# UNIVERSIDAD NACIONAL DEL ALTIPLANO
# INGENIERIA ESTADISTICA E INFORMATICA
# CURSO: SERIES DE TIEMPO
# TRABAJO ENCARGADO 01
library(readxl)
## Warning: package 'readxl' was built under R version 4.0.2
SerieA <- read_excel("E:/SERIES DE TIEMPO/TRABAJO 01/SerieA.xlsx")
attach(SerieA)
## The following object is masked _by_ .GlobalEnv:
##
## SerieA
names(SerieA)
## [1] "SerieA"
#file.choose()
#View(SerieA)
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
SerieA.ts=ts(SerieA, start=c(1984,1), frequency = 12)
print(SerieA.ts)
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct
## 1984 9.500 10.138 10.720 10.967 10.911 10.801 10.670 10.540 10.398 10.312
## 1985 10.533 10.770 11.097 11.267 11.332 11.273 11.152 11.010 10.919 10.845
## 1986 11.333 11.664 12.245 12.543 12.521 12.336 12.048 11.879 11.749 11.618
## 1987 11.644 11.902 11.875 11.772 11.633 11.457 11.352 11.173 11.056 10.937
## 1988 10.844 11.044 11.159 11.553 11.564 11.427 11.282 11.134 10.987 10.880
## 1989 10.721 10.829 10.928 11.022 10.982 10.869 10.749 10.619 10.509 10.396
## 1990 10.275 10.327 10.288 10.226 10.128 10.063 9.956 9.840 9.735 9.690
## 1991 9.786 9.829 9.931 10.079 10.039 9.955 9.857 9.718 9.615 9.515
## 1992 9.452 9.590 9.629 9.535 9.413 9.267 9.152 9.040 8.985 8.894
## 1993 8.868 9.122 9.217 9.286 9.257 9.131 9.025 8.905 8.822 8.776
## 1994 8.894 9.213 9.423 9.523 9.522 9.415 9.299 9.173 9.104 9.009
## 1995 8.971 9.004 9.193 9.250 9.139 9.015 8.896 8.778 8.687 8.585
## 1996 8.500 8.776 8.844 8.874 8.783 8.659 8.520 8.416 8.306 8.196
## 1997 8.287 8.716 9.183 9.362 9.331 9.209 9.098 9.005 8.915 8.875
## 1998 8.807 8.878 8.979 9.039 8.915 8.768 8.663 8.543 8.420 8.305
## 1999 8.177 8.287 8.595 8.920 8.950 8.828 8.703 8.586 8.497 8.477
## 2000 8.337 8.634 8.961 9.005 8.906 8.801 8.674 8.576 8.478 8.425
## 2001 8.620 9.257 9.907 10.180 10.141 10.047 9.947 9.854 9.787 9.716
## 2002 9.578 9.777 10.138 10.323 10.373 10.278 10.153 10.074 10.000 9.947
## 2003 10.052 10.386 10.714 10.895 10.854 10.739 10.611 10.492 10.375 10.267
## 2004 10.325 10.760 10.883 10.901 10.801 10.640 10.535 10.420 10.337 10.222
## 2005 10.043 10.184 10.354 10.366 10.244 10.099 9.961 9.827 9.715 9.656
## 2006 9.750 10.131 10.208 10.347 10.260 10.132 10.010 9.873 9.766 9.668
## 2007 9.702 9.745 9.931 10.112 10.081 9.935 9.826 9.704 9.655 9.563
## 2008 9.527 9.766 9.930 9.901 9.782 9.650 9.526 9.393 9.277 9.168
## Nov Dec
## 1984 10.282 10.334
## 1985 10.821 10.993
## 1986 11.472 11.421
## 1987 10.863 10.813
## 1988 10.749 10.624
## 1989 10.276 10.183
## 1990 9.718 9.747
## 1991 9.436 9.372
## 1992 8.818 8.806
## 1993 8.759 8.795
## 1994 8.930 8.882
## 1995 8.484 8.435
## 1996 8.135 8.117
## 1997 8.837 8.773
## 1998 8.237 8.191
## 1999 8.396 8.301
## 2000 8.356 8.293
## 2001 9.645 9.563
## 2002 9.910 9.947
## 2003 10.174 10.068
## 2004 10.100 10.014
## 2005 9.585 9.552
## 2006 9.620 9.597
## 2007 9.455 9.452
## 2008 9.071 9.023
class(SerieA.ts)
## [1] "ts"
start(SerieA.ts)
## [1] 1984 1
end(SerieA.ts)
## [1] 2008 12
plot(SerieA.ts, main="Serie de tiempo", ylab="Precio", col="red")
serielog=log(SerieA.ts)
serielog
## Jan Feb Mar Apr May Jun Jul Aug
## 1984 2.251292 2.316291 2.372111 2.394891 2.389771 2.379639 2.367436 2.355178
## 1985 2.354513 2.376764 2.406675 2.421878 2.427631 2.422410 2.411619 2.398804
## 1986 2.427719 2.456507 2.505118 2.529163 2.527407 2.512522 2.488899 2.474772
## 1987 2.454791 2.476706 2.474435 2.465724 2.453846 2.438601 2.429394 2.413500
## 1988 2.383612 2.401887 2.412246 2.446945 2.447897 2.435979 2.423209 2.410003
## 1989 2.372204 2.382228 2.391328 2.399893 2.396258 2.385915 2.374813 2.362645
## 1990 2.329714 2.334762 2.330978 2.324933 2.315304 2.308865 2.298175 2.286456
## 1991 2.280953 2.285337 2.295661 2.310454 2.306478 2.298075 2.288182 2.273980
## 1992 2.246226 2.260721 2.264779 2.254969 2.242092 2.226460 2.213972 2.201659
## 1993 2.182449 2.210689 2.221050 2.228508 2.225380 2.211675 2.199999 2.186613
## 1994 2.185377 2.220616 2.243154 2.253710 2.253605 2.242304 2.229907 2.216264
## 1995 2.193997 2.197669 2.218442 2.224624 2.212551 2.198890 2.185602 2.172249
## 1996 2.140066 2.172021 2.179739 2.183126 2.172818 2.158599 2.142416 2.130135
## 1997 2.114688 2.165160 2.217354 2.236659 2.233342 2.220181 2.208055 2.197780
## 1998 2.175547 2.183576 2.194889 2.201549 2.187735 2.171109 2.159061 2.145112
## 1999 2.101325 2.114688 2.151181 2.188296 2.191654 2.177928 2.163668 2.150133
## 2000 2.120703 2.155708 2.192882 2.197780 2.186725 2.174865 2.160330 2.148968
## 2001 2.154085 2.225380 2.293242 2.320425 2.316587 2.307274 2.297271 2.287877
## 2002 2.259469 2.280033 2.316291 2.334374 2.339206 2.330006 2.317769 2.309958
## 2003 2.307772 2.340459 2.371551 2.388304 2.384534 2.373882 2.361891 2.350613
## 2004 2.334568 2.375836 2.387202 2.388855 2.379639 2.364620 2.354703 2.343727
## 2005 2.306876 2.320818 2.337373 2.338531 2.326692 2.312436 2.298677 2.285134
## 2006 2.277267 2.315600 2.323172 2.336697 2.328253 2.315699 2.303585 2.289804
## 2007 2.272332 2.276754 2.295661 2.313723 2.310652 2.296064 2.285032 2.272538
## 2008 2.254130 2.278907 2.295560 2.292636 2.280544 2.266958 2.254025 2.239965
## Sep Oct Nov Dec
## 1984 2.341613 2.333308 2.330395 2.335439
## 1985 2.390504 2.383704 2.381489 2.397259
## 1986 2.463768 2.452556 2.439909 2.435454
## 1987 2.402973 2.392152 2.385363 2.380749
## 1988 2.396713 2.386926 2.374813 2.363116
## 1989 2.352232 2.341421 2.329811 2.320720
## 1990 2.275728 2.271094 2.273980 2.276960
## 1991 2.263324 2.252870 2.244532 2.237727
## 1992 2.195557 2.185377 2.176795 2.175433
## 1993 2.177249 2.172021 2.170082 2.174183
## 1994 2.208714 2.198224 2.189416 2.184027
## 1995 2.161828 2.150016 2.138182 2.132390
## 1996 2.116978 2.103646 2.096176 2.093961
## 1997 2.187735 2.183238 2.178947 2.171679
## 1998 2.130610 2.116858 2.108636 2.103036
## 1999 2.139713 2.137357 2.127755 2.116376
## 2000 2.137475 2.131203 2.122980 2.115412
## 2001 2.281055 2.273774 2.266440 2.257901
## 2002 2.302585 2.297271 2.293544 2.297271
## 2003 2.339399 2.328935 2.319835 2.309362
## 2004 2.335730 2.324542 2.312535 2.303984
## 2005 2.273671 2.267579 2.260199 2.256751
## 2006 2.278907 2.268821 2.263844 2.261451
## 2007 2.267476 2.257901 2.246544 2.246226
## 2008 2.227538 2.215719 2.205083 2.199777
plot(serielog)
#Stationarity: To know the number of differences that are required to achieve that the series
#be stationary
ndiffs(SerieA.ts)
## [1] 1
#Paso 2.Prueba de DickeyFuller
adf.test(SerieA.ts)
##
## Augmented Dickey-Fuller Test
##
## data: SerieA.ts
## Dickey-Fuller = -1.2334, Lag order = 6, p-value = 0.8994
## alternative hypothesis: stationary
seriedif=diff(SerieA.ts)
plot(seriedif)
acf(seriedif)
ndiffs(seriedif)
## [1] 0
adf.test(seriedif)
## Warning in adf.test(seriedif): p-value smaller than printed p-value
##
## Augmented Dickey-Fuller Test
##
## data: seriedif
## Dickey-Fuller = -10.613, Lag order = 6, p-value = 0.01
## alternative hypothesis: stationary
#Prueba de Dickey Fuller con dos diferencias
seriedif2=diff(SerieA.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 = -11.117, Lag order = 6, 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(SerieA.ts,order=c(1,2,1))
summary(modelo1)
##
## Call:
## arima(x = SerieA.ts, order = c(1, 2, 1))
##
## Coefficients:
## ar1 ma1
## 0.0191 0.2969
## s.e. 0.1602 0.1504
##
## sigma^2 estimated as 0.01243: log likelihood = 230.89, aic = -455.78
##
## Training set error measures:
## ME RMSE MAE MPE MAPE MASE
## Training set -0.001708912 0.111109 0.07294355 -0.0009988697 0.7348677 0.5865616
## ACF1
## Training set 0.001412786
tsdiag(modelo1)
Box.test(residuals(modelo1),type="Ljung-Box")
##
## Box-Ljung test
##
## data: residuals(modelo1)
## X-squared = 0.0006048, df = 1, p-value = 0.9804
error=residuals(modelo1)
plot(error)
#Pronosticos Arima
pronostico=forecast::forecast(modelo1,h=10)
pronostico
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## Jan 2009 8.989383 8.846517 9.132249 8.770888 9.207878
## Feb 2009 8.956041 8.595642 9.316440 8.404858 9.507224
## Mar 2009 8.922704 8.290233 9.555174 7.955424 9.889984
## Apr 2009 8.889367 7.939540 9.839193 7.436733 10.342001
## May 2009 8.856030 7.549241 10.162819 6.857468 10.854592
## Jun 2009 8.822693 7.123294 10.522092 6.223686 11.421700
## Jul 2009 8.789356 6.664667 10.914045 5.539925 12.038787
## Aug 2009 8.756019 6.175691 11.336347 4.809748 12.702290
## Sep 2009 8.722682 5.658261 11.787103 4.036054 13.409310
## Oct 2009 8.689345 5.113955 12.264736 3.221257 14.157433
plot(pronostico)
