PROYECTO FINAL SERIES DE TIEMPO
JONATHAN EMILIANO SANTIAGO
2022-02-06
#EN PRIMER LUGAR DESCARGO LAS LIBRERIAS QUE HEMOS USADO A LO LARGO DEL CURSO, LAS CUALES PUEDEN AYUDARNOS EN EL PROYECTO PRECIO DE PETROLEO Y PRECIO DE ACERO.
#LAS LIBRERIAS SE INSTALAN Y LUEGO SE HABILITAN
library(readxl)
library(xts)## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numericlibrary(zoo)
library(tseries)## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoolibrary(forecast)
library(astsa)##
## Attaching package: 'astsa'## The following object is masked from 'package:forecast':
##
## gaslibrary(lmtest)
library(quantmod)## Loading required package: TTRgetSymbols(Symbols = "DCOILWTICO", src = "FRED")## [1] "DCOILWTICO"#EN UN PRINICPIO PENSE DESCARGAR LA BASE DE DATOS Y CONVERTIRLO EN EXCEL PARA LOGRAR EXPORTAR A R. PERO PUDE EXTRAERLOS DE FRED.
doil = DCOILWTICO
doil.xts <- to.monthly(doil,indexAt = "firstof")## Warning in to.period(x, "months", indexAt = indexAt, name = name, ...): missing
## values removed from data#USAMOS TS CON EL FIN DE CONVERTIR LOS DATOS (OBJETOS) EN SERIE TEMPORAL. #EL PROYECTO MENCIONA QUE UTILICEMOS LOS DATOS DE LOS ULTIMOS 5 AÑOS, PERO AL COLOCAL QUE EMPIEZA EN 2015 ME LANZA PRODUCTOS HASTA 2046. AHORA SOLO NECESITAMOS HASTA EL AÑO 2022. POR LO CUAL SE EXPORTAREMOS TODA LA DATA.
doil<-ts(coredata(doil.xts$doil.Close),start=c(1986,1),frequency=12)
doil## Jan Feb Mar Apr May Jun Jul Aug Sep Oct
## 1986 18.95 13.23 10.25 13.38 14.30 12.80 11.23 15.93 14.70 15.25
## 1987 18.73 16.45 18.82 18.76 19.36 20.22 21.43 19.76 19.62 19.96
## 1988 16.97 15.98 17.09 18.10 17.54 15.20 16.37 15.19 13.33 13.54
## 1989 17.00 18.21 20.27 20.38 19.93 20.29 18.33 18.83 20.15 19.88
## 1990 22.69 21.55 20.34 18.50 17.47 17.05 20.57 27.45 39.53 35.31
## 1991 21.90 19.28 19.63 20.99 21.16 20.56 21.70 22.28 22.25 23.29
## 1992 18.93 18.69 19.49 20.88 22.13 21.84 21.83 21.46 21.83 20.68
## 1993 20.27 20.53 20.44 20.54 20.04 18.82 17.94 18.24 18.72 16.97
## 1994 15.24 14.50 14.78 16.92 18.30 19.37 20.30 17.60 18.36 18.16
## 1995 18.48 18.52 19.18 20.36 18.88 17.38 17.62 17.89 17.54 17.67
## 1996 17.76 19.59 21.43 20.95 19.77 20.92 20.46 22.25 24.20 23.25
## 1997 24.15 20.30 20.35 20.20 21.00 19.82 20.19 19.66 21.13 21.10
## 1998 17.21 15.44 15.75 15.56 15.21 14.30 14.27 13.29 16.19 14.48
## 1999 12.81 12.31 16.66 18.69 16.85 19.33 20.52 22.15 24.54 21.79
## 2000 27.65 30.57 26.86 25.71 29.03 32.44 27.50 33.09 30.87 32.70
## 2001 28.62 27.35 26.37 28.48 28.39 26.37 26.70 26.65 23.44 21.20
## 2002 19.71 21.78 26.21 27.32 25.37 26.79 27.02 28.97 30.59 27.18
## 2003 33.51 36.76 31.14 26.09 29.56 30.15 30.56 31.76 29.19 29.24
## 2004 33.16 36.08 35.75 37.31 39.90 36.92 43.72 42.23 49.56 51.78
## 2005 48.25 51.75 55.31 49.20 52.08 56.63 60.71 68.63 66.21 59.80
## 2006 67.86 61.37 66.25 71.80 71.42 73.94 74.56 70.38 62.90 58.72
## 2007 58.17 61.78 65.94 65.78 64.02 70.47 78.20 73.98 81.64 94.16
## 2008 91.67 101.78 101.54 113.70 127.35 139.96 124.17 115.55 100.70 68.10
## 2009 41.73 44.15 49.64 50.35 66.31 69.82 69.26 69.97 70.46 77.04
## 2010 72.85 79.72 83.45 86.07 74.00 75.59 78.85 71.93 79.95 81.45
## 2011 90.99 97.10 106.19 113.39 102.70 95.30 95.68 88.81 78.93 93.19
## 2012 98.46 107.08 103.03 104.89 86.52 85.04 88.08 96.47 92.18 86.23
## 2013 97.65 92.03 97.24 93.22 91.93 96.36 105.10 107.98 102.36 96.29
## 2014 97.55 102.88 101.57 100.07 103.40 106.07 98.23 97.86 91.17 80.53
## 2015 47.79 49.84 47.72 59.62 60.25 59.48 47.11 49.20 45.06 46.60
## 2016 33.66 32.74 36.94 45.98 49.10 48.27 41.54 44.68 47.72 46.83
## 2017 52.75 54.00 50.54 49.31 48.29 46.02 50.21 47.26 51.67 54.36
## 2018 64.82 61.43 64.87 68.56 66.98 74.13 69.88 69.84 73.16 65.31
## 2019 53.84 57.21 60.19 63.83 53.49 58.20 58.53 55.07 54.09 54.02
## 2020 51.58 44.83 20.51 19.23 35.57 39.27 40.10 42.61 40.05 35.64
## 2021 52.16 61.55 59.19 63.50 66.31 73.52 73.93 68.43 75.22 83.50
## 2022 89.16 96.13 100.53 104.59 114.38 120.92
## Nov Dec
## 1986 15.00 17.93
## 1987 18.52 16.74
## 1988 15.42 17.12
## 1989 19.87 21.84
## 1990 29.08 28.48
## 1991 21.48 19.15
## 1992 19.91 19.49
## 1993 15.36 14.19
## 1994 18.06 17.77
## 1995 18.27 19.54
## 1996 23.70 25.90
## 1997 19.13 17.65
## 1998 11.37 12.14
## 1999 24.87 25.76
## 2000 33.61 26.72
## 2001 19.46 19.96
## 2002 26.87 31.21
## 2003 30.33 32.51
## 2004 49.16 43.36
## 2005 57.33 61.06
## 2006 62.97 60.85
## 2007 88.60 95.95
## 2008 55.21 44.60
## 2009 77.19 79.39
## 2010 84.12 91.38
## 2011 100.36 98.83
## 2012 88.54 91.83
## 2013 92.55 98.17
## 2014 65.94 53.45
## 2015 40.43 37.13
## 2016 49.41 53.75
## 2017 57.40 60.46
## 2018 50.78 45.15
## 2019 58.12 61.14
## 2020 45.20 48.35
## 2021 66.14 75.33
## 2022plot(doil)
#UNA VEZ TENIENDO EN R LOS DATOS DE TIEMPO (X) Y PRECIO (Y). PODEMOS
IMPRIMIR LA GRAFICA PARA QUE HAYA UNA MEJOR VIZUALIZACIÓN DE LOS DATOS.
VEMOS QUE TIENE TENDENCIA A LA ALZA, ALCANZANDO SU PUNTO MAXIMO HASTA EL
2006 Y CAE EN LOS PROXIMOS AÑOS, HASTA EL 2010. VUELVE A CAER EN 2019,
COMENZANDO A RECUPERARSE EN 2021
logdoil= log(doil)plot(logdoil)
dlog = diff(logdoil,lag=12)
plot(dlog)
#RECONOCEMOS COMO UNA SERIE NO ESTACIONARIA AQUELLA QUE TIENE VARIABLES
QUE PUEDEN CRECER O DECRECER A LO LARGO DEL TIEMPO. DE ESTA MANERA
NECESITAMOS CONVERTIR LA SERIE A UNA ESTACIONARIA.
#AHORA LOS DATOS SE VEN DE MÁS CONTANTE, COMO LO VIMOS EN LAS PRIMERAS CLASES, CON UNA MEDIA SIMILAR Y UNA VARIANZA SIMILAR. PERO PARA COMPROBAR QUE TODO ESTA EN ORDEN NECESITAMOS HACER UNA PRUEBA FULLER. PARA CONFIRMAR O NEGAR QUE HAY DATOS ESTACIONARIOS.
adf.test(dlog, k=1)## Warning in adf.test(dlog, k = 1): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: dlog
## Dickey-Fuller = -5.6563, Lag order = 1, p-value = 0.01
## alternative hypothesis: stationary#PARA QUE LA PRUEBA SEA ACEPTADA ES NECESARIO QUE LOS VALORES P-VALUE: SERAN MENOR A .05, EN ESTE CASO ES .01 #LA PRUEBA FULLER ES ACEPTADA, LOS DATOS SON ESTACIONARIOS.
modelo1 <- auto.arima(doil,
lambda = 0,
d=0,D=1,
max.p=2, max.q=1,
max.P = 1,max.Q = 1
)
coeftest(modelo1)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ar1 1.0848030 0.0478216 22.6844 < 2.2e-16 ***
## ar2 -0.1818902 0.0480468 -3.7857 0.0001533 ***
## sar1 -0.4641317 0.0449958 -10.3150 < 2.2e-16 ***
## drift 0.0042193 0.0037092 1.1375 0.2553226
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1modelo1$aic## [1] -504.3253#POR CADA VALOR DE PERIODO, EN UN VARIABLE DE 1% AFECTARA 1.08% DE CRECIMIENTO EN EL VALOR DEL MES. #POR CADA VALOR DE DOS PERIODOS, EN UNA VARIABLE DE 1% AFECTARA EL NEGTIVAMENTE .18% EN EL VALOR DE DOS MESES. #POR OTRO LADO, EL DRIFT NO ES DE ALTO IMPACTO YA QUE ES MENOR A .05, SIENDO ESTE .004
ACERO DATOS Y EVALUACIÓN
getSymbols(Symbols = "PCU3312213312211", src = "FRED")## [1] "PCU3312213312211"#SE EXTRAEN LOS DATOS DE LA MISMA PLATAFORMA EN EL MISMO PERIODO DE TIEMPO
acero = PCU3312213312211
acero1.xts <- PCU3312213312211[index(doil.xts)]
head(acero1.xts)## PCU3312213312211
## 1986-01-01 104.8
## 1986-02-01 104.4
## 1986-03-01 104.4
## 1986-04-01 104.8
## 1986-05-01 105.4
## 1986-06-01 106.5dataacero<-ts(coredata(acero1.xts$PCU3312213312211),start=c(1986,1),frequency=12)
dataacero## Jan Feb Mar Apr May Jun Jul Aug Sep
## 1986 104.800 104.400 104.400 104.800 105.400 106.500 106.400 106.500 106.500
## 1987 106.400 106.600 106.600 106.200 106.200 107.100 107.900 108.000 109.100
## 1988 114.400 116.500 117.100 120.500 124.800 127.100 129.600 130.100 129.800
## 1989 128.000 129.500 130.300 131.000 126.100 124.900 124.600 123.700 123.200
## 1990 122.000 120.900 120.800 120.700 120.500 121.000 121.100 121.100 121.000
## 1991 120.800 120.800 120.100 120.200 120.000 120.300 119.800 119.700 119.600
## 1992 119.400 118.700 118.700 118.300 118.200 118.200 118.200 118.000 118.100
## 1993 118.300 118.600 120.000 120.400 121.700 121.700 122.100 122.400 122.000
## 1994 123.200 123.300 123.200 123.700 125.100 125.300 126.500 127.700 127.900
## 1995 129.500 131.100 131.400 130.600 130.800 131.100 132.400 132.500 130.400
## 1996 129.500 126.700 121.400 122.300 122.100 121.800 121.700 124.300 124.300
## 1997 124.100 124.000 124.300 124.500 124.700 124.400 124.600 124.600 124.400
## 1998 122.900 122.400 122.400 122.100 121.800 121.800 117.600 117.500 117.400
## 1999 114.400 114.300 114.200 114.000 114.000 113.700 113.500 113.800 115.700
## 2000 117.500 119.000 119.400 120.800 121.200 120.600 121.200 120.100 119.100
## 2001 113.100 112.000 111.900 111.300 111.100 110.500 110.000 109.300 109.700
## 2002 107.500 109.800 112.900 116.400 122.300 124.800 125.400 125.900 123.100
## 2003 124.400 124.500 124.300 124.400 124.000 123.800 124.500 125.000 125.000
## 2004 132.700 144.300 150.800 156.600 156.900 154.900 151.000 161.500 168.700
## 2005 169.100 173.800 173.800 172.200 170.800 161.000 156.600 150.500 160.600
## 2006 161.000 160.900 161.900 163.800 166.800 170.300 171.900 171.800 172.100
## 2007 162.500 163.900 165.900 167.200 166.900 165.200 163.800 163.200 162.200
## 2008 172.900 177.200 185.400 204.200 223.100 237.500 248.300 250.700 245.900
## 2009 201.500 196.200 186.800 180.800 171.900 166.800 173.800 178.800 185.500
## 2010 183.200 188.000 189.900 192.200 194.000 193.700 190.700 186.000 182.900
## 2011 186.800 197.700 207.500 221.300 225.700 215.700 211.400 212.300 208.700
## 2012 205.300 206.200 207.800 205.900 205.200 203.800 202.800 198.900 199.800
## 2013 190.900 193.200 192.800 193.000 192.400 189.800 189.300 191.400 193.200
## 2014 193.000 193.400 194.500 195.200 195.800 197.600 198.400 198.700 198.200
## 2015 192.100 188.200 184.200 179.100 173.900 172.000 168.500 167.400 165.600
## 2016 151.800 150.900 153.100 154.600 158.800 168.200 169.400 183.200 184.100
## 2017 179.900 193.500 195.800 197.400 198.300 196.200 196.600 192.200 191.600
## 2018 192.500 195.900 203.600 221.900 231.400 235.500 238.600 241.200 238.800
## 2019 218.700 220.100 213.700 212.800 209.200 201.400 193.200 198.900 195.100
## 2020 193.800 201.500 196.800 193.900 179.700 181.400 174.300 166.500 176.000
## 2021 238.900 271.100 324.300 345.600 374.100 412.000 451.634 505.535 530.233
## 2022 477.791 439.830 384.413 431.157 471.678
## Oct Nov Dec
## 1986 107.100 107.100 107.200
## 1987 110.500 111.000 111.100
## 1988 129.100 128.200 128.000
## 1989 122.900 122.900 122.700
## 1990 120.800 120.600 120.500
## 1991 119.600 119.600 119.300
## 1992 118.200 116.900 117.200
## 1993 122.000 123.200 122.900
## 1994 127.900 127.900 128.000
## 1995 130.700 129.900 129.700
## 1996 124.200 124.000 124.000
## 1997 124.200 123.500 123.200
## 1998 116.100 116.500 114.400
## 1999 115.400 116.100 117.200
## 2000 119.600 116.200 116.200
## 2001 108.900 108.900 108.400
## 2002 123.400 123.100 123.600
## 2003 125.300 127.000 128.200
## 2004 164.800 162.500 169.100
## 2005 160.700 162.700 161.400
## 2006 170.900 166.300 164.900
## 2007 162.200 163.300 166.400
## 2008 238.600 228.500 215.400
## 2009 183.400 178.700 179.600
## 2010 180.600 178.800 182.800
## 2011 210.200 206.200 204.300
## 2012 196.100 191.700 190.500
## 2013 193.000 193.600 193.600
## 2014 196.900 196.700 194.100
## 2015 162.500 158.700 153.500
## 2016 178.400 174.000 175.600
## 2017 190.400 188.600 190.900
## 2018 230.900 226.400 224.900
## 2019 187.000 185.700 189.100
## 2020 192.000 197.600 226.300
## 2021 544.388 548.596 500.488
## 2022#EXTRAEMOS LOS DATOS QUE EMPATEN CON LOS QUE SE EXTRAJERON DEL ACERO
plot(dataacero)
logdatacero = log(dataacero)
plot(logdatacero)
#PODEMOS APRECIAR UN COMPORTAMIENTO CRECIENTE A LO LARGO DE LOS AÑOS,
SIN NINGUNA CRISIS QUE DETERMINE UNA CAIDE IMPORTANTE, MAS BIEN,
UNICAMENTE CAMBIOS VARIABLES DEL PRECIO DEBIDO A UN TEMA DE MERCADO
AFECTADO POR LA OFERTA Y DEMANDA.
alog = diff(logdatacero,lag=12)
plot(alog)
#NUEVAMENTE COMO LO HICIMOS CON EL ACERO, BUSCAMOS QUE SE GENERE UNA
FUNCIÓN ESTACIONARIA. LO COMPROBAREMOS COMO EN LA FUNCIÓN ANTERIOR CON
FULLER.
adf.test(alog, k=1)## Warning in adf.test(alog, k = 1): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: alog
## Dickey-Fuller = -4.8826, Lag order = 1, p-value = 0.01
## alternative hypothesis: stationary#SE ACEPTA QUE ES UNA FUNCION ESTACIONARA PORQUE EL VALOR DE P-VALUE ES MENOR A .05
modelo2 <- auto.arima(dataacero,
lambda = 0,
d=0,D=1,
max.p=2, max.q=1,
max.P = 1,max.Q = 1
)
coeftest(modelo2)##
## z test of coefficients:
##
## Estimate Std. Error z value Pr(>|z|)
## ma1 0.98034855 0.01009087 97.1520 < 2.2e-16 ***
## sma1 -0.35949951 0.06722504 -5.3477 8.908e-08 ***
## drift 0.00292050 0.00049149 5.9422 2.813e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#POR CADA VALOR DE PERIODO, EN UN VARIABLE DE 1% AFECTARA .98% DE CRECIMIENTO EN EL VALOR DEL MES. #POR CADA VALOR DE DOS PERIODOS, EN UNA VARIABLE DE 1% AFECTARA EL NEGTIVAMENTE .35% EN EL VALOR DE DOS MESES. #POR OTRO LADO, EL DRIFT NO ES DE ALTO IMPACTO YA QUE ES MENOR A .05, SIENDO ESTE .0029
plot(doil)
plot(dataacero)
dosvariables = merge(acero1.xts, doil.xts)
dosvariables = na.omit(dosvariables)
dosvariables## PCU3312213312211 doil.Open doil.High doil.Low doil.Close
## 1986-01-01 104.800 25.56 26.53 18.95 18.95
## 1986-02-01 104.400 17.42 17.70 13.23 13.23
## 1986-03-01 104.400 11.98 14.05 10.25 10.25
## 1986-04-01 104.800 11.13 14.39 11.13 13.38
## 1986-05-01 105.400 13.80 17.13 13.80 14.30
## 1986-06-01 106.500 13.80 14.44 12.38 12.80
## 1986-07-01 106.400 12.39 13.07 10.83 11.23
## 1986-08-01 106.500 11.56 15.93 11.56 15.93
## 1986-09-01 106.500 16.43 16.43 13.80 14.70
## 1986-10-01 107.100 15.23 15.60 13.73 15.25
## 1986-11-01 107.100 14.70 15.68 14.70 15.00
## 1986-12-01 107.200 15.29 17.93 14.93 17.93
## 1987-01-01 106.400 18.13 19.13 17.98 18.73
## 1987-02-01 106.600 18.59 18.59 16.43 16.45
## 1987-03-01 106.600 16.43 18.94 16.43 18.82
## 1987-04-01 106.200 18.78 19.03 18.07 18.76
## 1987-05-01 106.200 18.84 19.97 18.84 19.36
## 1987-06-01 107.100 19.55 20.65 19.55 20.22
## 1987-07-01 107.900 20.47 22.44 20.47 21.43
## 1987-08-01 108.000 22.21 22.21 19.18 19.76
## 1987-09-01 109.100 19.61 19.77 18.99 19.62
## 1987-10-01 110.500 19.62 20.23 19.33 19.96
## 1987-11-01 111.000 19.64 19.64 18.28 18.52
## 1987-12-01 111.100 18.44 18.87 15.12 16.74
## 1988-01-01 114.400 17.77 17.89 16.56 16.97
## 1988-02-01 116.500 16.83 17.70 15.77 15.98
## 1988-03-01 117.100 15.57 17.09 15.35 17.09
## 1988-04-01 120.500 16.99 18.54 16.72 18.10
## 1988-05-01 124.800 17.12 17.72 17.01 17.54
## 1988-06-01 127.100 17.60 17.67 15.20 15.20
## 1988-07-01 129.600 14.92 16.37 14.35 16.37
## 1988-08-01 130.100 16.07 16.07 15.12 15.19
## 1988-09-01 129.800 15.05 15.38 13.33 13.33
## 1988-10-01 129.100 13.03 15.33 12.58 13.54
## 1988-11-01 128.200 13.52 15.43 13.30 15.42
## 1988-12-01 128.000 15.63 17.68 15.36 17.12
## 1989-01-01 128.000 17.38 19.28 16.99 17.00
## 1989-02-01 129.500 17.50 18.64 17.11 18.21
## 1989-03-01 130.300 18.30 21.03 18.12 20.27
## 1989-04-01 131.000 20.03 24.62 19.85 20.38
## 1989-05-01 126.100 20.66 21.77 19.41 19.93
## 1989-06-01 124.900 19.83 20.88 19.30 20.29
## 1989-07-01 124.600 20.55 20.98 17.96 18.33
## 1989-08-01 123.700 17.91 19.15 17.91 18.83
## 1989-09-01 123.200 18.88 20.15 18.88 20.15
## 1989-10-01 122.900 19.99 20.91 19.48 19.88
## 1989-11-01 122.900 20.09 20.52 19.33 19.87
## 1989-12-01 122.700 20.26 22.20 20.22 21.84
## 1990-01-01 122.000 22.88 24.48 21.64 22.69
## 1990-02-01 120.900 22.71 23.04 21.13 21.55
## 1990-03-01 120.800 21.19 21.62 19.34 20.34
## 1990-04-01 120.700 20.51 20.51 16.95 18.50
## 1990-05-01 120.500 18.76 19.73 16.02 17.47
## 1990-06-01 121.000 17.51 17.60 15.43 17.05
## 1990-07-01 121.100 16.94 20.57 16.49 20.57
## 1990-08-01 121.100 21.59 31.67 21.59 27.45
## 1990-09-01 121.000 27.45 39.77 27.45 39.53
## 1990-10-01 120.800 37.08 41.07 28.46 35.31
## 1990-11-01 120.600 35.30 35.61 29.08 29.08
## 1990-12-01 120.500 29.40 29.40 25.30 28.48
## 1991-01-01 120.800 26.53 32.25 20.05 21.90
## 1991-02-01 120.800 21.33 22.78 17.43 19.28
## 1991-03-01 120.100 19.43 20.78 19.00 19.63
## 1991-04-01 120.200 19.28 21.85 19.28 20.99
## 1991-05-01 120.000 21.28 21.92 20.73 21.16
## 1991-06-01 120.300 21.16 21.16 19.70 20.56
## 1991-07-01 119.800 20.78 22.20 20.69 21.70
## 1991-08-01 119.700 21.33 22.50 21.29 22.28
## 1991-09-01 119.600 22.28 22.42 21.36 22.25
## 1991-10-01 119.600 22.10 24.12 22.10 23.29
## 1991-11-01 119.600 23.85 23.85 21.04 21.48
## 1991-12-01 119.300 21.10 21.10 18.28 19.15
## 1992-01-01 119.400 19.43 19.43 17.89 18.93
## 1992-02-01 118.700 18.97 19.91 18.14 18.69
## 1992-03-01 118.700 18.36 19.49 18.36 19.49
## 1992-04-01 118.300 19.85 20.88 19.79 20.88
## 1992-05-01 118.200 20.88 22.13 20.12 22.13
## 1992-06-01 118.200 22.07 23.03 21.84 21.84
## 1992-07-01 118.200 21.90 22.11 21.25 21.83
## 1992-08-01 118.000 21.60 21.85 21.00 21.46
## 1992-09-01 118.100 21.72 22.39 21.51 21.83
## 1992-10-01 118.200 21.83 22.37 20.68 20.68
## 1992-11-01 116.900 20.77 20.77 19.91 19.91
## 1992-12-01 117.200 19.56 19.97 18.69 19.49
## 1993-01-01 118.300 19.03 20.38 18.21 20.27
## 1993-02-01 118.600 20.32 20.63 19.30 20.53
## 1993-03-01 120.000 20.62 21.05 19.52 20.44
## 1993-04-01 120.400 20.54 20.67 19.79 20.54
## 1993-05-01 121.700 20.58 20.58 19.15 20.04
## 1993-06-01 121.700 20.20 20.20 18.35 18.82
## 1993-07-01 122.100 18.44 18.50 17.20 17.94
## 1993-08-01 122.400 17.90 18.82 17.30 18.24
## 1993-09-01 122.000 17.92 18.73 16.74 18.72
## 1993-10-01 122.000 18.63 18.76 16.97 16.97
## 1993-11-01 123.200 17.50 17.50 15.30 15.36
## 1993-12-01 122.900 15.45 15.45 13.98 14.19
## 1994-01-01 123.200 14.52 15.50 14.36 15.24
## 1994-02-01 123.300 15.91 16.06 13.89 14.50
## 1994-03-01 123.200 14.78 15.37 14.14 14.78
## 1994-04-01 123.700 15.67 17.84 15.57 16.92
## 1994-05-01 125.100 17.18 18.93 16.85 18.30
## 1994-06-01 125.300 18.29 20.72 17.78 19.37
## 1994-07-01 126.500 19.52 20.40 19.15 20.30
## 1994-08-01 127.700 20.65 20.65 16.87 17.60
## 1994-09-01 127.900 17.47 18.36 16.72 18.36
## 1994-10-01 127.900 18.16 18.27 16.98 18.16
## 1994-11-01 127.900 18.66 18.97 17.38 18.06
## 1994-12-01 128.000 17.77 17.77 16.60 17.77
## 1995-01-01 129.500 17.45 18.82 17.40 18.48
## 1995-02-01 131.100 18.48 18.94 18.28 18.52
## 1995-03-01 131.400 18.31 19.21 17.90 19.18
## 1995-04-01 130.600 19.05 20.52 19.05 20.36
## 1995-05-01 130.800 20.53 20.53 18.70 18.88
## 1995-06-01 131.100 18.89 19.25 17.38 17.38
## 1995-07-01 132.400 17.33 17.62 17.03 17.62
## 1995-08-01 132.500 17.59 19.91 17.40 17.89
## 1995-09-01 130.400 18.08 19.01 17.27 17.54
## 1995-10-01 130.700 17.67 17.67 16.86 17.67
## 1995-11-01 129.900 17.74 18.56 17.62 18.27
## 1995-12-01 129.700 18.43 19.71 18.43 19.54
## 1996-01-01 129.500 19.83 20.50 17.33 17.76
## 1996-02-01 126.700 17.63 22.14 17.53 19.59
## 1996-03-01 121.400 19.45 24.56 19.24 21.43
## 1996-04-01 122.300 22.29 25.15 20.95 20.95
## 1996-05-01 122.100 20.81 23.02 19.77 19.77
## 1996-06-01 121.800 19.86 21.53 19.73 20.92
## 1996-07-01 121.700 21.48 22.43 20.13 20.46
## 1996-08-01 124.300 20.95 23.10 20.95 22.25
## 1996-09-01 124.300 23.35 24.95 23.25 24.20
## 1996-10-01 124.200 24.35 25.85 23.25 23.25
## 1996-11-01 124.000 23.00 25.75 22.65 23.70
## 1996-12-01 124.000 24.70 26.55 23.40 25.90
## 1997-01-01 124.100 25.55 26.55 23.85 24.15
## 1997-02-01 124.000 24.20 24.20 20.30 20.30
## 1997-03-01 124.300 20.25 22.00 20.15 20.35
## 1997-04-01 124.500 20.30 20.40 19.15 20.20
## 1997-05-01 124.700 19.90 22.10 19.60 21.00
## 1997-06-01 124.400 21.15 21.15 18.60 19.82
## 1997-07-01 124.600 20.11 20.43 18.92 20.19
## 1997-08-01 124.600 20.27 20.81 19.29 19.66
## 1997-09-01 124.400 19.73 21.29 19.30 21.13
## 1997-10-01 124.200 21.02 22.86 20.40 21.10
## 1997-11-01 123.500 20.91 21.01 19.13 19.13
## 1997-12-01 123.200 18.76 18.86 17.60 17.65
## 1998-01-01 122.900 17.41 17.93 15.65 17.21
## 1998-02-01 122.400 17.07 17.07 15.14 15.44
## 1998-03-01 122.400 15.32 16.92 13.41 15.75
## 1998-04-01 122.100 15.69 16.08 13.09 15.56
## 1998-05-01 121.800 16.25 16.25 13.01 15.21
## 1998-06-01 121.800 14.99 15.24 11.69 14.30
## 1998-07-01 117.600 14.47 14.90 13.44 14.27
## 1998-08-01 117.500 13.93 13.93 12.76 13.29
## 1998-09-01 117.400 13.62 16.19 13.62 16.19
## 1998-10-01 116.100 15.52 15.71 13.39 14.48
## 1998-11-01 116.500 14.45 14.45 10.86 11.37
## 1998-12-01 114.400 11.27 12.55 10.82 12.14
## 1999-01-01 114.400 12.42 13.43 11.82 12.81
## 1999-02-01 114.300 12.36 12.61 11.38 12.31
## 1999-03-01 114.200 12.28 16.66 12.28 16.66
## 1999-04-01 114.000 16.65 18.69 15.92 18.69
## 1999-05-01 114.000 18.83 18.94 16.77 16.85
## 1999-06-01 113.700 16.31 19.33 16.31 19.33
## 1999-07-01 113.500 19.39 21.09 19.38 20.52
## 1999-08-01 113.800 20.46 22.15 20.21 22.15
## 1999-09-01 115.700 21.79 24.81 21.54 24.54
## 1999-10-01 115.400 24.51 24.51 20.81 21.79
## 1999-11-01 116.100 22.44 28.03 22.44 24.87
## 1999-12-01 117.200 25.01 26.81 25.01 25.76
## 2000-01-01 117.500 25.56 30.28 24.65 27.65
## 2000-02-01 119.000 28.28 30.57 27.52 30.57
## 2000-03-01 119.400 31.71 33.90 26.36 26.86
## 2000-04-01 120.800 26.28 27.41 23.91 25.71
## 2000-05-01 121.200 25.84 30.43 25.84 29.03
## 2000-06-01 120.600 30.19 34.76 29.29 32.44
## 2000-07-01 121.200 30.76 31.94 27.50 27.50
## 2000-08-01 120.100 27.85 34.01 27.85 33.09
## 2000-09-01 119.100 33.42 37.22 30.26 30.87
## 2000-10-01 119.600 32.05 36.06 30.66 32.70
## 2000-11-01 116.200 33.14 36.24 32.59 33.61
## 2000-12-01 116.200 32.06 32.06 25.82 26.72
## 2001-01-01 113.100 27.29 32.21 27.29 28.62
## 2001-02-01 112.000 29.88 31.57 27.35 27.35
## 2001-03-01 111.900 27.78 28.95 25.99 26.37
## 2001-04-01 111.300 25.70 28.81 25.24 28.48
## 2001-05-01 111.100 28.37 29.96 27.35 28.39
## 2001-06-01 110.500 27.88 29.13 25.67 26.37
## 2001-07-01 110.000 26.02 28.10 24.65 26.70
## 2001-08-01 109.300 26.83 28.34 25.63 26.65
## 2001-09-01 109.700 26.94 29.59 21.46 23.44
## 2001-10-01 108.900 23.12 23.49 21.20 21.20
## 2001-11-01 108.900 20.47 22.23 17.50 19.46
## 2001-12-01 108.400 20.27 21.32 18.04 19.96
## 2002-01-01 107.500 21.13 21.47 18.02 19.71
## 2002-02-01 109.800 20.40 21.78 19.75 21.78
## 2002-03-01 112.900 22.37 26.21 22.37 26.21
## 2002-04-01 116.400 26.82 27.75 23.51 27.32
## 2002-05-01 122.300 26.58 29.17 24.78 25.37
## 2002-06-01 124.800 25.10 26.79 24.21 26.79
## 2002-07-01 125.400 26.79 27.88 26.14 27.02
## 2002-08-01 125.900 26.51 30.37 26.51 28.97
## 2002-09-01 123.100 27.76 30.85 27.76 30.59
## 2002-10-01 123.400 30.71 30.71 26.81 27.18
## 2002-11-01 123.100 27.04 27.73 25.28 26.87
## 2002-12-01 123.600 27.27 32.68 26.80 31.21
## 2003-01-01 124.400 31.97 34.98 30.66 33.51
## 2003-02-01 124.500 32.84 37.96 32.84 36.76
## 2003-03-01 124.300 36.10 37.87 27.18 31.14
## 2003-04-01 124.400 29.48 30.76 25.25 26.09
## 2003-05-01 124.000 26.05 29.74 25.65 29.56
## 2003-06-01 123.800 30.72 32.17 28.97 30.15
## 2003-07-01 124.500 30.41 31.96 29.98 30.56
## 2003-08-01 125.000 32.23 32.41 30.76 31.76
## 2003-09-01 125.000 29.57 29.57 26.93 29.19
## 2003-10-01 125.300 29.43 32.01 28.67 29.24
## 2003-11-01 127.000 28.81 33.16 28.81 30.33
## 2003-12-01 128.200 29.89 33.72 29.89 32.51
## 2004-01-01 132.700 33.71 36.21 32.86 33.16
## 2004-02-01 144.300 34.02 37.28 32.49 36.08
## 2004-03-01 150.800 36.85 38.21 35.41 35.75
## 2004-04-01 156.600 34.47 37.79 34.29 37.31
## 2004-05-01 156.900 38.26 42.03 38.26 39.90
## 2004-06-01 154.900 42.33 42.33 35.60 36.92
## 2004-07-01 151.000 38.56 43.72 38.37 43.72
## 2004-08-01 161.500 43.83 48.66 42.23 42.23
## 2004-09-01 168.700 43.89 49.76 42.77 49.56
## 2004-10-01 164.800 50.16 56.37 49.85 51.78
## 2004-11-01 162.500 50.10 50.90 46.10 49.16
## 2004-12-01 169.100 45.56 46.31 40.71 43.36
## 2005-01-01 169.100 42.16 49.43 42.16 48.25
## 2005-02-01 173.800 47.10 52.20 45.35 51.75
## 2005-03-01 173.800 51.67 56.80 49.43 55.31
## 2005-04-01 172.200 57.26 57.26 49.20 49.20
## 2005-05-01 170.800 50.94 52.08 46.99 52.08
## 2005-06-01 161.000 54.40 59.78 52.51 56.63
## 2005-07-01 156.600 59.11 61.24 56.73 60.71
## 2005-08-01 150.500 61.51 69.91 60.76 68.63
## 2005-09-01 160.600 69.50 69.50 62.91 66.21
## 2005-10-01 160.700 65.36 65.36 59.80 59.80
## 2005-11-01 162.700 59.85 61.70 56.20 57.33
## 2005-12-01 161.400 58.46 61.36 57.31 61.06
## 2006-01-01 161.000 63.11 68.36 62.81 67.86
## 2006-02-01 160.900 66.61 66.61 57.61 61.37
## 2006-03-01 161.900 62.01 66.70 59.91 66.25
## 2006-04-01 163.800 66.07 73.73 65.75 71.80
## 2006-05-01 166.800 73.75 74.62 68.44 71.42
## 2006-06-01 170.300 70.11 73.94 68.48 73.94
## 2006-07-01 171.900 75.20 76.80 72.79 74.56
## 2006-08-01 171.800 74.93 77.05 69.74 70.38
## 2006-09-01 172.100 69.24 69.24 59.79 62.90
## 2006-10-01 170.900 60.96 60.96 56.74 58.72
## 2006-11-01 166.300 58.64 62.97 55.90 62.97
## 2006-12-01 164.900 63.43 63.43 60.31 60.85
## 2007-01-01 162.500 60.77 60.77 50.51 58.17
## 2007-02-01 163.900 57.35 61.78 57.35 61.78
## 2007-03-01 165.900 61.97 66.10 56.41 65.94
## 2007-04-01 167.200 66.03 66.45 61.51 65.78
## 2007-05-01 166.900 64.43 66.25 61.48 64.02
## 2007-06-01 165.200 65.09 70.47 64.78 70.47
## 2007-07-01 163.800 71.11 78.20 71.11 78.20
## 2007-08-01 163.200 76.49 76.84 69.30 73.98
## 2007-09-01 162.200 75.07 83.85 75.07 81.64
## 2007-10-01 162.200 80.31 94.16 78.97 94.16
## 2007-11-01 163.300 93.53 99.16 88.60 88.60
## 2007-12-01 166.400 89.29 96.63 87.45 95.95
## 2008-01-01 172.900 99.64 99.64 87.65 91.67
## 2008-02-01 177.200 89.03 102.60 87.16 101.78
## 2008-03-01 185.400 102.42 110.21 99.72 101.54
## 2008-04-01 204.200 100.92 119.64 100.92 113.70
## 2008-05-01 223.100 112.60 132.99 112.60 127.35
## 2008-06-01 237.500 127.75 139.96 122.30 139.96
## 2008-07-01 248.300 141.06 145.31 122.21 124.17
## 2008-08-01 250.700 125.03 125.03 112.92 115.55
## 2008-09-01 245.900 109.63 122.61 91.49 100.70
## 2008-10-01 238.600 98.23 98.23 61.92 68.10
## 2008-11-01 228.500 63.93 70.41 48.86 55.21
## 2008-12-01 215.400 49.34 49.34 30.28 44.60
## 2009-01-01 201.500 46.17 48.61 35.38 41.73
## 2009-02-01 196.200 41.35 44.15 34.03 44.15
## 2009-03-01 186.800 40.07 53.87 40.07 49.64
## 2009-04-01 180.800 48.46 52.61 45.82 50.35
## 2009-05-01 171.900 52.18 66.31 52.18 66.31
## 2009-06-01 166.800 68.59 72.69 66.14 69.82
## 2009-07-01 173.800 69.32 69.32 59.62 69.26
## 2009-08-01 178.800 71.59 73.68 66.72 69.97
## 2009-09-01 185.500 68.11 72.50 65.74 70.46
## 2009-10-01 183.400 70.67 81.03 69.60 77.04
## 2009-11-01 178.700 78.08 80.30 74.88 77.19
## 2009-12-01 179.600 78.39 79.39 69.48 79.39
## 2010-01-01 183.200 81.52 83.12 72.85 72.85
## 2010-02-01 188.000 74.41 80.04 71.15 79.72
## 2010-03-01 189.900 78.71 83.45 78.71 83.45
## 2010-04-01 192.200 84.53 86.54 81.52 86.07
## 2010-05-01 194.000 86.19 86.19 64.78 74.00
## 2010-06-01 193.700 72.70 78.45 71.43 75.59
## 2010-07-01 190.700 72.95 79.01 71.96 78.85
## 2010-08-01 186.000 81.25 82.52 71.24 71.93
## 2010-09-01 182.900 73.97 79.95 72.96 79.95
## 2010-10-01 180.600 81.57 83.21 79.57 81.45
## 2010-11-01 178.800 82.94 87.77 80.43 84.12
## 2010-12-01 182.800 86.75 91.48 86.75 91.38
## 2011-01-01 186.800 91.59 91.85 84.45 90.99
## 2011-02-01 197.700 89.54 97.10 83.13 97.10
## 2011-03-01 207.500 99.63 106.19 97.23 106.19
## 2011-04-01 221.300 107.55 113.39 105.75 113.39
## 2011-05-01 225.700 113.03 113.03 96.40 102.70
## 2011-06-01 215.700 100.30 101.95 90.65 95.30
## 2011-07-01 211.400 94.81 99.61 94.81 95.68
## 2011-08-01 212.300 94.98 94.98 79.32 88.81
## 2011-09-01 208.700 88.93 90.21 78.93 78.93
## 2011-10-01 210.200 77.34 93.96 75.40 93.19
## 2011-11-01 206.200 92.19 102.59 92.19 100.36
## 2011-12-01 204.300 100.20 101.29 93.55 98.83
## 2012-01-01 205.300 102.96 103.22 98.15 98.46
## 2012-02-01 206.200 97.63 109.39 96.36 107.08
## 2012-03-01 207.800 108.76 108.76 102.79 103.03
## 2012-04-01 205.900 105.25 105.25 101.12 104.89
## 2012-05-01 205.200 106.17 106.17 86.52 86.52
## 2012-06-01 203.800 83.17 85.05 77.72 85.04
## 2012-07-01 202.800 83.72 92.78 83.72 88.08
## 2012-08-01 198.900 88.99 96.89 87.22 96.47
## 2012-09-01 199.800 95.34 98.94 89.92 92.18
## 2012-10-01 196.100 92.44 92.44 85.39 86.23
## 2012-11-01 191.700 87.05 89.05 84.50 88.54
## 2012-12-01 190.500 88.69 91.83 85.14 91.83
## 2013-01-01 190.900 93.14 97.98 92.97 97.65
## 2013-02-01 193.200 97.46 97.48 92.03 92.03
## 2013-03-01 192.800 90.71 97.24 90.13 97.24
## 2013-04-01 193.000 97.10 97.23 86.65 93.22
## 2013-05-01 192.400 90.74 96.29 90.74 91.93
## 2013-06-01 189.800 93.41 98.46 93.36 96.36
## 2013-07-01 189.300 97.94 108.00 97.94 105.10
## 2013-08-01 191.400 107.93 110.17 103.45 107.98
## 2013-09-01 193.200 108.67 110.62 102.36 102.36
## 2013-10-01 193.000 102.09 104.15 96.29 96.29
## 2013-11-01 193.600 94.56 95.35 92.05 92.55
## 2013-12-01 193.600 93.61 99.94 93.61 98.17
## 2014-01-01 193.000 95.14 98.25 91.36 97.55
## 2014-02-01 193.400 96.44 103.46 96.44 102.88
## 2014-03-01 194.500 105.34 105.34 98.29 101.57
## 2014-04-01 195.200 99.69 104.35 99.60 100.07
## 2014-05-01 195.800 99.69 105.01 99.69 103.40
## 2014-06-01 197.600 103.07 107.95 103.07 106.07
## 2014-07-01 198.400 106.06 106.06 98.23 98.23
## 2014-08-01 198.700 97.86 98.26 93.61 97.86
## 2014-09-01 198.200 92.92 95.55 91.17 91.17
## 2014-10-01 196.900 90.74 91.02 80.52 80.53
## 2014-11-01 196.700 78.77 78.77 65.94 65.94
## 2014-12-01 194.100 68.98 68.98 53.45 53.45
## 2015-01-01 192.100 52.72 52.72 44.08 47.79
## 2015-02-01 188.200 49.25 53.56 47.65 49.84
## 2015-03-01 184.200 49.59 51.53 43.39 47.72
## 2015-04-01 179.100 50.12 59.62 49.13 59.62
## 2015-05-01 173.900 59.10 60.93 57.29 60.25
## 2015-06-01 172.000 60.24 61.36 58.00 59.48
## 2015-07-01 168.500 56.94 56.94 47.11 47.11
## 2015-08-01 167.400 45.25 49.20 38.22 49.20
## 2015-09-01 165.600 45.38 47.12 44.07 45.06
## 2015-10-01 162.500 44.75 49.67 43.19 46.60
## 2015-11-01 158.700 46.12 47.88 39.27 40.43
## 2015-12-01 153.500 40.58 41.08 34.55 37.13
## 2016-01-01 151.800 36.81 36.81 26.68 33.66
## 2016-02-01 150.900 31.62 32.74 26.19 32.74
## 2016-03-01 153.100 34.39 41.45 34.39 36.94
## 2016-04-01 154.600 35.36 46.03 34.30 45.98
## 2016-05-01 158.800 44.75 49.36 43.45 49.10
## 2016-06-01 168.200 49.07 51.23 45.80 48.27
## 2016-07-01 169.400 49.02 49.02 41.13 41.54
## 2016-08-01 183.200 40.05 48.48 39.50 44.68
## 2016-09-01 184.100 43.17 47.72 43.04 47.72
## 2016-10-01 178.400 48.80 51.59 46.83 46.83
## 2016-11-01 174.000 46.66 49.41 43.29 49.41
## 2016-12-01 175.600 51.08 54.01 49.85 53.75
## 2017-01-01 179.900 52.36 53.98 50.82 52.75
## 2017-02-01 193.500 53.90 54.48 52.19 54.00
## 2017-03-01 195.800 53.82 53.82 47.00 50.54
## 2017-04-01 197.400 50.25 53.38 48.90 49.31
## 2017-05-01 198.300 48.83 51.12 45.55 48.29
## 2017-06-01 196.200 48.32 48.32 42.48 46.02
## 2017-07-01 196.600 45.11 50.21 44.25 50.21
## 2017-08-01 192.200 49.19 49.60 45.96 47.26
## 2017-09-01 191.600 47.32 52.14 47.32 51.67
## 2017-10-01 190.400 50.59 54.36 49.34 54.36
## 2017-11-01 188.600 54.32 58.94 54.32 57.40
## 2017-12-01 190.900 58.35 60.46 55.79 60.46
## 2018-01-01 192.500 60.37 66.27 60.37 64.82
## 2018-02-01 195.900 65.92 65.92 59.20 61.43
## 2018-03-01 203.600 60.98 65.80 60.13 64.87
## 2018-04-01 221.900 63.05 68.56 62.03 68.56
## 2018-05-01 231.400 67.28 72.26 66.80 66.98
## 2018-06-01 235.500 65.81 77.41 64.75 74.13
## 2018-07-01 238.600 73.89 74.19 67.90 69.88
## 2018-08-01 241.200 68.80 70.25 65.07 69.84
## 2018-09-01 238.800 69.82 73.40 67.55 73.16
## 2018-10-01 230.900 75.37 76.40 65.31 65.31
## 2018-11-01 226.400 63.67 63.67 50.06 50.78
## 2018-12-01 224.900 52.98 53.21 44.48 45.15
## 2019-01-01 218.700 46.31 54.18 46.31 53.84
## 2019-02-01 220.100 55.29 57.21 52.43 57.21
## 2019-03-01 213.700 55.76 60.19 55.76 60.19
## 2019-04-01 212.800 61.59 66.24 61.59 63.83
## 2019-05-01 209.200 63.55 63.55 53.49 53.49
## 2019-06-01 201.400 53.25 59.18 51.13 58.20
## 2019-07-01 193.200 58.91 60.28 55.08 58.53
## 2019-08-01 198.900 53.64 57.05 51.14 55.07
## 2019-09-01 195.100 53.91 63.10 53.91 54.09
## 2019-10-01 187.000 53.60 56.52 52.41 54.02
## 2019-11-01 185.700 56.04 58.36 54.93 58.12
## 2019-12-01 189.100 55.97 61.76 55.97 61.14
## 2020-01-01 193.800 61.17 63.27 51.58 51.58
## 2020-02-01 201.500 50.06 53.77 44.83 44.83
## 2020-03-01 196.800 46.78 47.27 14.10 20.51
## 2020-04-01 193.900 20.28 28.36 -36.98 19.23
## 2020-05-01 179.700 19.72 35.57 19.72 35.57
## 2020-06-01 181.400 35.49 40.60 35.49 39.27
## 2020-07-01 174.300 39.88 41.88 39.64 40.10
## 2020-08-01 166.500 40.83 43.21 40.83 42.61
## 2020-09-01 176.000 42.76 42.76 36.87 40.05
## 2020-10-01 192.000 38.51 41.37 35.64 35.64
## 2020-11-01 197.600 36.60 45.58 36.60 45.20
## 2020-12-01 226.300 44.54 49.04 44.54 48.35
## 2021-01-01 238.900 47.47 53.47 47.47 52.16
## 2021-02-01 271.100 53.55 63.43 53.55 61.55
## 2021-03-01 324.300 60.54 66.08 57.75 59.19
## 2021-04-01 345.600 61.41 65.00 58.73 63.50
## 2021-05-01 374.100 64.46 66.87 61.95 66.31
## 2021-06-01 412.000 67.80 74.21 67.80 73.52
## 2021-07-01 451.634 75.33 75.37 66.45 73.93
## 2021-08-01 505.535 71.31 71.31 62.25 68.43
## 2021-09-01 530.233 68.63 75.54 68.26 75.22
## 2021-10-01 544.388 76.01 85.64 76.01 83.50
## 2021-11-01 548.596 84.08 84.12 66.14 66.14
## 2021-12-01 500.488 65.44 76.83 65.44 75.33
## 2022-01-01 477.791 75.99 89.16 75.99 89.16
## 2022-02-01 439.830 88.22 96.13 88.16 96.13
## 2022-03-01 384.413 103.66 123.64 94.85 100.53
## 2022-04-01 431.157 99.32 108.24 94.22 104.59
## 2022-05-01 471.678 105.18 116.19 99.74 114.38#EN UNA SOLA TABLA COLOCAMOS LOS DATOS ORDENADOS DE AMBAS VARIABLES EN ESTE CASO LA DEL PETROLEO Y LA DEL PRECIO DEL ACERO.
plot(dosvariables)
#ENTENDEMOS QUE EL PRECIO DEL PETROLEO DEPENDE DEL PRECIO DEL ACERO.
#1. Realizar una investigación de los precios de referencia a nivel internacional del petróleo y del acero durante los últimos cinco años.
#LOS DATOS SE OBTUVIERON DE LA BASE DE DATOS FRED WTI
#2.1- ¿Qué precio de referencia del petróleo se debe utilizar para el análisis esperado?
#SE UTILIZARON TODOS LOS DATOS QUE LA BASE DE DATOS BRINDA DESDE 1986 HASTA EL AÑO PRESENTE 2022.
#2.2.-¿Qué precio de referencia para el acero se debería emplear?
#SE DEBEN DE UTILIZAR DATOS DE PRECIO DEL ACERO, DE LA MISMA BASE DE DATOS CON EL FIN QUE LOS DATOS DE AMBAS VARIABLES CONTENGAN LOS MISMOS RANGOS, SOBRE TODO EL MISMO PERIODO DE TIEMPO PARA QUE SE PUEDA COMPARAR DE MANERA CORRECTA.
#4.-¿Qué tipo de modelo de caminata aleatoria presenta cada variable?
#EL CAMBIO DE DATOS SEGÚN EL PERIODO DE TIEMPO Y NO CONSTANTE. LO REPRESENTAMOS O SE IDENTIFICA CON DATOS NO ESTACIONARIA, POR EL TIPO DE DATOS.
#5.-¿Existe cointe gración entre las variables estudiadas? ¿Cómo sustentarlo?
#PARA LLEGAR A LA COINTE GRACIÓN DE LAS VARIABLE PRIMERO DEBEMOS DE EXTRAER LOS DATOS, ANALIZARLOS, CONVERTIRLOS EN DATOS ESTACIONARIOS Y COLOCARLOS EN UNA MISMA VARIABLE, DE ESTA MANERA PODREMOS VER DE QUE MANERA SE COMPORTAN EN UN MISMO PERIODO DE TIEMPO.
#1.-¿Cuál es el comportamiento de las variables del petróleo y del acero? ¿Cómo hacerlo través del modelo ARIMA?
#SE ENTIENDE COMO DEPENDIENTE EL PRECIO DEL ACERO AL DEL PETROLEO, DE ESTA MANERA SE ANALIZA EN EL MISMO PERIODO DE TIEMPO.