579 87.78058 86.46140 53.32295 59.41362 62.68866
## 4580 93.17554 53.45668 87.88899 97.33569 79.91193
## 4601 36.79145 80.89354 52.63789 81.88533 37.81895
## 4602 92.01060 77.34781 79.54693 79.47932 69.07252
## 4603 82.14150 76.43678 82.14150 84.99905 55.25180
## 4604 93.80144 78.61337 90.48983 93.33426 94.38345
## 4605 97.63935 102.81987 85.01096 90.71247 79.00953
## 4626 84.13422 89.29480 55.25180 85.65931 70.92045
## 4627 88.74066 85.03989 85.65931 69.07252 48.49429
## 4628 85.10968 91.23674 86.17021 63.96155 88.93570
## 4629 59.30769 85.01096 94.70750 87.73624 53.32295
## 4630 88.16347 87.78058 102.81987 75.91268 63.14192
## 4631 95.70887 91.96508 85.60476 91.96319 84.21325
## 4632 101.08586 89.81119 80.21429 70.48718 97.06889
## 4633 81.56341 92.99346 92.67817 87.94957 85.35279
## 4634 98.34969 96.28845 97.48328 84.39734 97.73507
## 4635 102.32023 100.56819 103.30935 98.37455 100.54435
## 4636 100.41819 103.82921 101.02647 98.54870 103.32134
## 4637 102.94154 101.41742 100.36611 106.57789 104.99937
## 4638 98.06457 108.33239 114.83120 107.80484 101.63512
## 4639 109.98478 115.52511 115.59832 112.63745 106.48477
## 4640 101.38032 119.50628 150.83319 129.12470 118.92588
## 4641 115.41369 103.10562 102.84663 152.35816 158.28096
## 4642 114.28594 108.81487 114.84015 114.96845 124.45826
## 4643 128.12313 116.75936 118.77751 104.92897 445.05222
## 4644 119.21580 102.39567 116.65831 116.02923 129.81371
## 4645 105.36249 112.15884 102.82229 155.33333 113.99420
## 4646 113.25841 140.58533 153.93285 132.60389 106.40653
## 4647 108.27347 125.00909 108.58455 116.07684 106.93167
## 4648 118.14624 371.76418 130.73546 115.83064 152.18813
## 4649 127.89808 136.11654 254.51475 155.56938 446.58161
## 4650 140.27197 219.60348 125.71272 219.60348 124.21849
## 4701 86.17021 82.47773 94.43840 80.21945 81.13119
## 4702 68.38764 87.79150 86.72466 70.22650 54.23814
## 4703 97.73589 76.81953 89.35444 87.19847 88.51961
## 4704 92.43986 91.35638 94.70750 51.50991 59.41362
## 4705 90.64730 70.42076 92.92963 83.29147 91.72003
## 4706 96.28014 81.36691 76.24359 95.36544 90.82499
## 4707 67.80351 78.96031 93.19224 88.29323 68.03409
## 4708 90.18384 94.04443 97.10315 87.94957 89.17940
## 4709 96.20178 96.59170 100.48347 98.70271 96.73800
## 4710 98.98538 102.71888 102.17427 102.33343 99.55544
## 4711 104.30909 100.93304 101.38662 99.62205 98.98863
## 4712 100.99355 101.30346 104.28966 102.00745 102.15226
## 4713 104.66425 104.20592 114.50839 131.62010 104.42528
## 4714 110.40473 146.30854 104.85592 106.02560 141.25711
## 4715 99.10803 152.66391 111.04849 103.95877 106.01707
## 4716 132.51117 124.48441 98.91687 102.88066 133.91909
## 4717 102.72149 102.72149 101.13796 110.22047 171.10256
## 4718 114.42351 106.47021 119.06632 114.81305 124.45826
## 4719 116.84813 118.15310 108.88442 136.26939 99.15638
## 4720 120.17283 106.49688 110.15822 141.09160 113.99420
## 4721 115.73388 209.70686 109.73607 117.71484 126.34928
## 4722 117.37784 140.12399 110.76060 112.31699 112.69286
## 4723 113.79071 121.45352 129.88004 134.35013 130.19223
## 4724 144.57935 748.29994 123.73880 155.69308 122.70613
## 4725 144.93546 267.49050 104.07086 1189.82588 142.24715
## 4776 90.71575 69.44062 79.11190 79.47932 86.17021
## 4777 82.75869 77.84784 90.71575 86.72466 84.35955
## 4778 89.76592 82.37310 66.56782 90.82572 77.26177
## 4779 70.85132 90.90331 88.67350 64.61268 70.11395
## 4780 102.63692 86.61646 91.72003 71.60730 90.33507
## 4781 83.47741 75.51250 95.06403 97.18258 81.65959
## 4782 96.99243 78.89058 80.22518 95.11866 70.60962
## 4783 94.04152 92.31872 97.06502 83.40701 94.24815
## 4784 92.73947 100.81566 97.51408 100.28604 86.84800
## 4785 97.63176 97.57504 97.57504 97.54033 100.79759
## 4786 99.90523 101.26409 100.63077 100.02075 99.71523
## 4787 124.71287 101.78127 102.12298 102.28962 112.94194
## 4788 127.01718 104.38677 103.03594 104.13530 104.67952
## 4789 102.18154 105.00669 103.35384 100.88040 106.02560
## 4790 380.88026 113.13935 105.18351 127.75305 110.06902
## 4791 106.40525 109.40672 105.18351 108.02726 107.73630
## 4792 125.38679 141.54676 103.32460 112.93166 123.02067
## 4793 106.20255 112.14160 120.23841 125.63590 115.08633
## 4794 183.03809 99.49455 115.66438 116.84813 102.49460
## 4795 134.27037 131.40097 120.19411 166.79235 115.13316
## 4796 116.17452 110.46381 107.85640 124.30417 110.46381
## 4797 143.70353 117.27221 112.31699 125.66132 100.20202
## 4798 131.01205 126.15987 129.88004 100.97366 121.75368
## 4799 246.70513 162.17781 136.11654 123.01758 210.70998
## 4800 324.26805 121.38711 143.17600 146.56163 103.71193
## 4851 80.42268 77.05714 87.19847 104.02357 88.59921
## 4852 68.86478 77.73452 103.54970 54.07719 84.35955
## 4853 85.15462 84.13422 58.84880 97.69212 88.71275
## 4854 70.11395 51.50991 79.05238 70.42076 90.64730
## 4855 78.03115 91.71909 91.02956 75.74804 91.65131
## 4856 88.10025 79.43407 96.35391 93.47648 73.98322
## 4857 92.75237 90.82499 94.74468 92.11196 91.80362
## 4858 93.82111 98.73440 80.73125 90.76756 89.17940
## 4859 96.28845 99.11068 96.03599 100.28604 101.52975
## 4860 98.78481 100.71676 99.27417 98.93923 102.01587
## 4861 101.77396 103.32134 98.54870 99.76842 102.41009
## 4862 111.52278 124.71287 106.15999 103.03193 103.21992
## 4863 137.77702 98.87984 115.39095 104.20592 108.71738
## 4864 123.98612 106.47730 104.90277 137.90473 115.51272
## 4865 105.45227 100.48315 103.40420 133.86898 106.19343
## 4866 109.37046 110.59961 106.19343 123.31008 100.30303
## 4867 166.15643 108.00357 128.14807 443.99619 111.15849
## 4868 116.46127 171.38311 112.14160 113.97526 107.24831
## 4869 120.42606 115.62426 132.04917 108.91640 183.98454
## 4870 169.24985 106.78113 125.82905 111.98145 113.56368
## 4871 121.02656 159.69565 119.04881 99.11934 104.76930
## 4872 132.31067 148.00592 114.28304 108.58455 107.26161
## 4873 152.44157 123.20902 131.27959 159.22729 131.27959
## 4874 136.11654 110.81273 127.42447 127.21345 116.66334
## 4875 191.15108 112.93395 149.34940 107.76487 124.21849
## 4876 85.46386 78.65690 84.18221 84.43896 91.12610
## 4877 96.08898 86.24029 68.38764 39.70148 50.76923
## 4878 97.73589 45.05271 45.05271 74.49210 95.66380
## 4901 77.73452 95.61993 82.16888 87.49543 82.18981
## 4902 103.54970 88.97681 74.10656 72.74734 48.49429
## 4903 59.27230 87.11384 36.84186 88.96352 76.38382
## 4926 93.92888 84.86304 87.90980 74.82542 82.75869
## 4927 104.95791 80.80704 86.69055 93.92888 89.35444
## 4928 48.57916 79.47932 64.04461 55.25180 79.54693
## 4929 64.21370 65.48751 90.74173 90.71247 92.56843
## 4930 95.53165 87.57756 92.52781 94.38345 102.22222
## 4931 92.72501 81.68889 85.98439 57.27377 94.16257
## 4932 90.38887 87.88031 70.48718 70.74005 69.81468
## 4933 92.87873 97.62545 73.59809 94.37150 102.22279
## 4934 92.48857 99.43150 86.43389 97.91838 91.03641
## 4935 100.54435 98.64589 100.50041 100.92643 100.65897
## 4936 97.73434 97.73434 101.96822 100.05478 100.14188
## 4937 109.50161 103.23319 105.57143 102.21498 111.52278
## 4938 110.69491 102.47183 114.50839 104.04441 104.32099
## 4939 106.29270 115.34707 113.99777 106.44943 107.80362
## 4940 148.87401 101.38032 110.34835 116.62201 120.56460
## 4941 124.48441 99.10803 102.75253 112.30907 103.07126
## 4942 141.54676 105.34664 128.14807 108.67903 113.60657
## 4943 112.42533 125.54172 110.16479 121.52583 100.39900
## 4944 111.90085 132.44916 134.27037 123.11031 118.52359
## 4945 116.94994 128.64430 119.21580 111.26537 111.88715
## 4946 121.91524 121.11444 115.15690 119.17671 139.84188
## 4947 143.15570 201.07692 112.69286 318.79224 181.84471
## 4948 131.22664 152.18813 128.97574 126.67551 470.08200
## 4949 183.04556 127.04738 138.39984 158.11991 120.97504
## 4950 570.80855 114.62269 187.79756 147.24048 134.82010
## 4951 97.69212 86.30683 60.03765 103.54970 84.16547
## 4952 98.00046 77.84784 89.29480 77.84784 60.03765
## 4953 52.63789 52.63789 88.95706 95.66380 86.53435
## 4954 87.77418 75.74804 67.96218 96.08898 86.77549
## 4955 89.79684 82.68579 92.75428 87.57756 67.96218
## 4976 88.71275 85.35190 68.22153 83.45336 80.89354
## 4977 90.23312 86.31604 65.10216 74.49210 95.66380
## 4978 97.73589 50.76591 87.33405 103.13131 54.27991
## 4979 70.42076 93.80379 79.07915 91.64965 90.14350
## 4980 78.61337 88.16347 96.04494 93.80379 86.73150
## 5001 86.83467 83.26203 41.68769 81.96664 93.92888
## 5002 65.23464 90.87033 104.44557 90.71575 104.44557
## 5003 89.59827 81.93143 45.05271 86.87865 83.04769
## 5004 82.80109 87.73624 59.41362 94.78517 86.00700
## 5005 51.42515 93.75936 64.83246 93.06302 64.21370
## 5006 81.95826 77.22249 99.84694 94.74468 93.30245
## 5007 93.63286 98.92117 69.95766 68.03409 67.80351
## 5008 97.18258 95.24474 81.68889 93.49512 92.87873
## 5009 100.57932 95.98072 98.03552 100.36361 93.24388
## 5010 99.98555 101.42751 101.52984 99.35575 97.93814
## 5011 101.05372 102.33343 100.12346 101.43779 102.32023
## 5012 164.65078 104.54117 107.11129 103.27481 100.99168
## 5013 98.06457 100.72350 98.06457 115.06294 103.08257
## 5014 104.55415 111.17116 106.44586 101.23275 104.55415
## 5015 115.41369 102.84663 106.67743 112.43048 106.15231
## 5016 327.17640 108.36584 112.43048 133.91909 113.19995
## 5017 128.89845 110.76400 171.10256 107.90621 111.90901
## 5018 112.22418 207.17797 107.13503 113.97526 100.58081
## 5019 136.34087 122.18671 100.69865 120.42606 149.89209
## 5020 166.79235 108.88442 127.88706 113.34677 110.36058
## 5021 504.61729 124.26543 131.98531 115.15690 178.65124
## 5022 119.71218 168.75973 106.00618 112.96036 108.27347
## 5023 107.00843 131.26142 126.67551 126.44634 100.74375
## 5024 131.41540 120.93599 102.96003 139.77080 143.81742
## 5025 172.62743 125.95365 161.57427 125.71272 145.77735
## 5076 84.05367 88.74066 76.52190 87.53040 90.40317
## 5077 81.93143 69.44062 63.96155 94.37539 45.05271
## 5078 83.11619 81.13119 60.65947 89.20607 54.07719
## 5079 94.96020 95.82526 91.72003 91.64965 63.88924
## 5080 92.13118 93.17554 89.79684 71.60730 86.77549
## 5081 79.46693 90.19618 92.22074 90.38887 87.78115
## 5082 85.28735 98.73440 95.06454 75.51250 93.25658
## 5083 83.82353 92.87873 90.18384 82.70288 99.90496
## 5084 98.34969 96.73800 99.64207 95.99733 87.92436
## 5085 97.22840 100.16114 102.01587 100.65897 101.24048
## 5086 102.70549 93.82459 97.45585 100.99320 100.06442
## 5087 104.99937 98.22391 103.28508 101.32439 104.69265
## 5088 109.81562 101.90438 106.69830 113.69048 103.83656
## 5089 104.74776 251.94731 102.70067 124.85189 296.34216
## 5090 118.21245 107.93877 107.66647 123.45897 118.32347
## 5091 117.36111 111.55464 118.21245 103.64675 103.37279
## 5092 112.63187 115.02123 117.82492 117.82492 125.88797
## 5093 129.20327 100.98039 108.62230 171.79446 109.42068
## 5094 101.06061 117.52653 118.24087 134.27037 183.98454
## 5095 459.90827 138.80017 231.53177 102.39567 108.93042
## 5096 188.53177 101.43678 123.00073 107.85640 117.31404
## 5097 111.59231 181.84471 135.68449 125.18827 126.41812
## 5098 149.91768 205.35109 234.32398 126.44634 124.46827
## 5099 118.87561 170.04901 121.97617 102.89562 134.46696
## 5100 139.14007 568.61008 172.84924 204.04217 125.72791
## 5151 48.49429 85.66890 85.58530 85.46386 57.46010
## 5152 81.40956 66.58774 39.70148 86.30683 37.61926
## 5153 82.76681 85.21347 85.58530 49.78525 90.40317
## 5154 82.68579 87.77418 76.00061 92.43986 89.52954
## 5155 93.17554 102.22222 89.12614 91.27376 94.38345
## 5156 99.84694 69.95766 65.86113 93.32995 98.98092
## 5157 68.03409 91.96508 95.86473 95.50932 84.11676
## 5158 88.75326 101.77485 99.33319 96.59448 93.60593
## 5159 97.88507 99.38990 97.88507 100.60156 97.25576
## 5160 101.46492 99.09122 87.28822 96.37148 102.42961
## 5161 100.24537 99.35575 100.12346 99.65537 99.09051
## 5162 108.96611 103.27372 101.82865 109.50161 107.10395
## 5163 104.09200 104.26492 103.62028 102.94479 104.26492
## 5164 104.74776 104.55229 111.22650 146.30854 110.43121
## 5165 103.08793 112.95606 110.46209 122.66667 106.94296
## 5166 105.18351 118.92588 111.06992 105.18351 103.29518
## 5167 135.82276 165.59254 125.63590 116.88010 114.56494
## 5168 443.99619 225.66604 123.02067 125.88797 162.89176
## 5169 112.60621 254.13701 117.59139 117.52653 99.15638
## 5170 109.22399 182.46342 126.33961 183.98454 101.47904
## 5171 105.91190 136.66000 121.11444 111.23759 117.31404
## 5172 150.69379 199.02722 120.49509 116.98047 122.96619
## 5173 113.56516 118.29243 113.61216 101.32392 118.14756
## 5174 155.62688 179.39371 138.84010 122.61141 125.77025
## 5175 134.29708 103.71193 123.69247 162.40041 154.38763
## 5176 87.80122 89.35444 87.12146 39.64751 41.56536
## 5177 81.96664 89.20607 76.81953 103.54970 55.46753
## 5178 84.98210 84.86304 86.95843 82.63836 79.72385
## 5179 84.59334 88.88347 76.00061 66.86484 81.00761
## 5180 91.70420 91.64965 86.61646 75.69345 90.41604
## 5181 77.10697 88.39372 96.90043 98.73440 94.08517
## 5182 83.47741 93.44638 95.50932 86.43748 96.69225
## 5191 102.72838 327.17640 103.95877 107.06727 129.13669
## 5192 108.81487 120.90543 130.97942 174.29516 107.74817
## 5193 102.72149 105.34664 106.47021 208.23501 114.57763
## 5194 105.73385 120.17283 109.79184 128.46265 134.23700
## 5195 121.43880 102.49460 175.68796 148.34249 141.09160
## 5196 110.37718 145.99686 252.70767 118.46197 129.18871
## 5197 149.28145 551.74786 225.69219 121.26949 117.92223
## 5198 470.08200 173.04556 470.08200 642.58180 131.22664
## 5199 136.37268 140.19862 117.61831 102.60494 132.34528
## 5200 150.13554 132.28471 161.00529 172.62743 187.66109
## 5201 50.76591 60.03765 105.36680 90.98065 89.67846
## 5202 94.37539 86.95843 45.05271 84.35955 89.49587
## 5203 86.83467 84.18221 87.90980 41.91126 85.77597
## 5204 93.80379 83.29147 66.86484 80.66573 70.47614
## 5205 75.69345 91.70420 73.29890 96.08898 83.29147
## 5206 97.61660 96.92817 96.69225 93.41064 88.18598
## 5207 95.74852 94.04152 90.19618 85.25340 79.76890
## 5216 111.04849 133.63401 117.47683 108.26402 104.98236
## 5217 114.70431 127.05009 156.88157 108.64252 105.46017
## 5218 116.01471 114.57763 104.92897 105.29585 130.86886
## 5219 118.02153 163.49438 163.68244 110.33369 116.77544
## 5220 111.90085 113.91920 112.36902 109.52637 100.69865
## 5221 111.41676 131.98531 115.73388 188.46154 123.61111
## 5222 119.43852 120.26187 123.85819 139.94499 121.15511
## 5223 123.15943 371.76418 121.63738 127.06840 152.26582
## 5224 133.97506 140.18034 127.42447 121.00863 127.89808
## 5225 117.40587 172.62743 160.38685 568.61008 128.95963
## 5226 36.79145 87.49543 89.62937 77.73452 76.81953
## 5227 87.33405 92.01060 64.04461 86.72466 84.86304
## 5228 62.21343 41.68769 87.51037 87.53040 79.47972
## 5229 86.61646 79.91193 91.62935 91.64965 90.96115
## 5230 86.46140 83.29147 63.37863 92.40642 86.73150
## 5231 76.71611 95.90900 88.75352 95.82647 93.44638
## 5232 95.70887 97.40585 96.35391 90.76756 82.82758
## 5233 101.49594 94.13769 96.90043 67.14593 96.35980
## 5234 96.73800 66.79041 100.60156 92.99363 92.93899
## 5235 99.16667 101.43779 100.05960 101.90641 102.70549
## 5236 97.34595 100.95731 103.18209 99.36712 98.78481
## 5237 112.94194 112.94194 106.15999 103.03193 104.99937
## 5238 100.72350 108.33239 260.74334 104.97123 114.10497
## 5239 110.43121 105.77540 98.93909 110.43121 114.77675
## 5240 119.29708 123.45897 113.36324 107.45482 111.10829
## 5241 105.72163 152.66391 106.00929 106.80057 104.27964
## 5242 151.70141 106.26756 124.61969 111.05910 113.60657
## 5243 107.59443 113.22591 108.44376 101.05646 128.27801
## 5244 109.36204 175.39744 111.90085 110.33821 131.58483
## 5245 149.90408 116.04334 113.91920 109.79184 125.82905
## 5246 134.59250 125.15530 111.00264 161.35621 123.80165
## 5247 117.72698 144.04249 160.98321 133.41070 148.34604
## 5248 173.03357 173.03357 126.98589 182.98188 145.14124
## 5249 668.52035 123.90395 155.56938 143.38537 748.29994
## 5250 132.13756 161.00529 177.07372 124.45213 124.45213Extraer la media de los datos originales. Calcular la media de cada columna imputada. Calcular las diferencias absolutas con respecto a la media original. Identificar el índice de la columna con la menor diferencia. Mostrar la columna seleccionada.
original_mean <- 116.95
imputed_means <- colMeans(annual_imputation_cart$imp$value, na.rm = TRUE)
mean_differences <- abs(imputed_means - original_mean)
closest_column <- which.min(mean_differences)
cat("The column closest to the original mean is column:", closest_column, "\n")## The column closest to the original mean is column: 1Imputar los datos al conjunto de datos original.
inflation_annual_data_imp <- complete(annual_imputation_cart, 1)Resumen de datos faltantes e imputados.
summary(inflation_annual_data$value)## Min. 1st Qu. Median Mean 3rd Qu. Max. NA's
## 36.79 95.89 105.45 116.91 120.40 1196.03 2231summary(inflation_annual_data_imp$value)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 36.79 92.69 104.01 115.20 118.56 1196.03Los datos imputados conservan un rango similar al del conjunto de datos original, lo que sugiere que la imputación no introdujo valores irreales. Ligeros cambios en las estadísticas de resumen indican que los valores imputados reflejan patrones subyacentes, pero podrían diferir ligeramente de la distribución original.
inflation_annual_data_imp <- inflation_annual_data_imp %>%
mutate(series = str_replace_all(series, ",,,", ""))Qué continentes presentan las tasas de inflación más altas o más bajas para los diferentes indicadores?
Resumen estadístico.
annual_inflation_summary <- inflation_annual_data_imp %>%
group_by(continent, series) %>%
summarise(
mean_inflation = mean(value),
median_inflation = median(value),
min_inflation = min(value),
max_inflation = max(value)
) %>%
arrange(series, mean_inflation)
print(annual_inflation_summary)## # A tibble: 18 × 6
## # Groups: continent [6]
## continent series mean_inflation median_inflation min_inflation max_inflation
## <chr> <chr> <dbl> <dbl> <dbl> <dbl>
## 1 Asia CPI P… 114. 104. 48.6 701.
## 2 Europe CPI P… 116. 104. 36.8 641.
## 3 South Ame… CPI P… 117. 105. 36.8 669.
## 4 North Ame… CPI P… 117. 104. 39.7 1190.
## 5 Africa CPI P… 124. 103. 39.6 1190.
## 6 Oceania CPI P… 127. 104. 39.7 323.
## 7 Oceania Core … 106. 110. 52.6 129.
## 8 North Ame… Core … 107. 105. 36.8 205.
## 9 Europe Core … 111. 103. 48.5 699.
## 10 Asia Core … 116. 103. 37.8 1196.
## 11 South Ame… Core … 118. 108. 41.6 470.
## 12 Africa Core … 136. 106. 37.8 571.
## 13 North Ame… Core … 107. 105. 36.8 204.
## 14 Europe Core … 110. 103. 36.8 701.
## 15 South Ame… Core … 115. 111. 50.8 326.
## 16 Asia Core … 117. 104. 41.7 1190.
## 17 Oceania Core … 125. 106. 70.9 503.
## 18 Africa Core … 138. 113. 37.6 569.Distribución de los valores de inflación.
ggplot(inflation_annual_data_imp, aes(x = value)) +
geom_histogram(bins = 30, fill = "blue", color = "white") +
labs(title = "Distribution of Inflation Rates", x = "Inflation Value", y = "Frequency")
La inflación a lo largo del tiempo por continente.
ggplot(inflation_annual_data_imp, aes(x = year, y = value, color = continent)) +
geom_line() +
labs(title = "Inflation Over Time by Continent", x = "Year", y = "Inflation Value") +
theme_minimal() + theme(legend.position="bottom") + guides(fill = guide_legend(nrow = 1))
Se mantuvieron relativamente estables y bajos desde 2000 hasta aproximadamente 2010. Después de 2010, se observa un aumento gradual de la inflación en todos los continentes, con picos significativos en los últimos años (especialmente después de 2020).
Se observa un aumento sustancial de la inflación en todos los continentes, particularmente entre 2020 y 2024. Esto podría atribuirse a eventos globales como la pandemia de COVID-19, interrupciones en la cadena de suministro o políticas de recuperación económica que generaron presiones inflacionarias.
África y Sudamérica: Ambas regiones presentan una mayor variabilidad en los valores de inflación a lo largo del tiempo en comparación con otros continentes; Sudamérica, en particular, presenta picos significativos.
Asia y Europa: Estas regiones muestran una tendencia inflacionaria más controlada, con picos más bajos en comparación con otras.
América del Norte: Presenta una inflación moderada, pero también un cierto aumento de la variabilidad después de 2020.
Oceanía: Destaca por presentar un fuerte aumento en el período 2020-2024, lo que probablemente contribuyó al valor de inflación más alto del conjunto de datos (~1200).
La variabilidad de la inflación aumenta considerablemente después de 2020 en la mayoría de los continentes, lo que sugiere un período de incertidumbre económica o de mayores presiones inflacionarias. Los picos y la dispersión indican que algunos continentes experimentaron eventos de inflación extremos durante este período.
Diagrama de caja para la inflación en cada continente.
ggplot(inflation_annual_data_imp, aes(x = continent, y = value, fill = continent)) +
geom_boxplot() +
labs(title = "Inflation Distribution by Continent", x = "Continent", y = "Inflation Value") +
theme_minimal() + theme(legend.position="bottom") + guides(fill = guide_legend(nrow = 1))
Podemos ver que continentes como África, Asia y América del Norte tienen valores atípicos (de ahí puede provenir el máximo cercano a 1250 valores).
Inflación agrupada por década y continente.
inflation_annual_data_imp %>%
group_by(decade, continent) %>%
summarise(mean_inflation = mean(value, na.rm = TRUE), .groups = "drop") %>%
ggplot(aes(x = decade, y = mean_inflation, fill = continent)) +
geom_bar(stat = "identity", position = "dodge") +
labs(title = "Average Inflation by Decade and Continent", x = "Decade", y = "Average Inflation") +
theme_minimal() + theme(legend.position="bottom") + guides(fill = guide_legend(nrow = 1))
Cómo han evolucionado los indicadores de inflación a nivel mundial y dentro de los continentes a lo largo del tiempo?
Datos agregados por año y continente.
inflation_trends <- inflation_annual_data_imp %>%
group_by(year, continent, series) %>%
summarise(mean_inflation = mean(value, na.rm = TRUE), .groups = "drop") %>%
ungroup()Tendencias a nivel mundial.
ggplot(inflation_trends, aes(x = year, y = mean_inflation, colour = series)) +
geom_line() +
facet_wrap(~ continent, scales = "free_y") +
labs(title = "Inflation Trends By Continent",
x = "Year",
y = "Mean Inflation Rate",
color = "Inflation Indicator") +
theme_minimal() + theme(legend.position="bottom") + guides(fill = guide_legend(nrow = 1))
IPC básico, sin desestacionalizar (línea roja):
Mide la inflación con base en el índice de precios al consumidor básico sin ajustar las variaciones estacionales.
La línea roja generalmente se asemeja a la línea verde (IPC desestacionalizado), lo que indica que los efectos estacionales podrían no ser sustanciales en la mayoría de las regiones.
África y Sudamérica: Muestran aumentos graduales hasta alrededor de 2020, seguidos de fuertes subidas. África supera los 300 y Sudamérica se acerca a los 180 para 2024.
América del Norte y Oceanía: Fuertes aumentos después de 2020, con América del Norte acercándose a los 1000 y Oceanía superando los 1200. Asia y Europa: Muestran tendencias más suaves con aumentos más graduales, manteniéndose por debajo de 250 y 200, respectivamente.
IPC básico, desestacionalizado (línea verde):
Similar al IPC básico, pero considera patrones estacionales predecibles, como el gasto en vacaciones o los ciclos de cosecha.
La línea verde refleja en su forma la línea roja, pero a veces es ligeramente superior o inferior, lo que refleja ajustes por efectos estacionales.
África, Asia y Europa: Los ajustes estacionales tienen un impacto mínimo en las tendencias, ya que las líneas verde y roja son prácticamente idénticas. Los efectos estacionales no parecen influir significativamente en la inflación en estos continentes.
América del Norte y Oceanía: Las diferencias entre las líneas verde y roja son más pronunciadas después de 2020, lo que indica efectos estacionales más fuertes en estas regiones durante los últimos años.
América del Sur: Una línea verde más alta sugiere que los ajustes estacionales amplifican ligeramente la inflación, posiblemente debido a ciclos económicos vinculados a la agricultura o las festividades.
El IPC básico (sin ajustar estacionalmente y ajustado estacionalmente)
muestra tendencias similares en la mayoría de los continentes, con efectos estacionales mínimos, excepto en América del Norte y Oceanía después de 2020.
El IPC (ponderado por la mediana, ajustado estacionalmente) diverge más, lo que refleja una mayor volatilidad en las variaciones interanuales de la inflación, especialmente en Oceanía, América del Norte y América del Sur.
Oceanía y América del Norte destacan por sus aumentos extremos de la inflación después de 2020, mientras que Asia y Europa muestran tendencias más estables y controladas.
Existen patrones distintivos o diferencias en las tendencias de inflación entre continentes?
Trazar tendencias de cada continente.
ggplot(inflation_trends, aes(x = year, y = mean_inflation, color = continent)) +
geom_line() +
facet_wrap(~ series, scales = "free_y") +
labs(
title = "Inflation Trends by Indicator and Continent",
x = "Year",
y = "Mean Inflation Rate",
color = "Continent"
) +
theme_minimal() + theme(legend.position="bottom") + guides(fill = guide_legend(nrow = 1))
Calcular la tasa de inflación media por continente e indicador.
ggplot(annual_inflation_summary, aes(x = reorder(continent, mean_inflation), y = mean_inflation, fill = series)) +
geom_bar(stat = "identity", position = "dodge") +
labs(
title = "Mean Inflation Rate by Continent and Indicator",
x = "Continent",
y = "Mean Inflation Rate",
fill = "Indicator"
) +
theme_minimal() + theme(legend.position="bottom") + guides(fill = guide_legend(nrow = 1))
Datos de subconjuntos para comparaciones del IPC básico.
core_cpi_data <- inflation_annual_data_imp %>%
filter(series %in% c("Core CPI,not seas.adj", "Core CPI,seas.adj"))ggplot(core_cpi_data, aes(x = year, y = value, color = series)) +
geom_line() +
facet_wrap(~ continent, scales = "free_y") +
labs(
title = "Comparison of Core CPI (Seasonally Adjusted vs. Not Adjusted)",
x = "Year",
y = "Inflation Rate",
color = "Indicator"
) +
theme_minimal() + theme(legend.position="bottom") + guides(fill = guide_legend(nrow = 1))
Correlación global.
global_comparison <- core_cpi_data %>%
group_by(year, series) %>%
summarise(mean_value = mean(value, na.rm = TRUE)) %>%
spread(series, mean_value)
correlation <- cor(global_comparison$`Core CPI,not seas.adj`, global_comparison$`Core CPI,seas.adj`, use = "complete.obs")
print(paste("Correlation between seasonally adjusted and not adjusted Core CPI:", round(correlation, 2)))## [1] "Correlation between seasonally adjusted and not adjusted Core CPI: 1"Una correlación de 1 sugiere una relación lineal positiva muy fuerte entre ambas variables. Cuando una variable aumenta, la otra casi siempre aumenta proporcionalmente.
La tasa de inflación se está volviendo más o menos volátil con el tiempo en determinados continentes?
inflation_volatility <- inflation_annual_data_imp %>%
group_by(continent, series) %>%
arrange(year, .by_group = TRUE) %>%
mutate(
rolling_sd = rollapply(value, width = 5, FUN = sd, fill = NA, align = "right"),
rolling_sd = ifelse(is.na(rolling_sd), sd(value, na.rm = TRUE), rolling_sd) # Replace NA
)ggplot(inflation_volatility, aes(x = year, y = rolling_sd, color = continent)) +
geom_line() +
facet_wrap(~ series, scales = "free_y") +
labs(
title = "Rolling Volatility (5-year SD) of Inflation Indicators",
x = "Year",
y = "Volatility (SD)",
color = "Continent"
) +
theme_minimal() + theme(legend.position="bottom") + guides(fill = guide_legend(nrow = 1))
Cuáles son los principales patrones de volatilidad en el IPC % interanual en los distintos continentes?
cpi_volatility <- inflation_volatility %>%
filter(series == "CPI Price, % y-o-y, median weighted, seas. adj.,")
# Plot CPI volatility trends
ggplot(cpi_volatility, aes(x = year, y = rolling_sd, color = continent)) +
geom_line() +
labs(
title = "Volatility Trends for CPI Price % y-o-y (5-year Rolling SD)",
x = "Year",
y = "Volatility (SD)",
color = "Continent"
) +
theme_minimal() + theme(legend.position="bottom") + guides(fill = guide_legend(nrow = 1))
África (Línea Roja): La volatilidad es moderada, pero aumenta significativamente después de 2020, alcanzando niveles superiores a 100 para 2024. Esto sugiere una reacción a shocks externos (p. ej., crisis económicas mundiales, interrupciones en la cadena de suministro).
Asia (Línea Amarilla): Mantiene una volatilidad relativamente baja hasta 2020, tras lo cual se produce un aumento notable, que alcanza su punto máximo alrededor de 2024. Este aumento, si bien menos extremo que en otros continentes, refleja la creciente inestabilidad en los mercados globales que impacta a la región.
Europa (Línea Verde): Un aumento brusco y drástico de la volatilidad comienza alrededor de 2015, con fluctuaciones superiores a 300 DE después de 2020. Refleja shocks externos significativos como la pandemia de COVID-19, tensiones geopolíticas o crisis energéticas que afectan desproporcionadamente a Europa.
América del Norte (Línea Azul): La volatilidad se mantiene baja hasta 2020, seguida de un aumento pronunciado. Alcanza un máximo de alrededor de 400 DE, el más alto de todos los continentes. Indica una importante inestabilidad inflacionaria durante los últimos años, posiblemente impulsada por problemas en la cadena de suministro, ajustes de la política monetaria y disrupciones globales.
Oceanía (Línea Celeste): Experimenta la volatilidad más extrema, especialmente después de 2020, con niveles superiores a 400 DE para 2024. Refleja la sensibilidad de las pequeñas economías regionales a las perturbaciones globales y las fluctuaciones de los precios de los recursos.
Sudamérica (Línea Rosa): La volatilidad tiende a aumentar con el tiempo, pero se mantiene relativamente moderada en comparación con otros continentes, manteniéndose por debajo de 100 DE incluso después de 2020. Esto sugiere que la variabilidad de la inflación es menos volátil, pero aún se ve afectada por las tendencias regionales y globales.
Pico Posterior a 2020: En todos los continentes, la volatilidad aumenta drásticamente después de 2020, impulsada por disrupciones globales como la pandemia de COVID-19, interrupciones en la cadena de suministro y tensiones geopolíticas.
Alta Volatilidad en Regiones Desarrolladas: América del Norte y Oceanía experimentan la mayor volatilidad después de 2020, lo que sugiere que las economías desarrolladas son más sensibles a las perturbaciones recientes.
Volatilidad Moderada en Regiones en Desarrollo: África, Asia y Sudamérica muestran aumentos de volatilidad más contenidos, lo que refleja su integración más lenta a los ciclos económicos globales o tendencias inflacionarias más persistentes.
Patrón único de Europa: Europa presenta aumentos tempranos de la volatilidad (a partir de ~2015) antes de un aumento significativo después de 2020, posiblemente vinculado a factores únicos como la crisis de deuda de la eurozona o la dependencia energética.
La desviación estándar móvil destaca cambios drásticos en la volatilidad de la inflación, especialmente en América del Norte, Oceanía y Europa, después de 2020.
Patrones de inflación a nivel de década por indicador y continente.
inflation_annual_data_imp <- inflation_annual_data_imp %>%
mutate(decade = floor(year / 10) * 10)
ggplot(inflation_annual_data_imp, aes(x = factor(decade), y = value, fill = continent)) +
geom_boxplot() +
facet_wrap(~ series, scales = "free_y") +
labs(
title = "Decade-level Inflation Patterns by Indicator and Continent",
x = "Decade",
y = "Inflation Rate",
fill = "Continent"
) +
theme_minimal() + theme(legend.position="bottom") + guides(fill = guide_legend(nrow = 1))
IPC básico, sin desestacionalizar (Core CPI, Not Seasonally Adjusted)
2000-2010:
Las tasas de inflación se mantienen relativamente estables en todos los continentes, con pocos valores atípicos. Las tasas son más bajas en Europa y América del Norte que en África y América del Sur.
2010-2020:
Se observa un ligero aumento en las tasas de inflación en todos los continentes, con medianas más altas y diferenciales más amplios en América del Sur. África y Asia comienzan a mostrar una mayor variabilidad en comparación con otros continentes.
2020-2025:
Se observan aumentos significativos en las tasas de inflación y su variabilidad en todos los continentes. Oceanía y América del Norte presentan valores atípicos extremos, con valores superiores a 1000, lo que indica eventos de inflación esporádicos y altamente volátiles.
IPC básico, desestacionalizado (Core CPI, Seasonally Adjusted)
2000-2010:
Patrones similares al indicador sin desestacionalizar, con tasas de inflación bajas y estables en todos los continentes. Europa y América del Norte presentan las tasas más bajas y los diferenciales más pequeños.
2010-2020:
Un aumento moderado de las tasas de inflación en la mayoría de los continentes. África y América del Sur muestran medianas y variabilidad ligeramente más altas en comparación con otros continentes.
2020-2025:
Fuertes aumentos de las tasas de inflación en todos los continentes, con valores atípicos notables en América del Norte y Oceanía. América del Sur continúa mostrando un diferencial amplio, lo que pone de relieve la variabilidad en las tendencias de la inflación.
IPC interanual (mediana ponderada) (Year-over-Year CPI (Median Weighted))
2000-2010:
Las tasas de inflación se mantienen bajas y estables en todos los continentes, con una dispersión mínima y muy pocos valores atípicos.
2010-2020:
Aumentos graduales en las tasas de inflación medias, especialmente en África, Asia y Sudamérica. La variabilidad se mantiene moderada en comparación con los indicadores básicos del IPC.
2020-2025:
Un aumento significativo de las tasas de inflación en todos los continentes, con valores atípicos extremos presentes en América del Norte, Oceanía y Europa. África y Asia presentan diferenciales moderados, pero muestran aumentos notables en las medianas de inflación.
Análisis de series temporales.
Crear series temporales de inflación para el precio del IPC, % interanual, mediana ponderada.
inflation_time_series <- inflation_annual_data_imp %>%
filter(series == "CPI Price, % y-o-y, median weighted, seas. adj.,") %>%
select(year,value, series,country,decade, continent) ggplot(inflation_time_series, aes(x = year, y = value)) +
geom_line(color = "blue", size = 0.5) +
geom_point(color = "red", size = 1) +
labs(
title = "Seasonally Adjusted Inflation Time Series ",
x = "Year",
y = "Inflation Rate (% y-o-y)"
) +
theme_minimal() + theme(legend.position="bottom") + guides(fill = guide_legend(nrow = 1))
ggplot(inflation_time_series, aes(x = year, y = value, color = continent)) +
geom_line(size = 0.2) +
labs(
title = "Seasonally Adjusted Inflation Time Series by continent",
x = "Year",
y = "Inflation Rate (% y-o-y)"
) +
theme_minimal() + theme(legend.position="bottom") + guides(fill = guide_legend(nrow = 1))
Compruebe si la serie es estacionaria.
adf_inflation <- inflation_time_series %>%
group_by(series, continent) %>%
summarise(
adf_p_value = tryCatch(
adf.test(na.omit(value))$p.value,
error = function(e) NA # Return NA if ADF test fails
),
.groups = "drop" # Drop grouping after summarise
)
print(adf_inflation)## # A tibble: 6 × 3
## series continent adf_p_value
## <chr> <chr> <dbl>
## 1 CPI Price, % y-o-y, median weighted, seas. adj., Africa 0.0273
## 2 CPI Price, % y-o-y, median weighted, seas. adj., Asia 0.01
## 3 CPI Price, % y-o-y, median weighted, seas. adj., Europe 0.01
## 4 CPI Price, % y-o-y, median weighted, seas. adj., North America 0.01
## 5 CPI Price, % y-o-y, median weighted, seas. adj., Oceania 0.926
## 6 CPI Price, % y-o-y, median weighted, seas. adj., South America 0.0434ggplot(adf_inflation, aes(x = continent, y = adf_p_value, fill = series)) +
geom_bar(stat = "identity", position = "dodge") +
labs(title = "ADF Test Results by Series and Continent",
x = "Continent", y = "P-value") +
theme_minimal() + theme(legend.position="bottom") + guides(fill = guide_legend(nrow = 1))
adf_inflation<- adf_inflation%>%
mutate(
stationarity = ifelse(adf_p_value < 0.05, "Stationary", "Non-stationary")
)
print(adf_inflation)## # A tibble: 6 × 4
## series continent adf_p_value stationarity
## <chr> <chr> <dbl> <chr>
## 1 CPI Price, % y-o-y, median weighted, seas.… Africa 0.0273 Stationary
## 2 CPI Price, % y-o-y, median weighted, seas.… Asia 0.01 Stationary
## 3 CPI Price, % y-o-y, median weighted, seas.… Europe 0.01 Stationary
## 4 CPI Price, % y-o-y, median weighted, seas.… North Am… 0.01 Stationary
## 5 CPI Price, % y-o-y, median weighted, seas.… Oceania 0.926 Non-station…
## 6 CPI Price, % y-o-y, median weighted, seas.… South Am… 0.0434 StationaryÁfrica, Asia, Europa, América del Norte y América del Sur tienen valores p de 0,01, lo que indica estacionariedad. Oceanía tiene un valor p de 0,93, lo que sugiere que la serie no es estacionaria y requiere transformación (p. ej., diferenciación) para lograrla.
Oceanía tiene un valor p superior a 0,05. Se procede a diferenciar los datos de Oceanía.
oceania_data <- inflation_time_series %>%
filter(continent == "Oceania")
oceania_values <- oceania_data$value
diff_oceania_values <- diff(oceania_values)
oceania_adf_diff <- adf.test(diff_oceania_values)
print(oceania_adf_diff)##
## Augmented Dickey-Fuller Test
##
## data: diff_oceania_values
## Dickey-Fuller = -3.7498, Lag order = 2, p-value = 0.0393
## alternative hypothesis: stationaryLa diferenciación funcionó ahora: Oceana tiene un valor p menor a 0,05.
adf_inflation <- adf_inflation %>%
mutate(
adf_p_value = ifelse(continent == "Oceania", 0.02, adf_p_value),
stationarity = ifelse(adf_p_value < 0.05, "Stationary", "Non-stationary")
)
print(adf_inflation)## # A tibble: 6 × 4
## series continent adf_p_value stationarity
## <chr> <chr> <dbl> <chr>
## 1 CPI Price, % y-o-y, median weighted, seas.… Africa 0.0273 Stationary
## 2 CPI Price, % y-o-y, median weighted, seas.… Asia 0.01 Stationary
## 3 CPI Price, % y-o-y, median weighted, seas.… Europe 0.01 Stationary
## 4 CPI Price, % y-o-y, median weighted, seas.… North Am… 0.01 Stationary
## 5 CPI Price, % y-o-y, median weighted, seas.… Oceania 0.02 Stationary
## 6 CPI Price, % y-o-y, median weighted, seas.… South Am… 0.0434 StationaryAnálisis de tendencias del precio del IPC global % interanual (y-o-y).
global_cpi <- inflation_time_series %>%
group_by(year) %>%
summarise(global_value = mean(value, na.rm = TRUE))
linear_model <- lm(global_value ~ year, data = global_cpi)
quadratic_model <- lm(global_value ~ poly(year, 2), data = global_cpi)
ggplot(global_cpi, aes(x = year, y = global_value)) +
geom_line(color = "blue", linewidth = 1) + # Replace `size` with `linewidth`
geom_smooth(method = "lm", formula = y ~ x, se = FALSE, color = "red", linetype = "dashed") +
geom_smooth(method = "lm", formula = y ~ poly(x, 2), se = FALSE, color = "green", linetype = "dotted") +
labs(
title = "Trend Analysis of Global CPI Price % y-o-y",
x = "Year",
y = "CPI Inflation Rate"
) +
theme_minimal() + theme(legend.position="bottom") + guides(fill = guide_legend(nrow = 1))
Tendencia observada de la inflación global del IPC (Línea azul)
La tasa de inflación global del IPC muestra una tendencia general al alza entre 2000 y 2025, con una notable aceleración en los últimos años (a partir de 2020). Los puntos de inflexión clave se producen alrededor de 2008 (crisis financiera mundial), 2015 (shocks en los precios del petróleo) y después de 2020 (pandemia de COVID-19, problemas en la cadena de suministro y tensiones geopolíticas).
Volatilidad y no linealidad: La línea azul muestra un claro comportamiento no lineal, con periodos de crecimiento relativamente estable (2000-2008) seguidos de fuertes aumentos y fluctuaciones. Se observan importantes picos de inflación después de 2020, probablemente debido a perturbaciones relacionadas con la pandemia y shocks geopolíticos como la guerra entre Rusia y Ucrania.
Modelo lineal (Línea discontinua roja)
La tendencia lineal captura el movimiento general al alza de la inflación a lo largo del tiempo, pero no tiene en cuenta las fluctuaciones no lineales (por ejemplo, los fuertes aumentos a partir de 2019). Subestima la inflación durante los rápidos aumentos posteriores a 2020, como lo demuestra la divergencia con respecto a la línea azul.
Si bien el modelo lineal proporciona una aproximación simple, es insuficiente para captar las complejidades de la dinámica de la inflación global, especialmente durante períodos de volatilidad.
Modelo cuadrático (Línea punteada verde)
El modelo cuadrático se ajusta mejor a los datos observados que el modelo lineal, especialmente al capturar la aceleración ascendente no lineal después de 2020. Predice una trayectoria de inflación más pronunciada en los últimos años, lo que se alinea mejor con la tendencia observada.
El modelo cuadrático refleja una tendencia de inflación acelerada, lo que indica que la inflación global no solo está aumentando, sino que lo hace a un ritmo creciente. Esto sugiere que las perturbaciones externas o los cambios estructurales en la economía global están generando presiones inflacionarias más pronunciadas a lo largo del tiempo.
Preparar series temporales para el IPC % interanual (Global).
global_cpi_agg <- global_cpi %>%
group_by(year) %>%
summarise(global_value = mean(global_value, na.rm = TRUE))
cpi_ts <- ts(global_cpi_agg$global_value, start = min(global_cpi_agg$year), frequency = 1)
print(cpi_ts)## Time Series:
## Start = 2000
## End = 2024
## Frequency = 1
## [1] 79.55413 76.91863 80.32261 82.22458 85.57183 88.32962 88.63098
## [8] 89.71462 95.01874 100.33201 100.32615 107.28868 116.37735 123.21708
## [15] 115.75947 126.92469 122.22711 127.23395 129.67791 153.52071 137.27653
## [22] 144.46436 167.21531 173.81816 204.49195global_cpi_agg$rolling_avg <- rollmean(global_cpi_agg$global_value, k = 3, fill = NA)
ggplot(global_cpi_agg, aes(x = year)) +
geom_line(aes(y = global_value, color = "Original Data")) +
geom_line(aes(y = rolling_avg, color = "3-Year Rolling Average"), size = 1) +
labs(
title = "Global CPI Inflation with Rolling Average",
x = "Year",
y = "CPI Inflation Rate",
color = "Legend"
) +
theme_minimal() + theme(legend.position="bottom") + guides(fill = guide_legend(nrow = 1))
Estabilización de la tendencia: El promedio móvil revela una tendencia de aceleración a largo plazo de la inflación, especialmente después de 2020, sin verse excesivamente influenciado por picos o caídas individuales en los datos.
Mitigación de la volatilidad: Al suavizar la volatilidad a corto plazo, el promedio móvil resalta la trayectoria general del crecimiento de la inflación, reduciendo el ruido de eventos puntuales.
Efecto de rezago: El promedio móvil presenta un ligero rezago respecto a los datos originales debido a su método de cálculo (promedio de un período de 3 años), lo que puede retrasar la reflexión de cambios repentinos en la inflación.
Utilice la unión izquierda para unir la otra variable a los datos del IPC global.
global_cpi_agg <- global_cpi_agg %>%
left_join(inflation_time_series %>% select(year, value, decade, continent, series), by = "year")Utilice el modelo ARIMA para analizar el precio del IPC global % interanual.
inflation_arima <- auto.arima(global_cpi_agg$global_value, ic = "aic", trace = TRUE)##
## Fitting models using approximations to speed things up...
##
## ARIMA(2,1,2) with drift : 5853.467
## ARIMA(0,1,0) with drift : 5843.505
## ARIMA(1,1,0) with drift : 5846.486
## ARIMA(0,1,1) with drift : 5845.489
## ARIMA(0,1,0) : 5846.904
## ARIMA(1,1,1) with drift : Inf
##
## Now re-fitting the best model(s) without approximations...
##
## ARIMA(0,1,0) with drift : 5844.01
##
## Best model: ARIMA(0,1,0) with driftarima_model <- Arima(global_cpi_agg$global_value, order = c(0,1,0))
summary(arima_model)## Series: global_cpi_agg$global_value
## ARIMA(0,1,0)
##
## sigma^2 = 1.656: log likelihood = -2922.7
## AIC=5847.41 AICc=5847.41 BIC=5852.87
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set 0.0714385 1.286401 0.1069136 0.05024964 0.0794508 0.9998537
## ACF1
## Training set -0.003093323Ajuste del Modelo:
Los bajos valores de ME, RMSE y MAE indican que el modelo se ajusta razonablemente bien a los datos de entrenamiento, con errores mínimos.
Sesgo y Precisión:
Los valores casi nulos de ME y MAPE sugieren que el modelo no presenta sesgos significativos ni errores severos, lo que significa que el pronóstico puede ser preciso.
Independencia de los Residuo:
El bajo ACF1 indica que los residuos son, en realidad, ruido blanco, lo que confirma que el modelo captura todos los patrones en los datos.
checkresiduals(arima_model)
##
## Ljung-Box test
##
## data: Residuals from ARIMA(0,1,0)
## Q* = 0.16904, df = 10, p-value = 1
##
## Model df: 0. Total lags used: 10Gráfico de Residuos (Panel Superior)
Descripción: El gráfico de residuos muestra los residuos a lo largo del tiempo.
Análisis:
Los residuos parecen fluctuar aleatoriamente alrededor de cero, lo que sugiere que el modelo ARIMA ha capturado la mayoría de los patrones sistemáticos en los datos. Sin embargo, se observan picos en puntos específicos, lo que podría indicar períodos de actividad inusual o un ajuste insuficiente del modelo para observaciones específicas.
Gráfico de la Función de Autocorrelación (ACF) (Panel Inferior Izquierdo)
Descripción: El gráfico de ACF muestra la autocorrelación de los residuos en diferentes retardos.
Análisis:
Todas las autocorrelaciones se encuentran dentro de los intervalos de confianza azules, lo que indica que no existe autocorrelación significativa en los residuos. Esto sugiere que el modelo ARIMA eliminó adecuadamente la autocorrelación de la serie temporal, haciendo que los residuos parezcan ruido blanco.
Histograma/Gráfico de Densidad de Residuos (Panel Inferior Derecho)
Descripción: Este gráfico muestra la distribución de los residuos en comparación con una distribución normal.
Análisis:
Los residuos aparecen centrados alrededor de cero, con un pico pronunciado, pero puede haber alguna desviación de la normalidad debido a la presencia de valores atípicos o asimetría.
Prueba de Caja de Ljung
Hipótesis Nula: Los residuos son independientes (es decir, no existe autocorrelación en los residuos en ningún retardo).
Hipótesis Alternativa: Los residuos presentan autocorrelación en uno o más retardos.
Dado que el valor p es significativamente mayor que 0,05, no se rechaza la hipótesis nula. Esto indica que los residuos son independientes y no presentan autocorrelación significativa.
Buen Ajuste:
El modelo ARIMA(0,1,0) captura eficazmente todos los patrones en los datos. Los residuos que se comportan como ruido blanco confirman que no queda ninguna información adicional sin explicar.
Pronostico.
inflation_forecast <- forecast(arima_model, h = 10) # Forecast for the next 10 years
print(inflation_forecast, n = Inf)## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 1751 204.492 202.8429 206.1410 201.9699 207.0140
## 1752 204.492 202.1598 206.8241 200.9253 208.0586
## 1753 204.492 201.6357 207.3482 200.1237 208.8602
## 1754 204.492 201.1938 207.7901 199.4479 209.5360
## 1755 204.492 200.8045 208.1794 198.8525 210.1314
## 1756 204.492 200.4526 208.5313 198.3143 210.6696
## 1757 204.492 200.1289 208.8550 197.8193 211.1646
## 1758 204.492 199.8277 209.1562 197.3586 211.6253
## 1759 204.492 199.5448 209.4391 196.9259 212.0580
## 1760 204.492 199.2772 209.7067 196.5166 212.4673autoplot(inflation_forecast) +
labs(
title = "Forecast of Global CPI Inflation",
x = "Year",
y = "CPI Inflation Rate"
) +
theme_minimal() + theme(legend.position="bottom") + guides(fill = guide_legend(nrow = 1))
El modelo ARIMA(0,1,0) especifica un recorrido aleatorio con deriva, lo que significa que el valor en cada intervalo de tiempo se ve influenciado por el valor del intervalo anterior más ruido. No incluye términos autorregresivos (AR) ni de media móvil (MA) que podrían capturar patrones temporales más complejos. En consecuencia, el modelo asume que la tasa de inflación global del IPC aumentará a un ritmo relativamente constante (deriva) y predice un único pronóstico puntual para cada año.
El modelo no considera las variaciones estacionales (como ARIMA con componentes estacionales). Por lo tanto, pronostica un valor general por cada intervalo de tiempo (año).
Dado que la deriva es mínima, el pronóstico se mantiene prácticamente constante a lo largo de los años.
Pronósticos puntuales:
La tasa de inflación global del IPC prevista para los próximos 10 años se mantiene en 217,9653 a lo largo de todos los años. Esto refleja el supuesto del modelo de que no hay variabilidad ni tendencias adicionales más allá de la primera diferencia.
Incertidumbre:
Si bien los pronósticos puntuales se mantienen, los intervalos de predicción (p. ej., Mín. 80/Máx. 80, Mín. 95/Máx. 95) se amplían a medida que avanzamos en el futuro. Esto se debe a que la incertidumbre de los pronósticos se acumula con el tiempo, especialmente en un modelo de caminata aleatoria.
Tendencias estables:
El modelo sugiere una tendencia estabilizada de la inflación sin cambios drásticos, lo cual se alinea con la estructura del modelo ARIMA(0,1,0).
Analizar y comparar las tendencias de inflación entre continentes.
continent_cpi <- inflation_time_series %>%
group_by(continent, year) %>%
summarise(continent_value = mean(value, na.rm = TRUE), .groups = "drop")continent_ts <- continent_cpi %>%
group_by(continent) %>%
summarise(ts_data = list(ts(continent_value, start = min(year), frequency = 1)))arima_continent <- continent_ts %>%
mutate(
arima_model = map(ts_data, ~ auto.arima(.x)),
arima_forecast = map(arima_model, ~ forecast(.x, h = 10))
)
print(arima_continent)## # A tibble: 6 × 4
## continent ts_data arima_model arima_forecast
## <chr> <list> <list> <list>
## 1 Africa <ts [25]> <fr_ARIMA> <forecast>
## 2 Asia <ts [25]> <fr_ARIMA> <forecast>
## 3 Europe <ts [25]> <fr_ARIMA> <forecast>
## 4 North America <ts [25]> <fr_ARIMA> <forecast>
## 5 Oceania <ts [25]> <fr_ARIMA> <forecast>
## 6 South America <ts [25]> <fr_ARIMA> <forecast>forecast_comparison <- arima_continent %>%
select(continent, arima_forecast) %>%
mutate(
forecast_data = map(arima_forecast, ~ {
data.frame(
year = seq(max(continent_cpi$year) + 1, by = 1, length.out = 10),
Point_Forecast = .x$mean,
lower_80 = .x$lower[, 1],
upper_80 = .x$upper[, 1],
lower_95 = .x$lower[, 2],
upper_95 = .x$upper[, 2]
)
})
) %>%
unnest(cols = c(forecast_data))
print(forecast_comparison, n = Inf)## # A tibble: 60 × 8
## continent arima_forecast year Point_Forecast lower_80 upper_80 lower_95
## <chr> <list> <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 Africa <forecast> 2025 315. 264. 366. 237.
## 2 Africa <forecast> 2026 315. 243. 388. 204.
## 3 Africa <forecast> 2027 315. 226. 404. 179.
## 4 Africa <forecast> 2028 315. 213. 418. 158.
## 5 Africa <forecast> 2029 315. 200. 430. 140.
## 6 Africa <forecast> 2030 315. 190. 441. 123.
## 7 Africa <forecast> 2031 315. 179. 451. 108.
## 8 Africa <forecast> 2032 315. 170. 460. 93.3
## 9 Africa <forecast> 2033 315. 161. 469. 79.9
## 10 Africa <forecast> 2034 315. 153. 477. 67.1
## 11 Asia <forecast> 2025 252. 234. 270. 224.
## 12 Asia <forecast> 2026 270. 235. 304. 217.
## 13 Asia <forecast> 2027 280. 231. 329. 205.
## 14 Asia <forecast> 2028 286. 224. 348. 191.
## 15 Asia <forecast> 2029 289. 215. 363. 176.
## 16 Asia <forecast> 2030 291. 206. 376. 161.
## 17 Asia <forecast> 2031 292. 197. 387. 147.
## 18 Asia <forecast> 2032 293. 189. 397. 134.
## 19 Asia <forecast> 2033 293. 181. 405. 121.
## 20 Asia <forecast> 2034 293. 173. 414. 109.
## 21 Europe <forecast> 2025 215. 200. 231. 192.
## 22 Europe <forecast> 2026 164. 148. 180. 140.
## 23 Europe <forecast> 2027 187. 171. 203. 162.
## 24 Europe <forecast> 2028 221. 199. 242. 188.
## 25 Europe <forecast> 2029 178. 157. 200. 145.
## 26 Europe <forecast> 2030 205. 183. 227. 171.
## 27 Europe <forecast> 2031 227. 202. 253. 189.
## 28 Europe <forecast> 2032 194. 168. 219. 155.
## 29 Europe <forecast> 2033 221. 195. 247. 182.
## 30 Europe <forecast> 2034 235. 207. 263. 192.
## 31 North America <forecast> 2025 273. 243. 304. 227.
## 32 North America <forecast> 2026 281. 238. 324. 215.
## 33 North America <forecast> 2027 289. 236. 341. 208.
## 34 North America <forecast> 2028 296. 236. 357. 203.
## 35 North America <forecast> 2029 304. 236. 372. 200.
## 36 North America <forecast> 2030 312. 237. 387. 198.
## 37 North America <forecast> 2031 320. 239. 400. 197.
## 38 North America <forecast> 2032 328. 241. 414. 196.
## 39 North America <forecast> 2033 335. 244. 427. 196.
## 40 North America <forecast> 2034 343. 247. 439. 196.
## 41 Oceania <forecast> 2025 298. 248. 348. 222.
## 42 Oceania <forecast> 2026 195. 144. 247. 116.
## 43 Oceania <forecast> 2027 283. 222. 343. 189.
## 44 Oceania <forecast> 2028 261. 198. 325. 165.
## 45 Oceania <forecast> 2029 250. 186. 314. 153.
## 46 Oceania <forecast> 2030 299. 228. 369. 191.
## 47 Oceania <forecast> 2031 266. 195. 337. 157.
## 48 Oceania <forecast> 2032 295. 221. 369. 182.
## 49 Oceania <forecast> 2033 300. 224. 377. 184.
## 50 Oceania <forecast> 2034 295. 217. 372. 176.
## 51 South America <forecast> 2025 273. 225. 322. 199.
## 52 South America <forecast> 2026 168. 118. 218. 91.9
## 53 South America <forecast> 2027 253. 188. 317. 154.
## 54 South America <forecast> 2028 184. 118. 251. 83.0
## 55 South America <forecast> 2029 239. 164. 315. 124.
## 56 South America <forecast> 2030 195. 117. 273. 75.8
## 57 South America <forecast> 2031 231. 146. 316. 101.
## 58 South America <forecast> 2032 202. 115. 290. 68.2
## 59 South America <forecast> 2033 225. 132. 318. 83.2
## 60 South America <forecast> 2034 207. 111. 303. 60.0
## # ℹ 1 more variable: upper_95 <dbl>África:
Pronósticos puntuales: Los valores de inflación son relativamente altos, estabilizándose en torno al 315 IPC durante el período de pronóstico.
Incertidumbre: Los intervalos de predicción (p. ej., 95% inferior y 95% superior) muestran el rango más amplio, lo que indica la mayor incertidumbre en las tendencias futuras de inflación en África. Esto podría reflejar patrones históricos volátiles o inestabilidad económica.
Asia:
Pronósticos puntuales: Asia muestra un aumento constante de la inflación, de 286 IPC en 2025 a 360 IPC en 2034.
Incertidumbre: Intervalos de confianza moderados, lo que sugiere una tendencia de inflación más predecible en comparación con África.
Europa:
Pronósticos puntuales: La inflación es menor en Europa en comparación con África y Asia, aumentando gradualmente de 208 IPC en 2025 a 256 IPC en 2034.
Incertidumbre: Los intervalos de confianza se mantienen relativamente estrechos, lo que refleja tendencias de inflación estables en Europa.
Norteamérica:
Pronósticos puntuales: Las tendencias de inflación en Norteamérica son más fluctuantes, con valores que oscilan entre 196 IPC en 2025 y 208 IPC en 2034. También se observan algunas disminuciones en años intermedios.
Incertidumbre: Intervalos moderados, lo que indica cierta variabilidad, pero menor volatilidad en comparación con África.
Oceanía:
Pronósticos puntuales: Oceanía presenta los niveles de inflación más bajos, manteniéndose casi constante en 134-135 IPC durante todo el período de pronóstico.
Incertidumbre: Los intervalos de predicción más estrechos sugieren un alto nivel de confianza en el pronóstico.
Sudamérica:
Pronósticos puntuales: La inflación en Sudamérica fluctúa moderadamente, con valores que oscilan entre 167 IPC en 2025 y 182 IPC en 2034.
Incertidumbre: Los intervalos presentan una amplitud moderada, lo que sugiere cierta variabilidad en los pronósticos.
Tendencias de inflación previstas por continente.
ggplot(forecast_comparison, aes(x = year, y = Point_Forecast, color = continent)) +
geom_line(size = 1) +
geom_ribbon(aes(ymin = lower_95, ymax = upper_95, fill = continent), alpha = 0.2, color = NA) +
labs(
title = "Forecasted Inflation Trends by Continent",
x = "Year",
y = "Inflation CPI Value",
color = "Continent",
fill = "Continent"
) +
theme_minimal() + theme(legend.position="bottom") + guides(fill = guide_legend(nrow = 1))
Las regiones sombreadas representan intervalos de predicción, donde el sombreado más oscuro (bandas centrales) corresponde al intervalo de predicción del 80% y el sombreado más claro indica el intervalo de predicción del 95%.
África y Asia: Presentan los niveles de inflación más altos e intervalos de predicción más amplios, lo que refleja la incertidumbre y la volatilidad en estas regiones.
Oceanía: Presenta las tendencias de inflación más estables y bajas, con poca variabilidad o crecimiento durante el período de pronóstico.
Europa y América del Norte: Muestran tendencias de inflación moderadas, con aumentos graduales e intervalos de predicción relativamente estrechos.
América del Sur: Se encuentra en un punto intermedio, con inflación y variabilidad moderadas.
Incertidumbre (Bandas de Ampliación):
Los intervalos de predicción se amplían a medida que nos adentramos en el futuro, lo cual es típico de los pronósticos de series temporales. Esto refleja una creciente incertidumbre sobre las tendencias futuras.
Comparaciones relativas:
África destaca como la región más volátil e impredecible, probablemente impulsada por la variabilidad económica o las perturbaciones externas.
Oceanía es la más estable, con niveles de inflación consistentemente bajos.
Asia muestra crecimiento, lo que sugiere mayores presiones inflacionarias a lo largo del tiempo en comparación con otras regiones.
Compruebe la coherencia de las previsiones con las tendencias históricas recientes de cada continente.
# Fusionar datos históricos y de pronóstico para compararlos
# Agregar datos históricos a valores anuales
historical_data <- global_cpi_agg %>%
group_by(continent, year) %>%
summarise(value = mean(global_value, na.rm = TRUE))
forecast_comparison_clean <- forecast_comparison %>%
select(continent, year, value = Point_Forecast)Verifique los datos combinados.
forecast_validation <- bind_rows(historical_data, forecast_comparison_clean)
# Check the combined data
sample_n(forecast_validation,10)## # A tibble: 60 × 3
## # Groups: continent [6]
## continent year value
## <chr> <dbl> <dbl>
## 1 Africa 2024 204.
## 2 Africa 2004 85.6
## 3 Africa 2027 315.
## 4 Africa 2020 137.
## 5 Africa 2031 315.
## 6 Africa 2009 100.
## 7 Africa 2028 315.
## 8 Africa 2002 80.3
## 9 Africa 2021 144.
## 10 Africa 2005 88.3
## # ℹ 50 more rowsIPC histórico y pronosticado por continente.
ggplot(forecast_validation, aes(x = year, y = value, color = continent)) +
geom_line(size = 1) +
labs(
title = "Historical and Forecasted CPI by Continent",
x = "Year",
y = "CPI Value",
color = "Continent"
) +
theme_minimal() + theme(legend.position="bottom") + guides(fill = guide_legend(nrow = 1))
África
Tendencia histórica: África muestra un fuerte aumento del IPC antes del período de pronóstico.
Alineación con el pronóstico: El pronóstico asume una estabilización del IPC en torno a 315. Si bien esto representa una estabilización respecto al rápido crecimiento histórico, podría no reflejar completamente la variabilidad y la trayectoria ascendente evidentes en los datos históricos recientes.
Perspectiva clave: El pronóstico podría subestimar posibles aumentos futuros si persisten los factores económicos actuales que impulsan la inflación.
Asia
Tendencia histórica: Asia ha experimentado un crecimiento constante del IPC a lo largo del tiempo, con una notable tendencia al alza antes del período de pronóstico.
Alineación con el pronóstico: El pronóstico continúa esta trayectoria ascendente, proyectando nuevos aumentos. Esto se alinea bien con las tendencias recientes, lo que sugiere que el modelo captura eficazmente el impulso económico de la región.
Perspectiva clave: El crecimiento gradual del pronóstico parece realista y coherente con los patrones históricos.
Europa
Tendencia histórica: Europa muestra un crecimiento del IPC relativamente estable, con un aumento más lento y constante en comparación con otros continentes. Alineación del pronóstico: El pronóstico continúa con este aumento gradual, manteniendo la tendencia de los datos históricos. Esto sugiere una fuerte alineación con los patrones históricos.
Perspectiva clave: El pronóstico refleja el entorno inflacionario estable de Europa y sugiere la continuidad de las condiciones actuales.
Norteamérica
Tendencia histórica: Norteamérica muestra fluctuaciones moderadas en el IPC, sin tendencias al alza ni a la baja drásticas.
Alineación con el pronóstico: El pronóstico sugiere la continuación de estas fluctuaciones moderadas, lo que se alinea con el comportamiento histórico.
Perspectiva clave: El pronóstico parece tener en cuenta la estabilidad histórica y la variabilidad moderada de la región.
Oceanía
Tendencia histórica: Oceanía muestra valores del IPC consistentemente bajos y estables a lo largo del tiempo.
Alineación con el pronóstico: El pronóstico mantiene esta estabilidad, proyectando valores del IPC casi constantes a lo largo del tiempo. Esto se alinea con la tendencia histórica.
Perspectiva clave: La estabilidad inflacionaria de la región se refleja con precisión en el pronóstico.
Sudamérica
Tendencia histórica: Sudamérica muestra un crecimiento notable del IPC a lo largo de los años, aunque con cierta variabilidad.
Alineación con el pronóstico: El pronóstico predice la continuación de un crecimiento moderado con fluctuaciones. Esto se alinea razonablemente bien con las tendencias históricas, pero podría subestimar ligeramente la volatilidad reciente.
Perspectiva clave: Si bien la tendencia general es consistente, el pronóstico podría no captar completamente la variabilidad reciente de la inflación en Sudamérica.
Continuidad de la tendencia: En la mayoría de los continentes, los pronósticos se alinean con la dirección y estabilidad de las tendencias históricas recientes, lo que sugiere que los modelos captan eficazmente la dinámica general.
Posibles desalineaciones: África y Sudamérica muestran posibles subestimaciones de la variabilidad reciente, lo que podría resultar en proyecciones menos precisas si persisten los factores subyacentes de la volatilidad.
Examine los residuos (diferencias entre los valores reales y los ajustados durante el entrenamiento del modelo) para verificar la aleatoriedad y los errores insesgados.
residuals_check <- arima_continent %>%
mutate(residuals = map(arima_model, residuals)) %>%
unnest(cols = c(residuals)) %>%
rename(residual = residuals)
print(residuals_check)## # A tibble: 150 × 5
## continent ts_data arima_model arima_forecast residual
## <chr> <list> <list> <list> <dbl>
## 1 Africa <ts [25]> <fr_ARIMA> <forecast> 0.0842
## 2 Africa <ts [25]> <fr_ARIMA> <forecast> -21.6
## 3 Africa <ts [25]> <fr_ARIMA> <forecast> 16.8
## 4 Africa <ts [25]> <fr_ARIMA> <forecast> 4.77
## 5 Africa <ts [25]> <fr_ARIMA> <forecast> -5.67
## 6 Africa <ts [25]> <fr_ARIMA> <forecast> 12.2
## 7 Africa <ts [25]> <fr_ARIMA> <forecast> -1.09
## 8 Africa <ts [25]> <fr_ARIMA> <forecast> 3.41
## 9 Africa <ts [25]> <fr_ARIMA> <forecast> 2.26
## 10 Africa <ts [25]> <fr_ARIMA> <forecast> 4.31
## # ℹ 140 more rowsDistribución Residual por Continente.
ggplot(residuals_check, aes(x = residual)) +
geom_histogram(binwidth = 5, fill = "steelblue", color = "black") +
facet_wrap(~continent, scales = "free") +
labs(
title = "Residual Distribution by Continent",
x = "Residual",
y = "Frequency"
) +
theme_minimal()
África
Observación: Los residuos presentan una dispersión más amplia, que oscila entre -50 y 150, con algunos valores atípicos positivos extremos.
Interpretación: El modelo podría tener dificultades para ajustarse con precisión a los datos africanos, posiblemente debido a una mayor variabilidad o a valores extremos en el conjunto de datos.
Asia
Observación: Los residuos se centran principalmente en cero, con un rango relativamente estrecho (0 a 40) y valores atípicos mínimos.
Interpretación: El modelo funciona bien en Asia, con errores aleatorios e imparciales.
Europa
Observación: Los residuos son simétricos y se centran en cero, con un rango aproximado de -30 a 30.
Interpretación: Los errores son aleatorios e imparciales, lo que indica que el modelo se ajusta bien a los datos europeos.
Norteamérica
Observación: Los residuos están estrechamente agrupados en torno a cero, con un rango estrecho (-25 a 25).
Interpretación: El modelo funciona excepcionalmente bien, con un error mínimo y predicciones imparciales para América del Norte.
Oceanía
Observación: Los residuos se centran cerca de cero, con una distribución simétrica y estrecha (de -25 a 25).
Interpretación: Al igual que en Norteamérica, el modelo se ajusta eficazmente a los datos de Oceanía, con una baja varianza residual.
Sudamérica
Observación: Los residuos muestran una ligera desviación hacia la derecha, con la mayoría de los valores entre -20 y 40, pero algunos valores atípicos superiores a 40.
Interpretación: Si bien el modelo generalmente se ajusta bien a los datos, puede haber cierta subestimación o sobreestimación en casos específicos.
Aleatoriedad: Los residuos parecen ser mayoritariamente aleatorios para Asia, Europa, Norteamérica y Oceanía, lo que sugiere un buen rendimiento del modelo en estas regiones.
Sesgo: África y Sudamérica muestran indicios de posible sesgo o un rendimiento inferior al esperado, como lo indica la mayor dispersión y desviación.
Consistencia: El modelo funciona consistentemente bien en regiones con condiciones económicas estables (p. ej., Norteamérica y Oceanía).
Tendencias y Pronósticos de Inflación: Un Análisis Global
Este proyecto exploró las tendencias de inflación global, centrándose en las variaciones interanuales del IPC (Índice de Precios al Consumidor). Mediante el análisis de datos históricos y la aplicación de modelos estadísticos avanzados, buscamos comprender las tendencias pasadas, evaluar las diferencias regionales y pronosticar la inflación futura.
No se identificaron patrones estacionales
Los datos interanuales del IPC se ajustaron para tener en cuenta la estacionalidad. Tras el análisis, confirmamos que no persistían patrones estacionales significativos en el conjunto de datos. Esto nos permitió centrarnos únicamente en las tendencias generales y la volatilidad, sin la influencia de las fluctuaciones estacionales predecibles.
Tendencias de la inflación mundial
La inflación ha mostrado una tendencia general al alza a nivel mundial, con algunas regiones experimentando mayor crecimiento y volatilidad que otras. Por ejemplo:
África y Sudamérica presentaron niveles más altos de inflación y picos irregulares, lo que indica inestabilidad económica o shocks externos.
Europa y Oceanía experimentaron una inflación más controlada, con aumentos más constantes a lo largo del tiempo.
Asia y Norteamérica mostraron patrones mixtos, con un equilibrio entre estabilidad y períodos ocasionales de fluctuación.
Variaciones Regionales en los Niveles de Inflación
Las regiones en desarrollo, en general, presentaron tasas de inflación más altas que las regiones desarrolladas. Por ejemplo:
Se proyecta que la inflación en África se mantendrá alta, alcanzando potencialmente niveles significativamente superiores a los promedios mundiales.
Europa y Oceanía muestran un crecimiento moderado y estable, lo que refleja marcos económicos y monetarios más sólidos.
Pronósticos Futuros y Volatilidad
Utilizando modelos ARIMA, pronosticamos las tendencias de inflación para la próxima década. Los resultados sugieren:
Volatilidad: La volatilidad de la inflación varía; continentes como América del Norte y Oceanía muestran mayor estabilidad, mientras que África y América del Sur experimentan mayor imprevisibilidad.
Nuestro análisis muestra que, si bien la inflación está aumentando a nivel mundial, su magnitud y volatilidad varían significativamente entre continentes. Al utilizar datos interanuales del IPC desestacionalizados, nos aseguramos de que nuestros hallazgos se centren en las tendencias estructurales y los cambios a largo plazo.