# UNIVERSIDAD NACIONAL DEL ALTIPLANO
# INGENIERIA ESTADISTICA E INFORMATICA
# CURSO: SERIES DE TIEMPO
library(readxl)
## Warning: package 'readxl' was built under R version 4.0.2
Arimar <- read_excel("E:\\SERIES DE TIEMPO\\TAREA 02\\Arimar.xlsx")
Arimar
## # A tibble: 87 x 1
## Precio
## <dbl>
## 1 98.0
## 2 103.
## 3 101.
## 4 97.8
## 5 97.9
## 6 97.0
## 7 99.7
## 8 99.2
## 9 98.1
## 10 93.9
## # ... with 77 more rows
attach(Arimar)
names(Arimar)
## [1] "Precio"
#file.choose()
#View(Arimar)
library(astsa)
## Warning: package 'astsa' was built under R version 4.0.5
library(tseries)
## Warning: package 'tseries' was built under R version 4.0.5
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
library(lubridate)
## Warning: package 'lubridate' was built under R version 4.0.5
##
## Attaching package: 'lubridate'
## The following objects are masked from 'package:base':
##
## date, intersect, setdiff, union
library(tidyverse)
## Warning: package 'tidyverse' was built under R version 4.0.5
## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --
## v ggplot2 3.3.3 v purrr 0.3.4
## v tibble 3.1.5 v dplyr 1.0.7
## v tidyr 1.1.4 v stringr 1.4.0
## v readr 2.0.2 v forcats 0.5.1
## Warning: package 'ggplot2' was built under R version 4.0.3
## Warning: package 'tibble' was built under R version 4.0.5
## Warning: package 'tidyr' was built under R version 4.0.5
## Warning: package 'readr' was built under R version 4.0.5
## Warning: package 'dplyr' was built under R version 4.0.5
## Warning: package 'forcats' was built under R version 4.0.5
## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x lubridate::as.difftime() masks base::as.difftime()
## x lubridate::date() masks base::date()
## x dplyr::filter() masks stats::filter()
## x lubridate::intersect() masks base::intersect()
## x dplyr::lag() masks stats::lag()
## x lubridate::setdiff() masks base::setdiff()
## x lubridate::union() masks base::union()
library(forecast)
## Warning: package 'forecast' was built under R version 4.0.5
##
## Attaching package: 'forecast'
## The following object is masked from 'package:astsa':
##
## gas
#Series de Tiempo Univariadas
#Paso 1. Convertir a objeto de Serie de Tiempo en R
Arimar.ts=ts(Arimar, start=c(2013,1), frequency = 12)
print(Arimar.ts)
## Jan Feb Mar Apr May Jun Jul
## 2013 97.98278 103.35294 100.77090 97.75538 97.90686 96.99315 99.67255
## 2014 88.31081 90.82224 91.39522 93.88863 95.08631 97.01105 93.32017
## 2015 40.45127 45.98606 46.01733 49.32555 52.03910 52.82573 45.16595
## 2016 23.10238 23.72933 28.32656 31.33582 36.72636 39.80715 37.97153
## 2017 44.50008 44.17497 41.93243 43.22118 43.85074 41.15105 43.87771
## 2018 57.45399 56.15676 57.22458 58.15973 62.89929 64.63686 66.42162
## 2019 54.05666 57.37981 59.46449 62.07703 60.33674 56.90537 57.87580
## 2020 49.79299 44.63505 28.92302
## Aug Sep Oct Nov Dec
## 2013 99.24414 98.14572 93.87329 88.48590 89.40966
## 2014 89.50745 84.12824 72.50936 63.47980 50.18138
## 2015 38.41927 36.29036 34.86077 32.50883 26.19610
## 2016 37.74090 36.82666 40.66836 38.36162 42.32596
## 2017 45.55484 48.16237 48.89114 53.34505 54.05576
## 2018 64.26567 68.36348 71.15330 59.82583 51.86867
## 2019 49.58496 55.05522 51.00463 50.68969 54.54901
## 2020
class(Arimar.ts)
## [1] "ts"
start(Arimar.ts)
## [1] 2013 1
end(Arimar.ts)
## [1] 2020 3
plot(Arimar.ts, main="Serie de tiempo", ylab="Precio", col="red")
serielog=log(Arimar.ts)
serielog
## Jan Feb Mar Apr May Jun Jul Aug
## 2013 4.584792 4.638150 4.612850 4.582468 4.584017 4.574640 4.601890 4.597583
## 2014 4.480862 4.508904 4.515193 4.542109 4.554785 4.574825 4.536036 4.494322
## 2015 3.700098 3.828338 3.829018 3.898442 3.951995 3.966998 3.810343 3.648559
## 2016 3.139936 3.166712 3.343800 3.444762 3.603495 3.684046 3.636837 3.630744
## 2017 3.795491 3.788158 3.736059 3.766331 3.780792 3.717249 3.781407 3.818917
## 2018 4.050985 4.028147 4.046984 4.063193 4.141535 4.168785 4.196023 4.163026
## 2019 3.990033 4.049692 4.085379 4.128376 4.099941 4.041390 4.058299 3.903688
## 2020 3.907874 3.798519 3.364638
## Sep Oct Nov Dec
## 2013 4.586453 4.541946 4.482843 4.493229
## 2014 4.432342 4.283716 4.150722 3.915644
## 2015 3.591552 3.551362 3.481512 3.265610
## 2016 3.606222 3.705450 3.647058 3.745401
## 2017 3.874578 3.889596 3.976781 3.990016
## 2018 4.224839 4.264837 4.091438 3.948715
## 2019 4.008337 3.931916 3.925723 3.999100
## 2020
plot(serielog)
#Stationarity: To know the number of differences that are required to achieve that the series
#be stationary
ndiffs(Arimar.ts)
## [1] 1
#Paso 2.Prueba de DickeyFuller
adf.test(Arimar.ts)
##
## Augmented Dickey-Fuller Test
##
## data: Arimar.ts
## Dickey-Fuller = -1.6185, Lag order = 4, p-value = 0.7328
## alternative hypothesis: stationary
seriedif=diff(Arimar.ts)
plot(seriedif)
acf(seriedif)
ndiffs(seriedif)
## [1] 0
adf.test(seriedif)
##
## Augmented Dickey-Fuller Test
##
## data: seriedif
## Dickey-Fuller = -3.3327, Lag order = 4, p-value = 0.07162
## alternative hypothesis: stationary
#Prueba de Dickey Fuller con dos diferencias
seriedif2=diff(Arimar.ts, differences =2)
plot(seriedif2)
adf.test(seriedif2)
## Warning in adf.test(seriedif2): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: seriedif2
## Dickey-Fuller = -5.1673, Lag order = 4, p-value = 0.01
## alternative hypothesis: stationary
#Paso 4: Analisis visual de as graficas
plot(seriedif2, type="o", lty="dashed",main="Serie de Tiempo",col="red")
par(mfrow=c(2,1), mar=c(2,2,2,1)+.1)
acf(seriedif2)
pacf(seriedif2)
acf(ts(seriedif2, frequency=1))
pacf(ts(seriedif2, frequency=1))
#Modelo Arima
modelo1=arima(Arimar.ts,order=c(1,2,1))
summary(modelo1)
##
## Call:
## arima(x = Arimar.ts, order = c(1, 2, 1))
##
## Coefficients:
## ar1 ma1
## 0.4173 -1.000
## s.e. 0.1100 0.047
##
## sigma^2 estimated as 17.51: log likelihood = -244.07, aic = 494.14
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.1842755 4.136183 3.135096 -0.2061955 6.279221 0.9152235
## ACF1
## Training set -0.02472726
tsdiag(modelo1)
Box.test(residuals(modelo1),type="Ljung-Box")
##
## Box-Ljung test
##
## data: residuals(modelo1)
## X-squared = 0.055051, df = 1, p-value = 0.8145
error=residuals(modelo1)
plot(error)
#Pronosticos Arima
pronostico=forecast::forecast(modelo1,h=10)
pronostico
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Apr 2020 21.856654 16.4633719 27.24994 13.608341 30.10497
## May 2020 18.398192 8.9934192 27.80296 4.014833 32.78155
## Jun 2020 16.445341 3.6136910 29.27699 -3.178974 36.06966
## Jul 2020 15.120795 -0.6776994 30.91929 -9.040917 39.28251
## Aug 2020 14.058445 -4.3652157 32.48211 -14.118113 42.23500
## Sep 2020 13.105513 -7.6904599 33.90149 -18.699183 44.91021
## Oct 2020 12.198241 -10.7797404 35.17622 -22.943549 47.34003
## Nov 2020 11.310024 -13.7033148 36.32336 -26.944576 49.56462
## Dec 2020 10.429758 -16.5031190 37.36264 -30.760523 51.62004
## Jan 2021 9.552811 -19.2060240 38.31165 -34.430032 53.53565
plot(pronostico)
