R Notebook
“Librerías”
library(tseries)## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoolibrary(astsa)
library(forecast)##
## Attaching package: 'forecast'## The following object is masked from 'package:astsa':
##
## gaslibrary(MASS)—————– Instrucciones Laboratorio —————————–
#Para el presente laboratorio utilizaremos la series mensuales de desempleo y de las ventas de pollo
3. En caso que se determine que la serie tiene raíz unitaria, aplicar y describir el procedimiento
para eliminarla e incudir estacionariedad.
4. En caso de Identificar Estecionalidad en la serie, realizar el procedimiendo de diferenciación
estacional de la serie
4. En caso de haber aplicado el procedimiento anterior realizar la prueba estadística ADF para
determinar si la serie tiene raíz unitária y dar la interpretación de la prueba.
5. Obtener la gráfica de la serie con la que se realizará el pronóstico (serie en niveles
o diferenciada).
6. Obtener el acf y pacf de la serie para pronóstico y dar una intuición de cada una.
7. Buscar un modelo SARIMA(p,d,q)x(P,D,Q)s que mejor ajuste, considerando
la tabla de coeficientes, criterios de información y análisis de residuales.
8. Selección del modelo ajustado y su justificación.
9. Realizar le pronóstico de la serie para 24 días en adelante.
Series.Unemp<-unemp
Series.Chicken<-chicken1. Obtención y creación de la gráfica de la serie de datos original y una breve explicación de la gráfica.
plot(Series.Unemp, main= "Desempleo", col="blue")
plot(Series.Chicken, main= "Ventas de Pollo", col="red")
La gráfica de desempleo se ve en los primeros años una variación
aleatoria, es hasta el año 1955hasta cierto punto estacional, hasta el
año 1975 que tiene una alza importante. Las ventas de pollo desde el año
2002 hasta el 2016 van a la alza, ´con un comportamiento aleatorio.
log.Series.Unemp<-log(Series.Unemp)
log.Series.Chicken<-log(Series.Chicken)
plot(log.Series.Unemp, main="Desempleo", col="red")
plot(log.Series.Chicken, main="Ventas de pollo", col="blue")
2. Aplicar la prueba estadística ADF para determinar si la serie raíz unitária y dar la interpretación de la prueba.
adf.test(log.Series.Unemp)##
## Augmented Dickey-Fuller Test
##
## data: log.Series.Unemp
## Dickey-Fuller = -3.7221, Lag order = 7, p-value = 0.02315
## alternative hypothesis: stationaryadf.test(log.Series.Chicken)##
## Augmented Dickey-Fuller Test
##
## data: log.Series.Chicken
## Dickey-Fuller = -2.7479, Lag order = 5, p-value = 0.2637
## alternative hypothesis: stationaryLa serie de unemployment tiene un p-value <.05 por tanto no es estacionaria. La serie de ventas de pollo tiene un p-value>.05, por tanto es estacionaria.
3. En caso que se determine que la serie tiene raíz unitaria, aplicar y describir el procedimiento para eliminarla e incudir estacionariedad.
unemp.return.series<-diff(log.Series.Unemp)
chicken.return.series<-diff(log.Series.Chicken)- En caso de Identificar Estacionalidad en la serie, realizar el procedimiendo de diferenciación estacional de la serie
plot(unemp.return.series)
plot(chicken.return.series)
- En caso de haber aplicado el procedimiento anterior realizar la prueba estadística ADF para determinar si la serie tiene raíz unitária y dar la interpretación de la prueba.
adf.test(unemp.return.series)## Warning in adf.test(unemp.return.series): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: unemp.return.series
## Dickey-Fuller = -6.9076, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationaryadf.test(chicken.return.series)## Warning in adf.test(chicken.return.series): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: chicken.return.series
## Dickey-Fuller = -5.6403, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationary- Obtener la gráfica de la serie con la que se realizará el pronóstico (serie en niveles o diferenciada).
plot(unemp.return.series)
plot(chicken.return.series)
- Obtener el acf y pacf de la serie para pronóstico y dar una intuición de cada una.
acf2(unemp.return.series, max.lag = 20)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
## ACF 0.02 -0.1 -0.25 -0.10 0.25 -0.11 0.22 -0.12 -0.27 -0.16 0.00 0.74 -0.03
## PACF 0.02 -0.1 -0.25 -0.11 0.21 -0.21 0.25 -0.09 -0.32 -0.14 0.05 0.63 -0.13
## [,14] [,15] [,16] [,17] [,18] [,19] [,20]
## ACF -0.16 -0.28 -0.14 0.19 -0.14 0.22 -0.13
## PACF -0.19 -0.11 -0.15 -0.12 -0.12 0.07 -0.01acf2(chicken.return.series, max.lag = 20)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12]
## ACF 0.72 0.37 0.07 -0.08 -0.17 -0.20 -0.26 -0.22 -0.10 0.09 0.26 0.33
## PACF 0.72 -0.31 -0.13 0.05 -0.12 -0.05 -0.17 0.12 0.07 0.15 0.12 -0.02
## [,13] [,14] [,15] [,16] [,17] [,18] [,19] [,20]
## ACF 0.19 0.03 -0.07 -0.13 -0.21 -0.27 -0.31 -0.23
## PACF -0.24 0.03 0.04 -0.12 -0.10 -0.01 -0.06 0.06adf.test(chicken.return.series)## Warning in adf.test(chicken.return.series): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: chicken.return.series
## Dickey-Fuller = -5.6403, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationaryadf.test(unemp.return.series)## Warning in adf.test(unemp.return.series): p-value smaller than printed p-value##
## Augmented Dickey-Fuller Test
##
## data: unemp.return.series
## Dickey-Fuller = -6.9076, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationary- Buscar un modelo SARIMA(p,d,q)x(P,D,Q)s que mejor ajuste, considerando la tabla de coeficientes, criterios de información y análisis de residuales.
season12.diff.log.chicken<-diff(chicken.return.series, 12)
plot(season12.diff.log.chicken)
season12.diff.log.unemp<-diff(unemp.return.series, 12)
plot(season12.diff.log.unemp)
acf2(season12.diff.log.unemp)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
## ACF 0.15 0.28 0.18 0.12 0.15 0.05 -0.04 0.00 -0.08 -0.17 -0.03 -0.47 -0.16
## PACF 0.15 0.26 0.12 0.02 0.06 -0.02 -0.13 -0.03 -0.06 -0.16 0.05 -0.41 -0.06
## [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]
## ACF -0.16 -0.14 -0.16 -0.13 -0.1 0.02 0.01 -0.02 0.00 -0.02 0.00 0.11
## PACF 0.08 0.04 -0.07 0.01 0.0 0.04 0.08 -0.06 -0.15 0.00 -0.24 0.06
## [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]
## ACF 0.03 0.06 0.10 0.04 0.06 0.03 -0.08 0.01 -0.01 -0.08 -0.04 -0.10
## PACF 0.04 0.02 0.02 -0.01 -0.04 0.04 -0.07 -0.06 -0.08 -0.09 -0.20 0.02
## [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48]
## ACF -0.02 -0.06 -0.10 -0.10 -0.03 -0.17 0.03 -0.03 0.02 0.07 0.08
## PACF 0.06 -0.05 -0.04 -0.08 0.01 -0.10 0.01 -0.04 -0.01 -0.02 -0.05acf2(season12.diff.log.chicken)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
## ACF 0.75 0.47 0.23 0.14 0.1 0.06 -0.02 -0.10 -0.15 -0.20 -0.27 -0.39 -0.30
## PACF 0.75 -0.20 -0.10 0.14 0.0 -0.08 -0.09 -0.04 -0.01 -0.15 -0.11 -0.24 0.36
## [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]
## ACF -0.13 0.07 0.17 0.15 0.09 0.02 0.00 -0.07 -0.13 -0.21 -0.25 -0.25
## PACF 0.09 0.10 -0.01 -0.05 -0.04 -0.13 -0.07 -0.22 -0.08 -0.16 -0.20 0.17
## [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]
## ACF -0.25 -0.30 -0.32 -0.31 -0.28 -0.18 -0.06 0.09 0.18 0.20 0.18 0.17
## PACF -0.03 0.02 0.04 -0.09 -0.16 -0.02 0.08 0.00 0.00 -0.19 -0.07 0.22
## [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48]
## ACF 0.16 0.15 0.13 0.09 0.09 0.08 0.04 -0.04 -0.12 -0.10 -0.02
## PACF -0.01 -0.04 0.02 -0.06 -0.03 0.06 -0.02 -0.07 0.02 -0.07 -0.09adf.test(season12.diff.log.unemp)## Warning in adf.test(season12.diff.log.unemp): p-value smaller than printed p-
## value##
## Augmented Dickey-Fuller Test
##
## data: season12.diff.log.unemp
## Dickey-Fuller = -6.0573, Lag order = 7, p-value = 0.01
## alternative hypothesis: stationaryadf.test(season12.diff.log.chicken)## Warning in adf.test(season12.diff.log.chicken): p-value smaller than printed p-
## value##
## Augmented Dickey-Fuller Test
##
## data: season12.diff.log.chicken
## Dickey-Fuller = -4.2555, Lag order = 5, p-value = 0.01
## alternative hypothesis: stationarychicken.fti1<-sarima(log(chicken),p=1,d=1,q=1,
P=0,D=1,Q=1,
S=12)## initial value -4.228217
## iter 2 value -4.447270
## iter 3 value -4.866760
## iter 4 value -4.878667
## iter 5 value -4.885094
## iter 6 value -4.889257
## iter 7 value -4.891438
## iter 8 value -4.891934
## iter 9 value -4.892053
## iter 10 value -4.892123
## iter 11 value -4.892129
## iter 12 value -4.892131
## iter 13 value -4.892131
## iter 13 value -4.892131
## iter 13 value -4.892131
## final value -4.892131
## converged
## initial value -4.887102
## iter 2 value -4.888180
## iter 3 value -4.888690
## iter 4 value -4.888695
## iter 5 value -4.888697
## iter 6 value -4.888698
## iter 7 value -4.888698
## iter 7 value -4.888698
## iter 7 value -4.888698
## final value -4.888698
## converged
chicken.fti3<-sarima(log(chicken),p=1,d=1,q=1,
P=1,D=0,Q=1,
S=12)## initial value -4.372002
## iter 2 value -4.440306
## iter 3 value -4.844152
## iter 4 value -4.855042
## iter 5 value -4.866371
## iter 6 value -4.882210
## iter 7 value -4.896644
## iter 8 value -4.911045
## iter 9 value -4.936748
## iter 10 value -4.941209
## iter 11 value -4.949631
## iter 12 value -4.951322
## iter 13 value -4.952933
## iter 14 value -4.953267
## iter 15 value -4.953471
## iter 16 value -4.953560
## iter 17 value -4.953733
## iter 18 value -4.954552
## iter 19 value -4.954745
## iter 20 value -4.954805
## iter 21 value -4.954805
## iter 22 value -4.954805
## iter 22 value -4.954805
## iter 22 value -4.954805
## final value -4.954805
## converged
## initial value -4.872865
## iter 2 value -4.905968
## iter 3 value -4.907057
## iter 4 value -4.909450
## iter 5 value -4.912831
## iter 6 value -4.914046
## iter 7 value -4.915649
## iter 8 value -4.915887
## iter 9 value -4.915942
## iter 10 value -4.915956
## iter 11 value -4.915985
## iter 12 value -4.916028
## iter 13 value -4.916035
## iter 14 value -4.916049
## iter 15 value -4.916067
## iter 16 value -4.916076
## iter 17 value -4.916099
## iter 18 value -4.916124
## iter 19 value -4.916140
## iter 20 value -4.916144
## iter 21 value -4.916144
## iter 22 value -4.916144
## iter 23 value -4.916145
## iter 24 value -4.916145
## iter 25 value -4.916145
## iter 26 value -4.916146
## iter 27 value -4.916146
## iter 28 value -4.916146
## iter 29 value -4.916147
## iter 30 value -4.916147
## iter 30 value -4.916147
## iter 30 value -4.916147
## final value -4.916147
## converged
chicken.fti4<-sarima(log(chicken),p=0,d=1,q=1,
P=0,D=1,Q=1,
S=12)## initial value -4.228158
## iter 2 value -4.621534
## iter 3 value -4.715551
## iter 4 value -4.727036
## iter 5 value -4.733402
## iter 6 value -4.733585
## iter 7 value -4.733628
## iter 8 value -4.733643
## iter 8 value -4.733643
## iter 8 value -4.733643
## final value -4.733643
## converged
## initial value -4.754563
## iter 2 value -4.763053
## iter 3 value -4.764066
## iter 4 value -4.765008
## iter 5 value -4.765055
## iter 6 value -4.765059
## iter 6 value -4.765059
## final value -4.765059
## converged
chicken.fti5<-sarima(log(chicken),p=1,d=0,q=0,
P=1,D=1,Q=0,
S=12)## initial value -2.732654
## iter 2 value -4.270378
## iter 3 value -4.275620
## iter 4 value -4.289136
## iter 5 value -4.306748
## iter 6 value -4.306763
## iter 7 value -4.306780
## iter 8 value -4.306858
## iter 9 value -4.306869
## iter 10 value -4.306898
## iter 11 value -4.306908
## iter 12 value -4.306937
## iter 13 value -4.307002
## iter 14 value -4.307126
## iter 15 value -4.307279
## iter 16 value -4.307298
## iter 17 value -4.307346
## iter 18 value -4.307380
## iter 19 value -4.307381
## iter 20 value -4.307426
## iter 21 value -4.307442
## iter 22 value -4.307447
## iter 22 value -4.307447
## final value -4.307447
## converged
## initial value -4.306470
## iter 2 value -4.306506
## iter 3 value -4.306587
## iter 4 value -4.306694
## iter 5 value -4.306803
## iter 6 value -4.306844
## iter 7 value -4.306855
## iter 8 value -4.306857
## iter 9 value -4.306858
## iter 10 value -4.306868
## iter 11 value -4.306878
## iter 12 value -4.306892
## iter 13 value -4.306897
## iter 14 value -4.306899
## iter 15 value -4.306899
## iter 16 value -4.306900
## iter 17 value -4.306901
## iter 18 value -4.306902
## iter 19 value -4.306903
## iter 20 value -4.306903
## iter 20 value -4.306903
## iter 20 value -4.306903
## final value -4.306903
## converged
unemp.fti1<-sarima(log(unemp),p=1,d=1,q=1,
P=0,D=1,Q=1,
S=12)## initial value -2.551638
## iter 2 value -2.702571
## iter 3 value -2.737835
## iter 4 value -2.756882
## iter 5 value -2.758216
## iter 6 value -2.759291
## iter 7 value -2.759540
## iter 8 value -2.760214
## iter 9 value -2.760500
## iter 10 value -2.760825
## iter 11 value -2.762580
## iter 12 value -2.765570
## iter 13 value -2.768812
## iter 14 value -2.771957
## iter 15 value -2.775130
## iter 16 value -2.775185
## iter 17 value -2.775195
## iter 18 value -2.775206
## iter 19 value -2.775210
## iter 20 value -2.775214
## iter 21 value -2.775214
## iter 21 value -2.775214
## iter 21 value -2.775214
## final value -2.775214
## converged
## initial value -2.787571
## iter 2 value -2.788447
## iter 3 value -2.788740
## iter 4 value -2.788800
## iter 5 value -2.788829
## iter 6 value -2.788860
## iter 7 value -2.788919
## iter 8 value -2.788948
## iter 9 value -2.788952
## iter 10 value -2.788955
## iter 11 value -2.788955
## iter 12 value -2.788956
## iter 13 value -2.788956
## iter 14 value -2.788956
## iter 15 value -2.788956
## iter 15 value -2.788956
## final value -2.788956
## converged
unemp.fti1$ttable## Estimate SE t.value p.value
## ar1 0.8064 0.0721 11.1775 0
## ma1 -0.6742 0.0847 -7.9579 0
## sma1 -0.7118 0.0436 -16.3365 0season13.ddiff.log.serieChicken<-diff(chicken.return.series, 13)
plot(season13.ddiff.log.serieChicken)
acf2(season13.ddiff.log.serieChicken)
## [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [,11] [,12] [,13]
## ACF 0.67 0.34 0.11 0.09 0.10 0.11 -0.06 -0.12 -0.12 -0.03 -0.02 -0.08 -0.3
## PACF 0.67 -0.19 -0.05 0.17 -0.02 0.02 -0.27 0.12 -0.02 0.03 -0.06 -0.11 -0.3
## [,14] [,15] [,16] [,17] [,18] [,19] [,20] [,21] [,22] [,23] [,24] [,25]
## ACF -0.22 -0.06 0.09 0.08 0.01 -0.13 -0.12 -0.1 -0.05 -0.10 -0.11 -0.19
## PACF 0.35 0.03 -0.06 0.00 -0.05 -0.07 -0.12 0.0 0.00 -0.08 0.08 -0.21
## [,26] [,27] [,28] [,29] [,30] [,31] [,32] [,33] [,34] [,35] [,36] [,37]
## ACF -0.19 -0.23 -0.26 -0.32 -0.29 -0.21 -0.05 0.07 0.15 0.13 0.22 0.18
## PACF -0.31 0.05 -0.06 -0.18 0.00 0.08 -0.02 0.03 0.06 -0.01 0.18 -0.07
## [,38] [,39] [,40] [,41] [,42] [,43] [,44] [,45] [,46] [,47] [,48]
## ACF 0.15 0.10 0.06 -0.01 0.06 0.08 0.06 -0.01 -0.05 -0.03 0.13
## PACF -0.13 -0.14 -0.04 -0.04 0.09 -0.02 -0.04 -0.06 0.05 0.10 0.03adf.test(season13.ddiff.log.serieChicken)##
## Augmented Dickey-Fuller Test
##
## data: season13.ddiff.log.serieChicken
## Dickey-Fuller = -3.9264, Lag order = 5, p-value = 0.01451
## alternative hypothesis: stationarychicken.fti1<-sarima(log(Series.Chicken),p=1,d=1,q=1,
P=1,D=1,Q=1,
S=12)## initial value -4.215806
## iter 2 value -4.442822
## iter 3 value -4.796222
## iter 4 value -4.833307
## iter 5 value -4.838954
## iter 6 value -4.847489
## iter 7 value -4.850336
## iter 8 value -4.850991
## iter 9 value -4.851243
## iter 10 value -4.851267
## iter 11 value -4.851274
## iter 12 value -4.851276
## iter 13 value -4.851277
## iter 13 value -4.851277
## iter 13 value -4.851277
## final value -4.851277
## converged
## initial value -4.880157
## iter 2 value -4.886418
## iter 3 value -4.888499
## iter 4 value -4.888723
## iter 5 value -4.888787
## iter 6 value -4.888800
## iter 7 value -4.888807
## iter 8 value -4.888807
## iter 8 value -4.888807
## iter 8 value -4.888807
## final value -4.888807
## converged
chicken.fti2<-sarima(log(Series.Chicken),p=1,d=1,q=1,
P=0,D=1,Q=1,
S=12)## initial value -4.228217
## iter 2 value -4.447270
## iter 3 value -4.866760
## iter 4 value -4.878667
## iter 5 value -4.885094
## iter 6 value -4.889257
## iter 7 value -4.891438
## iter 8 value -4.891934
## iter 9 value -4.892053
## iter 10 value -4.892123
## iter 11 value -4.892129
## iter 12 value -4.892131
## iter 13 value -4.892131
## iter 13 value -4.892131
## iter 13 value -4.892131
## final value -4.892131
## converged
## initial value -4.887102
## iter 2 value -4.888180
## iter 3 value -4.888690
## iter 4 value -4.888695
## iter 5 value -4.888697
## iter 6 value -4.888698
## iter 7 value -4.888698
## iter 7 value -4.888698
## iter 7 value -4.888698
## final value -4.888698
## converged
8. Selección del modelo ajustado y su justificación.
library("PerformanceAnalytics")## Loading required package: xts## Loading required package: zoo##
## Attaching package: 'zoo'## The following objects are masked from 'package:base':
##
## as.Date, as.Date.numeric##
## Attaching package: 'PerformanceAnalytics'## The following object is masked from 'package:graphics':
##
## legendchicken.fti2$ttable #pvalues dentro de rango## Estimate SE t.value p.value
## ar1 0.6332 0.0753 8.4079 0.0000
## ma1 0.2449 0.0852 2.8749 0.0046
## sma1 -0.8241 0.0624 -13.2020 0.0000chicken.fti1$ttable #pvalues dentro de rango y ## Estimate SE t.value p.value
## ar1 0.6327 0.0755 8.3844 0.0000
## ma1 0.2455 0.0853 2.8773 0.0045
## sar1 -0.0182 0.0949 -0.1916 0.8483
## sma1 -0.8167 0.0728 -11.2178 0.00009. Realizar le pronóstico de la serie para 24 días en adelante.
SARIMA.forcast<-sarima.for(log(Series.Chicken), n.ahead = 24, 1, 1, 1, 0, 1, 1, 12)
SARIMA.forcast$pred## Jan Feb Mar Apr May Jun Jul Aug
## 2016 4.706076
## 2017 4.682485 4.685708 4.692149 4.698681 4.709161 4.718234 4.724330 4.723157
## 2018 4.709516 4.713153 4.719856 4.726554 4.737139 4.746279 4.752416
## Sep Oct Nov Dec
## 2016 4.701466 4.690623 4.682630 4.680135
## 2017 4.722610 4.714340 4.707977 4.706513
## 2018SARIMA.forcast$se## Jan Feb Mar Apr May Jun
## 2016
## 2017 0.044007359 0.049830879 0.055216309 0.060223945 0.064906774 0.069309834
## 2018 0.099682918 0.103708200 0.107602573 0.111372774 0.115026663 0.118572233
## Jul Aug Sep Oct Nov Dec
## 2016 0.007216761 0.015354066 0.023329223 0.030796920 0.037681753
## 2017 0.073470762 0.077833169 0.082329700 0.086820721 0.091230691 0.095522932
## 2018 0.122017091SARIMA.forcast<-sarima.for(log(Series.Unemp), n.ahead = 24, 1, 1, 1, 0, 1, 1, 12)
SARIMA.forcast$pred## Jan Feb Mar Apr May Jun Jul Aug
## 1979 6.515336 6.523716 6.474964 6.366666 6.310446 6.502138 6.474210 6.414748
## 1980 6.532327 6.539105 6.489061 6.379721 6.322661 6.513675 6.485200 6.425297
## Sep Oct Nov Dec
## 1979 6.390059 6.346154 6.379343 6.368991
## 1980 6.400253 6.356062 6.389019 6.378481SARIMA.forcast$se## Jan Feb Mar Apr May Jun
## 1979 0.06076454 0.09179104 0.11871120 0.14343310 0.16658312 0.18845187
## 1980 0.32167678 0.34318048 0.36419653 0.38467213 0.40458407 0.42392859
## Jul Aug Sep Oct Nov Dec
## 1979 0.20920972 0.22897545 0.24784207 0.26588779 0.28318099 0.29978269
## 1980 0.44271447 0.46095838 0.47868164 0.49590810 0.51266271 0.52897052