###TRABAJO INDIVIDUAL####
###################################
# INTEGRANTE:
# SUNICO YURICO CALLATA OLIVERA CON CÓD. EST. 222961
setwd("/Users/rosariocalratydelpilar/Downloads/series_tiempo")
dir()
## [1] "1series.R" "consumo_electricidad.txt"
## [3] "consumo_electricidad.xlsx" "pib.txt"
## [5] "pib.xlsx" "TAREA1_1.R"
## [7] "TAREA2.docx" "TAREA2.R"
## [9] "temperatura.txt" "temperatura.xlsx"
## [11] "trabajo1" "turismo.txt"
## [13] "turismo.xlsx"
#######################
#### 1) PBI
#Parte descriptiva de la serie
pbi = scan("pib.txt");pbi
## [1] 5.51 6.11 6.60 7.11 7.47 7.85 8.33 8.60 9.07 9.78 10.08 10.43
## [13] 11.16 11.92 12.47 12.41 12.67 12.88 12.92 12.81 12.86 12.74 12.83 13.00
## [25] 13.18 13.43 13.83 14.56 15.27 15.97 16.55 16.94 17.05 16.84 17.21 17.66
## [37] 18.05 18.70 19.46 20.28 21.13 21.65 21.92 22.22 22.57 22.98 23.51
# Muestra 47 datos del PBI
#Parte descriptiva de la serie
summary(pbi)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 5.51 10.79 13.00 14.22 17.43 23.51
# muestra el valor minimo y maximo, asi como su media
sd(pbi)
## [1] 4.954744
# muestra la desviacion estandar
boxplot(pbi)
# aparentemente no se visualiza datos atipicos
hist(pbi)
#Definir la serie temporal de los datos de PBI
#install.packages("tseries")
library(tseries)
## Warning: package 'tseries' was built under R version 4.3.3
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
pbi.ts <- ts(pbi,start=2000,frequency = 12)
pbi.ts
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2000 5.51 6.11 6.60 7.11 7.47 7.85 8.33 8.60 9.07 9.78 10.08 10.43
## 2001 11.16 11.92 12.47 12.41 12.67 12.88 12.92 12.81 12.86 12.74 12.83 13.00
## 2002 13.18 13.43 13.83 14.56 15.27 15.97 16.55 16.94 17.05 16.84 17.21 17.66
## 2003 18.05 18.70 19.46 20.28 21.13 21.65 21.92 22.22 22.57 22.98 23.51
plot(pbi.ts,type="o",col=4)
#Se verificará si cumple con las caracteristicas de serie temporal
#1) Tendencia
# Aplicando test de Mann-Kendall
#Considerando:
# Ho: No hay evidencia que existe tendencia en la serie temporal
# H1: Si hay evidencia que existe tendencia en la serie temporal (H1<0.05=aceptar)
library(Kendall)
resultado <- MannKendall(pbi.ts)
print(resultado)
## tau = 0.974, 2-sided pvalue =< 2.22e-16
# Considerando que el pvalue =2.22e-16 es menor a 0.05, se presume que
# existe TENDENCIA en los datos.
#2) Estacionalidad
# Aplicando test de Kruskal-Wallis
# Considerando:
# Ho: La serie temporal no presenta estacionalidad
# H1: la serie temporal si presenta estacionalidad (H1<0.05=aceptar)
#resultado <- kruskal.test(serie1 ~ estacion)
estacion = cycle(pbi.ts)
print(resultado)
## tau = 0.974, 2-sided pvalue =< 2.22e-16
# Considerando que el p-value = 2.22e-16 es mayor a 0.05, se presume que
# existe ESTACIONALIDAD en los datos.
#3) Heterocedasticidad
# Aplicando la prueba de Levene
# Ho: la variabilidad de los errores es constante a lo largo del tiempo(homocedasticidad).
# H1: la variabilidad de los errores no es constante a lo largo del tiempo(heterocedasticidad)
library(car)
## Loading required package: carData
resultado <- leveneTest(pbi.ts ~ as.factor(estacion))
print(resultado)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 11 0.1322 0.9995
## 35
# Considerando que p-value 0.9995, es decir mayor a 0.05, demostraria que los datos
# no tienen HETEROCEDASTICIDAD.Por lo que concluimos
# en aceptar la Ho, deduciendo que los datos presentan HOMOCEDASTICIDAD.
# SE PROCEDE A DESCOMPONER LA SERIE TEMPORAL SEGUN SUS CARACTERISTICAS
# La serie pbi.ts presenta unicamente TENDENCIA
# El modelo propuesto es: x_t = T_t + e_t
#utilizaremos Medias Móviles para estimar la componente de tendencia
tendencia = decompose(pbi.ts);tendencia
## $x
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2000 5.51 6.11 6.60 7.11 7.47 7.85 8.33 8.60 9.07 9.78 10.08 10.43
## 2001 11.16 11.92 12.47 12.41 12.67 12.88 12.92 12.81 12.86 12.74 12.83 13.00
## 2002 13.18 13.43 13.83 14.56 15.27 15.97 16.55 16.94 17.05 16.84 17.21 17.66
## 2003 18.05 18.70 19.46 20.28 21.13 21.65 21.92 22.22 22.57 22.98 23.51
##
## $seasonal
## Jan Feb Mar Apr May Jun
## 2000 -0.34815394 -0.17273727 0.02059606 0.14642940 0.38323495 0.45233218
## 2001 -0.34815394 -0.17273727 0.02059606 0.14642940 0.38323495 0.45233218
## 2002 -0.34815394 -0.17273727 0.02059606 0.14642940 0.38323495 0.45233218
## 2003 -0.34815394 -0.17273727 0.02059606 0.14642940 0.38323495 0.45233218
## Jul Aug Sep Oct Nov Dec
## 2000 0.32031829 0.15462384 0.01115162 -0.22370949 -0.34301505 -0.40107060
## 2001 0.32031829 0.15462384 0.01115162 -0.22370949 -0.34301505 -0.40107060
## 2002 0.32031829 0.15462384 0.01115162 -0.22370949 -0.34301505 -0.40107060
## 2003 0.32031829 0.15462384 0.01115162 -0.22370949 -0.34301505
##
## $trend
## Jan Feb Mar Apr May Jun Jul
## 2000 NA NA NA NA NA NA 8.313750
## 2001 11.007917 11.374583 11.707917 11.989167 12.227083 12.448750 12.640000
## 2002 13.767917 14.091250 14.437917 14.783333 15.136667 15.513333 15.910417
## 2003 18.683750 19.127500 19.577500 20.063333 20.581667 NA NA
## Aug Sep Oct Nov Dec
## 2000 8.791250 9.277917 9.743333 10.180833 10.607083
## 2001 12.787083 12.906667 13.052917 13.250833 13.487917
## 2002 16.332917 16.787083 17.260000 17.742500 18.223333
## 2003 NA NA NA NA
##
## $random
## Jan Feb Mar Apr May
## 2000 NA NA NA NA NA
## 2001 0.500237269 0.718153935 0.741487269 0.274403935 0.059681713
## 2002 -0.239762731 -0.488512731 -0.628512731 -0.369762731 -0.249901620
## 2003 -0.285596065 -0.254762731 -0.138096065 0.070237269 0.165098380
## Jun Jul Aug Sep Oct
## 2000 NA -0.304068287 -0.345873843 -0.219068287 0.260376157
## 2001 -0.021082176 -0.040318287 -0.131707176 -0.057818287 -0.089207176
## 2002 0.004334491 0.319265046 0.452459491 0.251765046 -0.196290509
## 2003 NA NA NA NA NA
## Nov Dec
## 2000 0.242181713 0.223987269
## 2001 -0.077818287 -0.086846065
## 2002 -0.189484954 -0.162262731
## 2003 NA
##
## $figure
## [1] -0.34815394 -0.17273727 0.02059606 0.14642940 0.38323495 0.45233218
## [7] 0.32031829 0.15462384 0.01115162 -0.22370949 -0.34301505 -0.40107060
##
## $type
## [1] "additive"
##
## attr(,"class")
## [1] "decomposed.ts"
trend = tendencia$trend
lines(trend,col=2)
# Estimar la tendencia T_t, MEDIANTE MEDIAS MOVILES
# x_t = T_t + e_t
# Medais moviles: k=3
tendencia3 = stats::filter(pbi.ts,sides=2,rep(1/3,3))
tendencia3
## Jan Feb Mar Apr May Jun Jul
## 2000 NA 6.073333 6.606667 7.060000 7.476667 7.883333 8.260000
## 2001 11.170000 11.850000 12.266667 12.516667 12.653333 12.823333 12.870000
## 2002 13.203333 13.480000 13.940000 14.553333 15.266667 15.930000 16.486667
## 2003 18.136667 18.736667 19.480000 20.290000 21.020000 21.566667 21.930000
## Aug Sep Oct Nov Dec
## 2000 8.666667 9.150000 9.643333 10.096667 10.556667
## 2001 12.863333 12.803333 12.810000 12.856667 13.003333
## 2002 16.846667 16.943333 17.033333 17.236667 17.640000
## 2003 22.236667 22.590000 23.020000 NA
# Medais moviles: k=2,
tendencia2 = stats::filter(pbi.ts,sides=2,rep(1/2,2))
tendencia2
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct
## 2000 5.810 6.355 6.855 7.290 7.660 8.090 8.465 8.835 9.425 9.930
## 2001 11.540 12.195 12.440 12.540 12.775 12.900 12.865 12.835 12.800 12.785
## 2002 13.305 13.630 14.195 14.915 15.620 16.260 16.745 16.995 16.945 17.025
## 2003 18.375 19.080 19.870 20.705 21.390 21.785 22.070 22.395 22.775 23.245
## Nov Dec
## 2000 10.255 10.795
## 2001 12.915 13.090
## 2002 17.435 17.855
## 2003 NA
# Medais moviles: k=7
tendencia7 = stats::filter(pbi.ts,sides=2,rep(1/7,7))
tendencia7
## Jan Feb Mar Apr May Jun Jul
## 2000 NA NA NA 6.997143 7.438571 7.861429 8.315714
## 2001 11.178571 11.591429 11.991429 12.347143 12.582857 12.717143 12.755714
## 2002 13.367143 13.728571 14.177143 14.684286 15.221429 15.738571 16.168571
## 2003 18.314286 18.927143 19.561429 20.170000 20.765714 21.318571 21.821429
## Aug Sep Oct Nov Dec
## 2000 8.740000 9.162857 9.635714 10.148571 10.701429
## 2001 12.815714 12.862857 12.905714 12.978571 13.124286
## 2002 16.547143 16.888571 17.185714 17.492857 17.852857
## 2003 22.282857 NA NA NA
plot(pbi.ts,type="o")
lines(tendencia3,col=2)
lines(tendencia2,col=4)
lines(tendencia7,col=3)
#estimando la componente irregular e_t = x_t - T_t
e3 = pbi.ts - tendencia3;e3
## Jan Feb Mar Apr May
## 2000 NA 0.036666667 -0.006666667 0.050000000 -0.006666667
## 2001 -0.010000000 0.070000000 0.203333333 -0.106666667 0.016666667
## 2002 -0.023333333 -0.050000000 -0.110000000 0.006666667 0.003333333
## 2003 -0.086666667 -0.036666667 -0.020000000 -0.010000000 0.110000000
## Jun Jul Aug Sep Oct
## 2000 -0.033333333 0.070000000 -0.066666667 -0.080000000 0.136666667
## 2001 0.056666667 0.050000000 -0.053333333 0.056666667 -0.070000000
## 2002 0.040000000 0.063333333 0.093333333 0.106666667 -0.193333333
## 2003 0.083333333 -0.010000000 -0.016666667 -0.020000000 -0.040000000
## Nov Dec
## 2000 -0.016666667 -0.126666667
## 2001 -0.026666667 -0.003333333
## 2002 -0.026666667 0.020000000
## 2003 NA
e2 = pbi.ts - tendencia2;e2
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct
## 2000 -0.300 -0.245 -0.255 -0.180 -0.190 -0.240 -0.135 -0.235 -0.355 -0.150
## 2001 -0.380 -0.275 0.030 -0.130 -0.105 -0.020 0.055 -0.025 0.060 -0.045
## 2002 -0.125 -0.200 -0.365 -0.355 -0.350 -0.290 -0.195 -0.055 0.105 -0.185
## 2003 -0.325 -0.380 -0.410 -0.425 -0.260 -0.135 -0.150 -0.175 -0.205 -0.265
## Nov Dec
## 2000 -0.175 -0.365
## 2001 -0.085 -0.090
## 2002 -0.225 -0.195
## 2003 NA
e7 = pbi.ts - tendencia7;e7
## Jan Feb Mar Apr May
## 2000 NA NA NA 0.112857143 0.031428571
## 2001 -0.018571429 0.328571429 0.478571429 0.062857143 0.087142857
## 2002 -0.187142857 -0.298571429 -0.347142857 -0.124285714 0.048571429
## 2003 -0.264285714 -0.227142857 -0.101428571 0.110000000 0.364285714
## Jun Jul Aug Sep Oct
## 2000 -0.011428571 0.014285714 -0.140000000 -0.092857143 0.144285714
## 2001 0.162857143 0.164285714 -0.005714286 -0.002857143 -0.165714286
## 2002 0.231428571 0.381428571 0.392857143 0.161428571 -0.345714286
## 2003 0.331428571 0.098571429 -0.062857143 NA NA
## Nov Dec
## 2000 -0.068571429 -0.271428571
## 2001 -0.148571429 -0.124285714
## 2002 -0.282857143 -0.192857143
## 2003 NA
ts.plot(cbind(e3,e2,e7), type="o",lty="dashed",col=c(2,4,3))
abline(h=0)
#Gráfica de la descomposición clásica k=3
par(mfrow=c(3,1))
plot(pbi.ts,type="o")
plot(tendencia3,col=2)
plot(e3,col=2)
# Muestra el grafico de serie temporal, tendencia y la estimacion de componentes
pbi.ts <- ts(pbi,start = 2008,frequency =16)
pbi.ts
## Time Series:
## Start = c(2008, 1)
## End = c(2010, 15)
## Frequency = 16
## [1] 5.51 6.11 6.60 7.11 7.47 7.85 8.33 8.60 9.07 9.78 10.08 10.43
## [13] 11.16 11.92 12.47 12.41 12.67 12.88 12.92 12.81 12.86 12.74 12.83 13.00
## [25] 13.18 13.43 13.83 14.56 15.27 15.97 16.55 16.94 17.05 16.84 17.21 17.66
## [37] 18.05 18.70 19.46 20.28 21.13 21.65 21.92 22.22 22.57 22.98 23.51
plot(pbi.ts)
# CONCLUIMOS QUE LOS DATOS DEL PBI SON DATOS QUE
# DEMUESTRAN TENDENCIA EXISTENTE A DIFERENCIA DE LA
# ESTACIONALIDAD HETEROCEDASTICIDAD, POR LO QUE
# CONCLUIMOS QUE ES UN MODELO ADITIVO.
##########################################################################
# 2) Temperatura
###################
#Parte descriptiva de la serie
temp = scan("temperatura.txt")
temp.ts <- ts(temp,start = 2000,frequency =12)
temp.ts
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2000 11.5 11.1 11.7 13.2 14.7 16.6 18.1 19.1 18.3 16.2 14.4 11.4
## 2001 11.0 11.4 12.3 11.6 17.0 18.2 19.7 20.2 18.0 17.2 14.1 13.7
## 2002 10.7 13.5 13.5 12.3 16.7 17.2 19.8 20.0 19.3 15.6 12.1 9.5
## 2003 10.0 9.6 11.9 12.0 14.9 16.3 19.0 19.8 19.1 14.4 12.8 11.4
## 2004 9.1 10.7 11.5 12.8 16.3 16.0 19.1 19.4 17.4 13.6 14.5 11.3
## 2005 12.2 10.9 12.0 12.6 14.7 17.3 18.2 19.4 16.9 13.6 11.8 12.2
## 2006 10.5 10.6 12.2 11.8 14.2 17.5 18.4 19.4 17.0 16.2 14.2 12.4
## 2007 11.0 11.7 12.4 13.7 16.3 17.8 19.9 20.3 17.2 17.8 14.7 12.6
## 2008 11.6 10.0 12.4 13.8 14.4 18.4 18.9 19.0 17.7 16.1 12.5 10.7
## 2009 10.2 12.8 15.0 15.2 16.4 17.3 18.8 20.0 18.9 18.4 14.0 12.1
## 2010 12.1 13.1 13.9 12.3 15.2 17.6 18.7 19.6 19.1 15.9 13.3 11.5
## 2011 11.2 10.5 12.4 13.4 15.9 17.1 20.2 20.7 19.0 15.7 12.2 11.6
## 2012 9.6 12.2 12.6 12.0 15.8 18.7 19.0 19.6 18.5 15.0 12.7 12.7
## 2013 10.0 10.0 12.6 11.8 14.1 17.4 18.2 19.2 17.2 16.2 10.2 7.6
## 2014 10.9 10.5 11.7 11.6 13.7 15.9 17.7 18.4 18.4 16.0 12.1 11.9
plot(temp.ts)
#Estacionalidad
estacion = cycle(temp.ts)
#H0: existe diferencias significativa entre periodos (No hay estacionalidad)
# test de Kruskal-Wallis
resultado <- kruskal.test(temp.ts ~ estacion)
print(resultado)
##
## Kruskal-Wallis rank sum test
##
## data: temp.ts by estacion
## Kruskal-Wallis chi-squared = 158.32, df = 11, p-value < 2.2e-16
###El modelo que podemos plantear con estacionalidad
### x_t = mu + S_t + e_t
#Media
media = mean(temp.ts);media
## [1] 14.74389
#Estimar la componente estacional (indice estacional): Ii = media(X_enero_i) - meadia
temp.ts
## Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
## 2000 11.5 11.1 11.7 13.2 14.7 16.6 18.1 19.1 18.3 16.2 14.4 11.4
## 2001 11.0 11.4 12.3 11.6 17.0 18.2 19.7 20.2 18.0 17.2 14.1 13.7
## 2002 10.7 13.5 13.5 12.3 16.7 17.2 19.8 20.0 19.3 15.6 12.1 9.5
## 2003 10.0 9.6 11.9 12.0 14.9 16.3 19.0 19.8 19.1 14.4 12.8 11.4
## 2004 9.1 10.7 11.5 12.8 16.3 16.0 19.1 19.4 17.4 13.6 14.5 11.3
## 2005 12.2 10.9 12.0 12.6 14.7 17.3 18.2 19.4 16.9 13.6 11.8 12.2
## 2006 10.5 10.6 12.2 11.8 14.2 17.5 18.4 19.4 17.0 16.2 14.2 12.4
## 2007 11.0 11.7 12.4 13.7 16.3 17.8 19.9 20.3 17.2 17.8 14.7 12.6
## 2008 11.6 10.0 12.4 13.8 14.4 18.4 18.9 19.0 17.7 16.1 12.5 10.7
## 2009 10.2 12.8 15.0 15.2 16.4 17.3 18.8 20.0 18.9 18.4 14.0 12.1
## 2010 12.1 13.1 13.9 12.3 15.2 17.6 18.7 19.6 19.1 15.9 13.3 11.5
## 2011 11.2 10.5 12.4 13.4 15.9 17.1 20.2 20.7 19.0 15.7 12.2 11.6
## 2012 9.6 12.2 12.6 12.0 15.8 18.7 19.0 19.6 18.5 15.0 12.7 12.7
## 2013 10.0 10.0 12.6 11.8 14.1 17.4 18.2 19.2 17.2 16.2 10.2 7.6
## 2014 10.9 10.5 11.7 11.6 13.7 15.9 17.7 18.4 18.4 16.0 12.1 11.9
enero = window(temp.ts,start=c(2000,1),freq=T)
enero
## Time Series:
## Start = 2000
## End = 2014
## Frequency = 1
## [1] 11.5 11.0 10.7 10.0 9.1 12.2 10.5 11.0 11.6 10.2 12.1 11.2 9.6 10.0 10.9
ISenero = mean(enero) - media;ISenero
## [1] -3.970556
# completar para los demás meses
###Otra opción practica
S <- 0
for (i in 1:12) {
S[i] = mean(window(temp.ts,start=c(2000,i),freq=T)) - media
}
S
## [1] -3.9705556 -3.5038889 -2.2038889 -2.0705556 0.6094444 2.5427778
## [7] 4.1694444 4.8627778 3.3894444 1.1161111 -1.7038889 -3.2372222
plot(S,type="o")
#estimamos la componente irregular: e_t = x_t - mu - S_t
e <- temp.ts - media - S
e
## Jan Feb Mar Apr May
## 2000 0.726666667 -0.140000000 -0.840000000 0.526666667 -0.653333333
## 2001 0.226666667 0.160000000 -0.240000000 -1.073333333 1.646666667
## 2002 -0.073333333 2.260000000 0.960000000 -0.373333333 1.346666667
## 2003 -0.773333333 -1.640000000 -0.640000000 -0.673333333 -0.453333333
## 2004 -1.673333333 -0.540000000 -1.040000000 0.126666667 0.946666667
## 2005 1.426666667 -0.340000000 -0.540000000 -0.073333333 -0.653333333
## 2006 -0.273333333 -0.640000000 -0.340000000 -0.873333333 -1.153333333
## 2007 0.226666667 0.460000000 -0.140000000 1.026666667 0.946666667
## 2008 0.826666667 -1.240000000 -0.140000000 1.126666667 -0.953333333
## 2009 -0.573333333 1.560000000 2.460000000 2.526666667 1.046666667
## 2010 1.326666667 1.860000000 1.360000000 -0.373333333 -0.153333333
## 2011 0.426666667 -0.740000000 -0.140000000 0.726666667 0.546666667
## 2012 -1.173333333 0.960000000 0.060000000 -0.673333333 0.446666667
## 2013 -0.773333333 -1.240000000 0.060000000 -0.873333333 -1.253333333
## 2014 0.126666667 -0.740000000 -0.840000000 -1.073333333 -1.653333333
## Jun Jul Aug Sep Oct
## 2000 -0.686666667 -0.813333333 -0.506666667 0.166666667 0.340000000
## 2001 0.913333333 0.786666667 0.593333333 -0.133333333 1.340000000
## 2002 -0.086666667 0.886666667 0.393333333 1.166666667 -0.260000000
## 2003 -0.986666667 0.086666667 0.193333333 0.966666667 -1.460000000
## 2004 -1.286666667 0.186666667 -0.206666667 -0.733333333 -2.260000000
## 2005 0.013333333 -0.713333333 -0.206666667 -1.233333333 -2.260000000
## 2006 0.213333333 -0.513333333 -0.206666667 -1.133333333 0.340000000
## 2007 0.513333333 0.986666667 0.693333333 -0.933333333 1.940000000
## 2008 1.113333333 -0.013333333 -0.606666667 -0.433333333 0.240000000
## 2009 0.013333333 -0.113333333 0.393333333 0.766666667 2.540000000
## 2010 0.313333333 -0.213333333 -0.006666667 0.966666667 0.040000000
## 2011 -0.186666667 1.286666667 1.093333333 0.866666667 -0.160000000
## 2012 1.413333333 0.086666667 -0.006666667 0.366666667 -0.860000000
## 2013 0.113333333 -0.713333333 -0.406666667 -0.933333333 0.340000000
## 2014 -1.386666667 -1.213333333 -1.206666667 0.266666667 0.140000000
## Nov Dec
## 2000 1.360000000 -0.106666667
## 2001 1.060000000 2.193333333
## 2002 -0.940000000 -2.006666667
## 2003 -0.240000000 -0.106666667
## 2004 1.460000000 -0.206666667
## 2005 -1.240000000 0.693333333
## 2006 1.160000000 0.893333333
## 2007 1.660000000 1.093333333
## 2008 -0.540000000 -0.806666667
## 2009 0.960000000 0.593333333
## 2010 0.260000000 -0.006666667
## 2011 -0.840000000 0.093333333
## 2012 -0.340000000 1.193333333
## 2013 -2.840000000 -3.906666667
## 2014 -0.940000000 0.393333333
#estandarizar las dimensiones media y S
S.ts = ts(S,start = start(temp.ts), end = end(temp.ts), frequency = frequency(temp.ts))
S.ts
## Jan Feb Mar Apr May Jun
## 2000 -3.9705556 -3.5038889 -2.2038889 -2.0705556 0.6094444 2.5427778
## 2001 -3.9705556 -3.5038889 -2.2038889 -2.0705556 0.6094444 2.5427778
## 2002 -3.9705556 -3.5038889 -2.2038889 -2.0705556 0.6094444 2.5427778
## 2003 -3.9705556 -3.5038889 -2.2038889 -2.0705556 0.6094444 2.5427778
## 2004 -3.9705556 -3.5038889 -2.2038889 -2.0705556 0.6094444 2.5427778
## 2005 -3.9705556 -3.5038889 -2.2038889 -2.0705556 0.6094444 2.5427778
## 2006 -3.9705556 -3.5038889 -2.2038889 -2.0705556 0.6094444 2.5427778
## 2007 -3.9705556 -3.5038889 -2.2038889 -2.0705556 0.6094444 2.5427778
## 2008 -3.9705556 -3.5038889 -2.2038889 -2.0705556 0.6094444 2.5427778
## 2009 -3.9705556 -3.5038889 -2.2038889 -2.0705556 0.6094444 2.5427778
## 2010 -3.9705556 -3.5038889 -2.2038889 -2.0705556 0.6094444 2.5427778
## 2011 -3.9705556 -3.5038889 -2.2038889 -2.0705556 0.6094444 2.5427778
## 2012 -3.9705556 -3.5038889 -2.2038889 -2.0705556 0.6094444 2.5427778
## 2013 -3.9705556 -3.5038889 -2.2038889 -2.0705556 0.6094444 2.5427778
## 2014 -3.9705556 -3.5038889 -2.2038889 -2.0705556 0.6094444 2.5427778
## Jul Aug Sep Oct Nov Dec
## 2000 4.1694444 4.8627778 3.3894444 1.1161111 -1.7038889 -3.2372222
## 2001 4.1694444 4.8627778 3.3894444 1.1161111 -1.7038889 -3.2372222
## 2002 4.1694444 4.8627778 3.3894444 1.1161111 -1.7038889 -3.2372222
## 2003 4.1694444 4.8627778 3.3894444 1.1161111 -1.7038889 -3.2372222
## 2004 4.1694444 4.8627778 3.3894444 1.1161111 -1.7038889 -3.2372222
## 2005 4.1694444 4.8627778 3.3894444 1.1161111 -1.7038889 -3.2372222
## 2006 4.1694444 4.8627778 3.3894444 1.1161111 -1.7038889 -3.2372222
## 2007 4.1694444 4.8627778 3.3894444 1.1161111 -1.7038889 -3.2372222
## 2008 4.1694444 4.8627778 3.3894444 1.1161111 -1.7038889 -3.2372222
## 2009 4.1694444 4.8627778 3.3894444 1.1161111 -1.7038889 -3.2372222
## 2010 4.1694444 4.8627778 3.3894444 1.1161111 -1.7038889 -3.2372222
## 2011 4.1694444 4.8627778 3.3894444 1.1161111 -1.7038889 -3.2372222
## 2012 4.1694444 4.8627778 3.3894444 1.1161111 -1.7038889 -3.2372222
## 2013 4.1694444 4.8627778 3.3894444 1.1161111 -1.7038889 -3.2372222
## 2014 4.1694444 4.8627778 3.3894444 1.1161111 -1.7038889 -3.2372222
media.ts = ts(media,start = start(temp.ts), end = end(temp.ts), frequency = frequency(temp.ts))
media.ts
## Jan Feb Mar Apr May Jun Jul Aug
## 2000 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389
## 2001 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389
## 2002 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389
## 2003 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389
## 2004 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389
## 2005 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389
## 2006 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389
## 2007 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389
## 2008 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389
## 2009 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389
## 2010 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389
## 2011 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389
## 2012 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389
## 2013 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389
## 2014 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389 14.74389
## Sep Oct Nov Dec
## 2000 14.74389 14.74389 14.74389 14.74389
## 2001 14.74389 14.74389 14.74389 14.74389
## 2002 14.74389 14.74389 14.74389 14.74389
## 2003 14.74389 14.74389 14.74389 14.74389
## 2004 14.74389 14.74389 14.74389 14.74389
## 2005 14.74389 14.74389 14.74389 14.74389
## 2006 14.74389 14.74389 14.74389 14.74389
## 2007 14.74389 14.74389 14.74389 14.74389
## 2008 14.74389 14.74389 14.74389 14.74389
## 2009 14.74389 14.74389 14.74389 14.74389
## 2010 14.74389 14.74389 14.74389 14.74389
## 2011 14.74389 14.74389 14.74389 14.74389
## 2012 14.74389 14.74389 14.74389 14.74389
## 2013 14.74389 14.74389 14.74389 14.74389
## 2014 14.74389 14.74389 14.74389 14.74389
e = temp.ts - media.ts - S.ts
e
## Jan Feb Mar Apr May
## 2000 0.726666667 -0.140000000 -0.840000000 0.526666667 -0.653333333
## 2001 0.226666667 0.160000000 -0.240000000 -1.073333333 1.646666667
## 2002 -0.073333333 2.260000000 0.960000000 -0.373333333 1.346666667
## 2003 -0.773333333 -1.640000000 -0.640000000 -0.673333333 -0.453333333
## 2004 -1.673333333 -0.540000000 -1.040000000 0.126666667 0.946666667
## 2005 1.426666667 -0.340000000 -0.540000000 -0.073333333 -0.653333333
## 2006 -0.273333333 -0.640000000 -0.340000000 -0.873333333 -1.153333333
## 2007 0.226666667 0.460000000 -0.140000000 1.026666667 0.946666667
## 2008 0.826666667 -1.240000000 -0.140000000 1.126666667 -0.953333333
## 2009 -0.573333333 1.560000000 2.460000000 2.526666667 1.046666667
## 2010 1.326666667 1.860000000 1.360000000 -0.373333333 -0.153333333
## 2011 0.426666667 -0.740000000 -0.140000000 0.726666667 0.546666667
## 2012 -1.173333333 0.960000000 0.060000000 -0.673333333 0.446666667
## 2013 -0.773333333 -1.240000000 0.060000000 -0.873333333 -1.253333333
## 2014 0.126666667 -0.740000000 -0.840000000 -1.073333333 -1.653333333
## Jun Jul Aug Sep Oct
## 2000 -0.686666667 -0.813333333 -0.506666667 0.166666667 0.340000000
## 2001 0.913333333 0.786666667 0.593333333 -0.133333333 1.340000000
## 2002 -0.086666667 0.886666667 0.393333333 1.166666667 -0.260000000
## 2003 -0.986666667 0.086666667 0.193333333 0.966666667 -1.460000000
## 2004 -1.286666667 0.186666667 -0.206666667 -0.733333333 -2.260000000
## 2005 0.013333333 -0.713333333 -0.206666667 -1.233333333 -2.260000000
## 2006 0.213333333 -0.513333333 -0.206666667 -1.133333333 0.340000000
## 2007 0.513333333 0.986666667 0.693333333 -0.933333333 1.940000000
## 2008 1.113333333 -0.013333333 -0.606666667 -0.433333333 0.240000000
## 2009 0.013333333 -0.113333333 0.393333333 0.766666667 2.540000000
## 2010 0.313333333 -0.213333333 -0.006666667 0.966666667 0.040000000
## 2011 -0.186666667 1.286666667 1.093333333 0.866666667 -0.160000000
## 2012 1.413333333 0.086666667 -0.006666667 0.366666667 -0.860000000
## 2013 0.113333333 -0.713333333 -0.406666667 -0.933333333 0.340000000
## 2014 -1.386666667 -1.213333333 -1.206666667 0.266666667 0.140000000
## Nov Dec
## 2000 1.360000000 -0.106666667
## 2001 1.060000000 2.193333333
## 2002 -0.940000000 -2.006666667
## 2003 -0.240000000 -0.106666667
## 2004 1.460000000 -0.206666667
## 2005 -1.240000000 0.693333333
## 2006 1.160000000 0.893333333
## 2007 1.660000000 1.093333333
## 2008 -0.540000000 -0.806666667
## 2009 0.960000000 0.593333333
## 2010 0.260000000 -0.006666667
## 2011 -0.840000000 0.093333333
## 2012 -0.340000000 1.193333333
## 2013 -2.840000000 -3.906666667
## 2014 -0.940000000 0.393333333
#Graficamos e
plot(e,type="o",col=2)
abline(h=0)
#Gráfica de la descomposición de la serie
par(mfrow=c(4,1))
plot(temp.ts,type="o")
plot(media.ts,type="o",col=2)
plot(S.ts,type="o",col=2)
plot(e,type="o",col=2)
# Otra forma de representar los indices estacionales
par(mfrow=c(1,1))
mes = c("Ene","Feb","Mar","Abr","May","Jun","Jul","Ago","Sep","Oct","Nov","Dic")
barplot(S,names.arg = mes, col=4)
# CONCLUIMOS QUE EN LOS DATOS DE TEMPERATURA NO EXISTE ESTACIONALIDAD
# POR LO QUE CONCLUIMOS QUE ES UN MODELO ADITIVO.
###################################
#3) TURISMO
#Parte descriptiva de la serie
turi = scan("turismo.txt");turi
## [1] 2698.17 2821.54 3310.27 4587.27 4517.06 4898.51 7549.73 8088.83
## [9] 5343.82 4296.97 2948.81 3347.92 2691.10 2883.64 3813.74 4580.32
## [17] 4890.64 5185.25 7463.75 8837.31 5473.77 4581.61 3302.69 3566.72
## [25] 2967.27 3205.28 4388.60 4674.83 5705.88 5492.33 8171.39 9569.10
## [33] 6049.68 4912.89 3461.19 3816.55 3356.11 3491.77 4103.80 5353.85
## [41] 6297.78 5982.82 8670.44 10343.53 6476.29 5633.05 3857.76 4194.63
## [49] 3595.66 3728.72 4613.27 5627.44 6569.79 6270.57 9500.94 10399.49
## [57] 6906.92 6319.11 4227.66 4300.74 3624.40 3920.10 4804.15 6533.25
## [65] 6185.49 6723.47 9561.02 10325.15 7688.81 6230.81 4312.61 4552.63
## [73] 3901.90 4091.71 4897.66 6587.96 6453.45 6972.08 9641.52 10761.35
## [81] 7492.79 6002.00 4209.16 4666.58 3925.79 4424.84 5784.98 6039.13
## [89] 6789.42 7131.02 9869.77 12199.27 7629.41 6528.66 4720.10 4981.97
## [97] 4279.48 4383.08 5488.20 6688.85 7269.85 7491.61 10106.19 11842.93
## [105] 7652.81 6791.20 4907.71 5358.37 4673.91 5086.67 5498.96 6982.28
## [113] 7536.28 7378.00 10447.97 11796.77
#Parte descriptiva de la serie
summary(turi)
## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 2691 4293 5481 5912 7019 12199
sd(turi)
## [1] 2226.345
boxplot(turi)
hist(turi)
#Definir la serie temporal
#install.packages("tseries")
library(tseries)
turi.ts <- ts(turi,start =2000, frequency = 12)
turi.ts
## Jan Feb Mar Apr May Jun Jul Aug
## 2000 2698.17 2821.54 3310.27 4587.27 4517.06 4898.51 7549.73 8088.83
## 2001 2691.10 2883.64 3813.74 4580.32 4890.64 5185.25 7463.75 8837.31
## 2002 2967.27 3205.28 4388.60 4674.83 5705.88 5492.33 8171.39 9569.10
## 2003 3356.11 3491.77 4103.80 5353.85 6297.78 5982.82 8670.44 10343.53
## 2004 3595.66 3728.72 4613.27 5627.44 6569.79 6270.57 9500.94 10399.49
## 2005 3624.40 3920.10 4804.15 6533.25 6185.49 6723.47 9561.02 10325.15
## 2006 3901.90 4091.71 4897.66 6587.96 6453.45 6972.08 9641.52 10761.35
## 2007 3925.79 4424.84 5784.98 6039.13 6789.42 7131.02 9869.77 12199.27
## 2008 4279.48 4383.08 5488.20 6688.85 7269.85 7491.61 10106.19 11842.93
## 2009 4673.91 5086.67 5498.96 6982.28 7536.28 7378.00 10447.97 11796.77
## Sep Oct Nov Dec
## 2000 5343.82 4296.97 2948.81 3347.92
## 2001 5473.77 4581.61 3302.69 3566.72
## 2002 6049.68 4912.89 3461.19 3816.55
## 2003 6476.29 5633.05 3857.76 4194.63
## 2004 6906.92 6319.11 4227.66 4300.74
## 2005 7688.81 6230.81 4312.61 4552.63
## 2006 7492.79 6002.00 4209.16 4666.58
## 2007 7629.41 6528.66 4720.10 4981.97
## 2008 7652.81 6791.20 4907.71 5358.37
## 2009
plot(turi.ts,type="o",col=4)
#Tendencia
# test de Mann-Kendall
library(Kendall)
resultado <- MannKendall(turi.ts)
print(resultado)
## tau = 0.321, 2-sided pvalue =3.5763e-07
# Si presenta tendencia, su p-value es menor a 0.05
#Estacionalidad
#estacion = c(rep("A",7),rep("B",7),rep("C",7),rep("D",7),rep("F",7))
estacion=cycle(turi.ts)
# test de Kruskal-Wallis## error en el modelo###########################
resultado <- kruskal.test(turi.ts ~ estacion)
print(resultado)
##
## Kruskal-Wallis rank sum test
##
## data: turi.ts by estacion
## Kruskal-Wallis chi-squared = 92.956, df = 11, p-value = 4.383e-15
# si presenta en sus datos existencia de estacinalidad,
# su p-value es menor a 0.05.
#Heterocedasticidad
#prueba de Levene##error en el modelo####################################
library(car)
resultado <- leveneTest(turi.ts ~ as.factor(estacion))
print(resultado)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 11 0.7626 0.6761
## 104
# no presenta en su datos heterocedasticidad por el valor
# que supera en p-value a o.o5
###Descomponer la serie según sus características
#La serie turi.ts presenta unicamente tendencia
# El modelo propuesto es: x_t = T_t + e_t
#utilizaremos Medias Móviles para estimar la componente de tendencia
tendencia = decompose(turi.ts);tendencia
## $x
## Jan Feb Mar Apr May Jun Jul Aug
## 2000 2698.17 2821.54 3310.27 4587.27 4517.06 4898.51 7549.73 8088.83
## 2001 2691.10 2883.64 3813.74 4580.32 4890.64 5185.25 7463.75 8837.31
## 2002 2967.27 3205.28 4388.60 4674.83 5705.88 5492.33 8171.39 9569.10
## 2003 3356.11 3491.77 4103.80 5353.85 6297.78 5982.82 8670.44 10343.53
## 2004 3595.66 3728.72 4613.27 5627.44 6569.79 6270.57 9500.94 10399.49
## 2005 3624.40 3920.10 4804.15 6533.25 6185.49 6723.47 9561.02 10325.15
## 2006 3901.90 4091.71 4897.66 6587.96 6453.45 6972.08 9641.52 10761.35
## 2007 3925.79 4424.84 5784.98 6039.13 6789.42 7131.02 9869.77 12199.27
## 2008 4279.48 4383.08 5488.20 6688.85 7269.85 7491.61 10106.19 11842.93
## 2009 4673.91 5086.67 5498.96 6982.28 7536.28 7378.00 10447.97 11796.77
## Sep Oct Nov Dec
## 2000 5343.82 4296.97 2948.81 3347.92
## 2001 5473.77 4581.61 3302.69 3566.72
## 2002 6049.68 4912.89 3461.19 3816.55
## 2003 6476.29 5633.05 3857.76 4194.63
## 2004 6906.92 6319.11 4227.66 4300.74
## 2005 7688.81 6230.81 4312.61 4552.63
## 2006 7492.79 6002.00 4209.16 4666.58
## 2007 7629.41 6528.66 4720.10 4981.97
## 2008 7652.81 6791.20 4907.71 5358.37
## 2009
##
## $seasonal
## Jan Feb Mar Apr May Jun
## 2000 -2274.3933 -2060.5119 -1138.7725 -139.8855 346.5049 461.6874
## 2001 -2274.3933 -2060.5119 -1138.7725 -139.8855 346.5049 461.6874
## 2002 -2274.3933 -2060.5119 -1138.7725 -139.8855 346.5049 461.6874
## 2003 -2274.3933 -2060.5119 -1138.7725 -139.8855 346.5049 461.6874
## 2004 -2274.3933 -2060.5119 -1138.7725 -139.8855 346.5049 461.6874
## 2005 -2274.3933 -2060.5119 -1138.7725 -139.8855 346.5049 461.6874
## 2006 -2274.3933 -2060.5119 -1138.7725 -139.8855 346.5049 461.6874
## 2007 -2274.3933 -2060.5119 -1138.7725 -139.8855 346.5049 461.6874
## 2008 -2274.3933 -2060.5119 -1138.7725 -139.8855 346.5049 461.6874
## 2009 -2274.3933 -2060.5119 -1138.7725 -139.8855 346.5049 461.6874
## Jul Aug Sep Oct Nov Dec
## 2000 3142.4038 4437.4602 899.8784 -167.7869 -1898.2539 -1608.3308
## 2001 3142.4038 4437.4602 899.8784 -167.7869 -1898.2539 -1608.3308
## 2002 3142.4038 4437.4602 899.8784 -167.7869 -1898.2539 -1608.3308
## 2003 3142.4038 4437.4602 899.8784 -167.7869 -1898.2539 -1608.3308
## 2004 3142.4038 4437.4602 899.8784 -167.7869 -1898.2539 -1608.3308
## 2005 3142.4038 4437.4602 899.8784 -167.7869 -1898.2539 -1608.3308
## 2006 3142.4038 4437.4602 899.8784 -167.7869 -1898.2539 -1608.3308
## 2007 3142.4038 4437.4602 899.8784 -167.7869 -1898.2539 -1608.3308
## 2008 3142.4038 4437.4602 899.8784 -167.7869 -1898.2539 -1608.3308
## 2009 3142.4038 4437.4602
##
## $trend
## Jan Feb Mar Apr May Jun Jul Aug
## 2000 NA NA NA NA NA NA 4533.780 4536.073
## 2001 4631.482 4659.086 4695.687 4712.962 4739.567 4763.428 4784.052 4808.961
## 2002 5001.155 5061.131 5115.619 5153.418 5173.826 5190.840 5217.451 5245.590
## 2003 5401.371 5454.433 5504.476 5552.258 5598.789 5631.066 5656.800 5676.655
## 2004 5833.033 5869.969 5890.244 5936.772 5980.771 6000.605 6006.223 6015.395
## 2005 6122.980 6122.386 6151.867 6180.767 6180.627 6194.662 6216.720 6235.433
## 2006 6301.337 6322.866 6332.873 6315.172 6301.328 6301.765 6307.509 6322.385
## 2007 6415.225 6484.649 6550.255 6577.892 6621.125 6655.555 6683.434 6696.431
## 2008 6804.038 6799.042 6785.169 6797.083 6815.840 6839.340 6871.458 6917.209
## 2009 6998.850 7011.168 NA NA NA NA NA NA
## Sep Oct Nov Dec
## 2000 4559.639 4580.327 4595.603 4623.117
## 2001 4846.315 4874.205 4912.112 4958.875
## 2002 5245.660 5262.086 5315.041 5360.140
## 2003 5707.755 5740.383 5763.116 5786.440
## 2004 6031.322 6077.018 6098.747 6101.606
## 2005 6246.480 6252.655 6266.100 6287.624
## 2006 6373.237 6387.340 6378.471 6399.092
## 2007 6682.325 6697.031 6744.120 6779.163
## 2008 6946.973 6959.648 6982.975 6989.343
## 2009
##
## $random
## Jan Feb Mar Apr May
## 2000 NA NA NA NA NA
## 2001 334.0116305 285.0660749 256.8253863 7.2438238 -195.4315408
## 2002 240.5082972 204.6606583 411.7537196 -338.7028429 185.5492925
## 2003 229.1320472 97.8489916 -261.9037804 -58.5228429 352.4863759
## 2004 37.0199638 -80.7372584 -138.2012804 -169.4470095 242.5142925
## 2005 -224.1867028 -141.7739251 -208.9446137 492.3688238 -341.6419575
## 2006 -125.0433695 -170.6439251 -296.4408637 412.6734071 -194.3827908
## 2007 -215.0421195 0.7027416 373.4974696 -398.8761762 -178.2098741
## 2008 -250.1650362 -355.4497584 -158.1966970 31.6521571 107.5055425
## 2009 -50.5467028 136.0144083 NA NA NA
## Jun Jul Aug Sep Oct
## 2000 NA -126.4542491 -884.7035084 -115.6971658 -115.5702214
## 2001 -39.8657595 -462.7059158 -409.1110084 -272.4234158 -124.8085547
## 2002 -160.1970095 -188.4646658 -113.9497584 -95.8584158 -181.4089714
## 2003 -109.9332595 -128.7642491 229.4152416 -131.3438325 60.4539453
## 2004 -191.7220095 352.3128342 -53.3651751 -24.2809158 409.8789453
## 2005 67.1204905 201.8961675 -347.7430917 542.4520009 145.9414453
## 2006 208.6271571 191.6074175 1.5052416 219.6749175 -217.5535547
## 2007 13.7771571 43.9324175 1065.3789916 47.2065842 -0.5839714
## 2008 190.5825738 92.3282509 488.2610749 -194.0417491 -0.6610547
## 2009 NA NA NA
## Nov Dec
## 2000 251.4605194 333.1341768
## 2001 288.8321861 216.1758435
## 2002 44.4030194 64.7404268
## 2003 -7.1023973 16.5212601
## 2004 27.1663527 -192.5349899
## 2005 -55.2361473 -126.6629065
## 2006 -271.0573973 -124.1816565
## 2007 -125.7665639 -188.8620732
## 2008 -177.0115639 -22.6420732
## 2009
##
## $figure
## [1] -2274.3933 -2060.5119 -1138.7725 -139.8855 346.5049 461.6874
## [7] 3142.4038 4437.4602 899.8784 -167.7869 -1898.2539 -1608.3308
##
## $type
## [1] "additive"
##
## attr(,"class")
## [1] "decomposed.ts"
trend = tendencia$trend
lines(trend,col=2)
################################
# Estimar la tendencia T_t
# x_t = T_t + E_t+ e_t
# Medais moviles: k=3
tendencia3 = stats::filter(turi.ts,sides=2,rep(1/3,3))
tendencia3
## Jan Feb Mar Apr May Jun Jul Aug
## 2000 NA 2943.327 3573.027 4138.200 4667.613 5655.100 6845.690 6994.127
## 2001 2974.220 3129.493 3759.233 4428.233 4885.403 5846.547 7162.103 7258.277
## 2002 3246.423 3520.383 4089.570 4923.103 5291.013 6456.533 7744.273 7930.057
## 2003 3554.810 3650.560 4316.473 5251.810 5878.150 6983.680 8332.263 8496.753
## 2004 3839.670 3979.217 4656.477 5603.500 6155.933 7447.100 8723.667 8935.783
## 2005 3948.413 4116.217 5085.833 5840.963 6480.737 7489.993 8869.880 9191.660
## 2006 4182.080 4297.090 5192.443 5979.690 6671.163 7689.017 9124.983 9298.553
## 2007 4339.070 4711.870 5416.317 6204.510 6653.190 7930.070 9733.353 9899.483
## 2008 4548.177 4716.920 5520.043 6482.300 7150.103 8289.217 9813.577 9867.310
## 2009 5039.650 5086.513 5855.970 6672.507 7298.853 8454.083 9874.247 NA
## Sep Oct Nov Dec
## 2000 5909.873 4196.533 3531.233 2995.943
## 2001 6297.563 4452.690 3817.007 3278.893
## 2002 6843.890 4807.920 4063.543 3544.617
## 2003 7484.290 5322.367 4561.813 3882.683
## 2004 7875.173 5817.897 4949.170 4050.933
## 2005 8081.590 6077.410 5032.017 4255.713
## 2006 8085.380 5901.317 4959.247 4267.177
## 2007 8785.780 6292.723 5410.243 4660.517
## 2008 8762.313 6450.573 5685.760 4979.997
## 2009
# Medais moviles: k=2,
tendencia2 = stats::filter(turi.ts,sides=2,rep(1/2,2))
tendencia2
## Jan Feb Mar Apr May Jun Jul
## 2000 2759.855 3065.905 3948.770 4552.165 4707.785 6224.120 7819.280
## 2001 2787.370 3348.690 4197.030 4735.480 5037.945 6324.500 8150.530
## 2002 3086.275 3796.940 4531.715 5190.355 5599.105 6831.860 8870.245
## 2003 3423.940 3797.785 4728.825 5825.815 6140.300 7326.630 9506.985
## 2004 3662.190 4170.995 5120.355 6098.615 6420.180 7885.755 9950.215
## 2005 3772.250 4362.125 5668.700 6359.370 6454.480 8142.245 9943.085
## 2006 3996.805 4494.685 5742.810 6520.705 6712.765 8306.800 10201.435
## 2007 4175.315 5104.910 5912.055 6414.275 6960.220 8500.395 11034.520
## 2008 4331.280 4935.640 6088.525 6979.350 7380.730 8798.900 10974.560
## 2009 4880.290 5292.815 6240.620 7259.280 7457.140 8912.985 11122.370
## Aug Sep Oct Nov Dec
## 2000 6716.325 4820.395 3622.890 3148.365 3019.510
## 2001 7155.540 5027.690 3942.150 3434.705 3266.995
## 2002 7809.390 5481.285 4187.040 3638.870 3586.330
## 2003 8409.910 6054.670 4745.405 4026.195 3895.145
## 2004 8653.205 6613.015 5273.385 4264.200 3962.570
## 2005 9006.980 6959.810 5271.710 4432.620 4227.265
## 2006 9127.070 6747.395 5105.580 4437.870 4296.185
## 2007 9914.340 7079.035 5624.380 4851.035 4630.725
## 2008 9747.870 7222.005 5849.455 5133.040 5016.140
## 2009 NA
# Medais moviles: k=7
tendencia7 = stats::filter(turi.ts,sides=2,rep(1/7,7))
tendencia7
## Jan Feb Mar Apr May Jun Jul Aug
## 2000 NA NA NA 4340.364 5110.459 5470.784 5611.741 5377.676
## 2001 3508.929 3593.739 3913.230 4501.206 5379.236 5749.254 5858.950 5676.431
## 2002 3812.429 3973.039 4285.844 4943.654 5886.773 6293.116 6368.014 6194.637
## 2003 4070.880 4268.721 4628.954 5322.367 6320.570 6746.930 6965.394 6751.667
## 2004 4464.361 4598.181 4942.869 5700.913 6672.889 7126.917 7370.609 7170.640
## 2005 4818.487 4799.399 5155.943 5907.411 6864.661 7403.049 7606.857 7289.623
## 2006 4939.326 4971.131 5351.056 6078.040 7057.961 7543.830 7701.593 7361.764
## 2007 5007.497 5119.986 5537.394 6280.707 7462.633 7920.429 8026.669 7838.236
## 2008 5295.763 5401.647 5797.577 6529.609 7610.101 8077.206 8263.349 8008.900
## 2009 5614.157 5720.597 6073.496 6800.581 7818.133 NA NA NA
## Sep Oct Nov Dec
## 2000 5210.656 4895.311 4228.727 3618.000
## 2001 5487.300 5170.446 4562.093 3926.563
## 2002 5924.733 5619.559 4951.041 4170.284
## 2003 6451.217 6110.194 5404.234 4585.626
## 2004 6846.490 6468.466 5671.203 4871.869
## 2005 7056.357 6653.276 5871.946 5096.590
## 2006 7106.497 6671.313 5926.073 5215.163
## 2007 7580.029 7172.666 6388.853 5430.129
## 2008 7735.831 7333.303 6616.229 5709.947
## 2009
###########################error en la funcion windows########
#windows()
plot(turi.ts,type="o")
lines(tendencia3,col=2)
lines(tendencia2,col=4)
lines(tendencia7,col=3)
#estimando la componente irregular e_t = x_t - T_t
e3 = turi.ts - tendencia3;e3
## Jan Feb Mar Apr May
## 2000 NA -121.7866667 -262.7566667 449.0700000 -150.5533333
## 2001 -283.1200000 -245.8533333 54.5066667 152.0866667 5.2366667
## 2002 -279.1533333 -315.1033333 299.0300000 -248.2733333 414.8666667
## 2003 -198.7000000 -158.7900000 -212.6733333 102.0400000 419.6300000
## 2004 -244.0100000 -250.4966667 -43.2066667 23.9400000 413.8566667
## 2005 -324.0133333 -196.1166667 -281.6833333 692.2866667 -295.2466667
## 2006 -280.1800000 -205.3800000 -294.7833333 608.2700000 -217.7133333
## 2007 -413.2800000 -287.0300000 368.6633333 -165.3800000 136.2300000
## 2008 -268.6966667 -333.8400000 -31.8433333 206.5500000 119.7466667
## 2009 -365.7400000 0.1566667 -357.0100000 309.7733333 237.4266667
## Jun Jul Aug Sep Oct
## 2000 -756.5900000 704.0400000 1094.7033333 -566.0533333 100.4366667
## 2001 -661.2966667 301.6466667 1579.0333333 -823.7933333 128.9200000
## 2002 -964.2033333 427.1166667 1639.0433333 -794.2100000 104.9700000
## 2003 -1000.8600000 338.1766667 1846.7766667 -1008.0000000 310.6833333
## 2004 -1176.5300000 777.2733333 1463.7066667 -968.2533333 501.2133333
## 2005 -766.5233333 691.1400000 1133.4900000 -392.7800000 153.4000000
## 2006 -716.9366667 516.5366667 1462.7966667 -592.5900000 100.6833333
## 2007 -799.0500000 136.4166667 2299.7866667 -1156.3700000 235.9366667
## 2008 -797.6066667 292.6133333 1975.6200000 -1109.5033333 340.6266667
## 2009 -1076.0833333 573.7233333 NA
## Nov Dec
## 2000 -582.4233333 351.9766667
## 2001 -514.3166667 287.8266667
## 2002 -602.3533333 271.9333333
## 2003 -704.0533333 311.9466667
## 2004 -721.5100000 249.8066667
## 2005 -719.4066667 296.9166667
## 2006 -750.0866667 399.4033333
## 2007 -690.1433333 321.4533333
## 2008 -778.0500000 378.3733333
## 2009
e2 = turi.ts - tendencia2;e2
## Jan Feb Mar Apr May Jun Jul
## 2000 -61.685 -244.365 -638.500 35.105 -190.725 -1325.610 -269.550
## 2001 -96.270 -465.050 -383.290 -155.160 -147.305 -1139.250 -686.780
## 2002 -119.005 -591.660 -143.115 -515.525 106.775 -1339.530 -698.855
## 2003 -67.830 -306.015 -625.025 -471.965 157.480 -1343.810 -836.545
## 2004 -66.530 -442.275 -507.085 -471.175 149.610 -1615.185 -449.275
## 2005 -147.850 -442.025 -864.550 173.880 -268.990 -1418.775 -382.065
## 2006 -94.905 -402.975 -845.150 67.255 -259.315 -1334.720 -559.915
## 2007 -249.525 -680.070 -127.075 -375.145 -170.800 -1369.375 -1164.750
## 2008 -51.800 -552.560 -600.325 -290.500 -110.880 -1307.290 -868.370
## 2009 -206.380 -206.145 -741.660 -277.000 79.140 -1534.985 -674.400
## Aug Sep Oct Nov Dec
## 2000 1372.505 523.425 674.080 -199.555 328.410
## 2001 1681.770 446.080 639.460 -132.015 299.725
## 2002 1759.710 568.395 725.850 -177.680 230.220
## 2003 1933.620 421.620 887.645 -168.435 299.485
## 2004 1746.285 293.905 1045.725 -36.540 338.170
## 2005 1318.170 729.000 959.100 -120.010 325.365
## 2006 1634.280 745.395 896.420 -228.710 370.395
## 2007 2284.930 550.375 904.280 -130.935 351.245
## 2008 2095.060 430.805 941.745 -225.330 342.230
## 2009 NA
e7 = turi.ts - tendencia7;e7
## Jan Feb Mar Apr May Jun
## 2000 NA NA NA 246.90571 -593.39857 -572.27429
## 2001 -817.82857 -710.09857 -99.49000 79.11429 -488.59571 -564.00429
## 2002 -845.15857 -767.75857 102.75571 -268.82429 -180.89286 -800.78571
## 2003 -714.77000 -776.95143 -525.15429 31.48286 -22.79000 -764.11000
## 2004 -868.70143 -869.46143 -329.59857 -73.47286 -103.09857 -856.34714
## 2005 -1194.08714 -879.29857 -351.79286 625.83857 -679.17143 -679.57857
## 2006 -1037.42571 -879.42143 -453.39571 509.92000 -604.51143 -571.75000
## 2007 -1081.70714 -695.14571 247.58571 -241.57714 -673.21286 -789.40857
## 2008 -1016.28286 -1018.56714 -309.37714 159.24143 -340.25143 -585.59571
## 2009 -940.24714 -633.92714 -574.53571 181.69857 -281.85286 NA
## Jul Aug Sep Oct Nov Dec
## 2000 1937.98857 2711.15429 133.16429 -598.34143 -1279.91714 -270.08000
## 2001 1604.80000 3160.87857 -13.53000 -588.83571 -1259.40286 -359.84286
## 2002 1803.37571 3374.46286 124.94714 -706.66857 -1489.85143 -353.73429
## 2003 1705.04571 3591.86286 25.07286 -477.14429 -1546.47429 -390.99571
## 2004 2130.33143 3228.85000 60.43000 -149.35571 -1443.54286 -571.12857
## 2005 1954.16286 3035.52714 632.45286 -422.46571 -1559.33571 -543.96000
## 2006 1939.92714 3399.58571 386.29286 -669.31286 -1716.91286 -548.58286
## 2007 1843.10143 4361.03429 49.38143 -644.00571 -1668.75286 -448.15857
## 2008 1842.84143 3834.03000 -83.02143 -542.10286 -1708.51857 -351.57714
## 2009 NA NA
#windows()
ts.plot(cbind(e3,e2,e7), type="o",lty="dashed",col=c(2,4,3))
abline(h=0)
#Gráfica de la descomposición clásica k=3
#windows()
par(mfrow=c(3,1))
plot(turi.ts,type="o")
plot(tendencia3,col=2)
plot(e3,col=2)
turi = scan("turismo.txt")
turi.ts <- ts(turi,start = 2000,frequency =12)
turi.ts
## Jan Feb Mar Apr May Jun Jul Aug
## 2000 2698.17 2821.54 3310.27 4587.27 4517.06 4898.51 7549.73 8088.83
## 2001 2691.10 2883.64 3813.74 4580.32 4890.64 5185.25 7463.75 8837.31
## 2002 2967.27 3205.28 4388.60 4674.83 5705.88 5492.33 8171.39 9569.10
## 2003 3356.11 3491.77 4103.80 5353.85 6297.78 5982.82 8670.44 10343.53
## 2004 3595.66 3728.72 4613.27 5627.44 6569.79 6270.57 9500.94 10399.49
## 2005 3624.40 3920.10 4804.15 6533.25 6185.49 6723.47 9561.02 10325.15
## 2006 3901.90 4091.71 4897.66 6587.96 6453.45 6972.08 9641.52 10761.35
## 2007 3925.79 4424.84 5784.98 6039.13 6789.42 7131.02 9869.77 12199.27
## 2008 4279.48 4383.08 5488.20 6688.85 7269.85 7491.61 10106.19 11842.93
## 2009 4673.91 5086.67 5498.96 6982.28 7536.28 7378.00 10447.97 11796.77
## Sep Oct Nov Dec
## 2000 5343.82 4296.97 2948.81 3347.92
## 2001 5473.77 4581.61 3302.69 3566.72
## 2002 6049.68 4912.89 3461.19 3816.55
## 2003 6476.29 5633.05 3857.76 4194.63
## 2004 6906.92 6319.11 4227.66 4300.74
## 2005 7688.81 6230.81 4312.61 4552.63
## 2006 7492.79 6002.00 4209.16 4666.58
## 2007 7629.41 6528.66 4720.10 4981.97
## 2008 7652.81 6791.20 4907.71 5358.37
## 2009
plot(turi.ts)
#Estacionalidad
estacion = cycle(turi.ts)
#H0: existe diferencias significativa entre periodos (No hay estacionalidad)
# test de Kruskal-Wallis
resultado <- kruskal.test(turi.ts ~ estacion)
print(resultado)
##
## Kruskal-Wallis rank sum test
##
## data: turi.ts by estacion
## Kruskal-Wallis chi-squared = 92.956, df = 11, p-value = 4.383e-15
###El modelo que podemos plantear con estacionalidad
### x_t = mu + S_t + e_t
#Media
media = mean(turi.ts);media
## [1] 5911.57
#Estimar la componente estacional (indice estacional): Ii = media(X_enero_i) - meadia
turi.ts
## Jan Feb Mar Apr May Jun Jul Aug
## 2000 2698.17 2821.54 3310.27 4587.27 4517.06 4898.51 7549.73 8088.83
## 2001 2691.10 2883.64 3813.74 4580.32 4890.64 5185.25 7463.75 8837.31
## 2002 2967.27 3205.28 4388.60 4674.83 5705.88 5492.33 8171.39 9569.10
## 2003 3356.11 3491.77 4103.80 5353.85 6297.78 5982.82 8670.44 10343.53
## 2004 3595.66 3728.72 4613.27 5627.44 6569.79 6270.57 9500.94 10399.49
## 2005 3624.40 3920.10 4804.15 6533.25 6185.49 6723.47 9561.02 10325.15
## 2006 3901.90 4091.71 4897.66 6587.96 6453.45 6972.08 9641.52 10761.35
## 2007 3925.79 4424.84 5784.98 6039.13 6789.42 7131.02 9869.77 12199.27
## 2008 4279.48 4383.08 5488.20 6688.85 7269.85 7491.61 10106.19 11842.93
## 2009 4673.91 5086.67 5498.96 6982.28 7536.28 7378.00 10447.97 11796.77
## Sep Oct Nov Dec
## 2000 5343.82 4296.97 2948.81 3347.92
## 2001 5473.77 4581.61 3302.69 3566.72
## 2002 6049.68 4912.89 3461.19 3816.55
## 2003 6476.29 5633.05 3857.76 4194.63
## 2004 6906.92 6319.11 4227.66 4300.74
## 2005 7688.81 6230.81 4312.61 4552.63
## 2006 7492.79 6002.00 4209.16 4666.58
## 2007 7629.41 6528.66 4720.10 4981.97
## 2008 7652.81 6791.20 4907.71 5358.37
## 2009
enero = window(turi.ts,start=c(2000,1),freq=T)
enero
## Time Series:
## Start = 2000
## End = 2009
## Frequency = 1
## [1] 2698.17 2691.10 2967.27 3356.11 3595.66 3624.40 3901.90 3925.79 4279.48
## [10] 4673.91
ISenero = mean(enero) - media;ISenero
## [1] -2340.191
# completar para los demás meses
###Otra opción practica
S <- 0
for (i in 1:12) {
S[i] = mean(window(turi.ts,start=c(2000,i),freq=T)) - media
}
S
## [1] -2340.1908 -2107.8348 -1241.2068 -146.0518 309.9942 440.9962
## [7] 3186.7022 4504.8032 834.4635 -211.9809 -1917.3820 -1602.0020
plot(S,type="o")
#estimamos la componente irregular: e_t = x_t - mu - S_t
e <- turi.ts - media - S
## Warning in `-.default`(turi.ts - media, S): longer object length is not a
## multiple of shorter object length
e
## Jan Feb Mar Apr May
## 2000 -873.209000 -982.195000 -1360.093000 -1178.248000 -1704.504000
## 2001 -880.279000 -920.095000 -856.623000 -1185.198000 -1330.924000
## 2002 -604.109000 -598.455000 -281.763000 -1090.688000 -515.684000
## 2003 -215.269000 -311.965000 -566.563000 -411.668000 76.216000
## 2004 24.281000 -75.015000 -57.093000 -138.078000 348.226000
## 2005 53.021000 116.365000 133.787000 767.732000 -36.074000
## 2006 330.521000 287.975000 227.297000 822.442000 231.886000
## 2007 354.411000 621.105000 1114.617000 273.612000 567.856000
## 2008 708.101000 579.345000 817.837000 923.332000 1048.286000
## 2009 1102.531000 1282.935000 828.597000 1216.762000 1314.716000
## Jun Jul Aug Sep Oct
## 2000 -1454.056000 -1548.542000 -2327.543000 -1402.213333 -1402.618889
## 2001 -1167.316000 -1634.522000 -1579.063000 -1272.263333 -1117.978889
## 2002 -860.236000 -926.882000 -847.273000 -696.353333 -786.698889
## 2003 -369.746000 -427.832000 -72.843000 -269.743333 -66.538889
## 2004 -81.996000 402.668000 -16.883000 160.886667 619.521111
## 2005 370.904000 462.748000 -91.223000 942.776667 531.221111
## 2006 619.514000 543.248000 344.977000 746.756667 302.411111
## 2007 778.454000 771.498000 1782.897000 883.376667 829.071111
## 2008 1139.044000 1007.918000 1426.557000 906.776667 1091.611111
## 2009 1025.434000 1349.698000 1380.397000
## Nov Dec
## 2000 -1045.377778 -961.647778
## 2001 -691.497778 -742.847778
## 2002 -532.997778 -493.017778
## 2003 -136.427778 -114.937778
## 2004 233.472222 -8.827778
## 2005 318.422222 243.062222
## 2006 214.972222 357.012222
## 2007 725.912222 672.402222
## 2008 913.522222 1048.802222
## 2009
#estandarizar las dimensiones media y S
S.ts = ts(S,start = start(turi.ts), end = end(turi.ts), frequency = frequency(turi.ts))
S.ts
## Jan Feb Mar Apr May Jun
## 2000 -2340.1908 -2107.8348 -1241.2068 -146.0518 309.9942 440.9962
## 2001 -2340.1908 -2107.8348 -1241.2068 -146.0518 309.9942 440.9962
## 2002 -2340.1908 -2107.8348 -1241.2068 -146.0518 309.9942 440.9962
## 2003 -2340.1908 -2107.8348 -1241.2068 -146.0518 309.9942 440.9962
## 2004 -2340.1908 -2107.8348 -1241.2068 -146.0518 309.9942 440.9962
## 2005 -2340.1908 -2107.8348 -1241.2068 -146.0518 309.9942 440.9962
## 2006 -2340.1908 -2107.8348 -1241.2068 -146.0518 309.9942 440.9962
## 2007 -2340.1908 -2107.8348 -1241.2068 -146.0518 309.9942 440.9962
## 2008 -2340.1908 -2107.8348 -1241.2068 -146.0518 309.9942 440.9962
## 2009 -2340.1908 -2107.8348 -1241.2068 -146.0518 309.9942 440.9962
## Jul Aug Sep Oct Nov Dec
## 2000 3186.7022 4504.8032 834.4635 -211.9809 -1917.3820 -1602.0020
## 2001 3186.7022 4504.8032 834.4635 -211.9809 -1917.3820 -1602.0020
## 2002 3186.7022 4504.8032 834.4635 -211.9809 -1917.3820 -1602.0020
## 2003 3186.7022 4504.8032 834.4635 -211.9809 -1917.3820 -1602.0020
## 2004 3186.7022 4504.8032 834.4635 -211.9809 -1917.3820 -1602.0020
## 2005 3186.7022 4504.8032 834.4635 -211.9809 -1917.3820 -1602.0020
## 2006 3186.7022 4504.8032 834.4635 -211.9809 -1917.3820 -1602.0020
## 2007 3186.7022 4504.8032 834.4635 -211.9809 -1917.3820 -1602.0020
## 2008 3186.7022 4504.8032 834.4635 -211.9809 -1917.3820 -1602.0020
## 2009 3186.7022 4504.8032
media.ts = ts(media,start = start(turi.ts), end = end(turi.ts), frequency = frequency(turi.ts))
media.ts
## Jan Feb Mar Apr May Jun Jul Aug Sep
## 2000 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57
## 2001 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57
## 2002 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57
## 2003 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57
## 2004 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57
## 2005 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57
## 2006 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57
## 2007 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57
## 2008 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57
## 2009 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57 5911.57
## Oct Nov Dec
## 2000 5911.57 5911.57 5911.57
## 2001 5911.57 5911.57 5911.57
## 2002 5911.57 5911.57 5911.57
## 2003 5911.57 5911.57 5911.57
## 2004 5911.57 5911.57 5911.57
## 2005 5911.57 5911.57 5911.57
## 2006 5911.57 5911.57 5911.57
## 2007 5911.57 5911.57 5911.57
## 2008 5911.57 5911.57 5911.57
## 2009
e = turi.ts - media.ts - S.ts
e
## Jan Feb Mar Apr May
## 2000 -873.209000 -982.195000 -1360.093000 -1178.248000 -1704.504000
## 2001 -880.279000 -920.095000 -856.623000 -1185.198000 -1330.924000
## 2002 -604.109000 -598.455000 -281.763000 -1090.688000 -515.684000
## 2003 -215.269000 -311.965000 -566.563000 -411.668000 76.216000
## 2004 24.281000 -75.015000 -57.093000 -138.078000 348.226000
## 2005 53.021000 116.365000 133.787000 767.732000 -36.074000
## 2006 330.521000 287.975000 227.297000 822.442000 231.886000
## 2007 354.411000 621.105000 1114.617000 273.612000 567.856000
## 2008 708.101000 579.345000 817.837000 923.332000 1048.286000
## 2009 1102.531000 1282.935000 828.597000 1216.762000 1314.716000
## Jun Jul Aug Sep Oct
## 2000 -1454.056000 -1548.542000 -2327.543000 -1402.213333 -1402.618889
## 2001 -1167.316000 -1634.522000 -1579.063000 -1272.263333 -1117.978889
## 2002 -860.236000 -926.882000 -847.273000 -696.353333 -786.698889
## 2003 -369.746000 -427.832000 -72.843000 -269.743333 -66.538889
## 2004 -81.996000 402.668000 -16.883000 160.886667 619.521111
## 2005 370.904000 462.748000 -91.223000 942.776667 531.221111
## 2006 619.514000 543.248000 344.977000 746.756667 302.411111
## 2007 778.454000 771.498000 1782.897000 883.376667 829.071111
## 2008 1139.044000 1007.918000 1426.557000 906.776667 1091.611111
## 2009 1025.434000 1349.698000 1380.397000
## Nov Dec
## 2000 -1045.377778 -961.647778
## 2001 -691.497778 -742.847778
## 2002 -532.997778 -493.017778
## 2003 -136.427778 -114.937778
## 2004 233.472222 -8.827778
## 2005 318.422222 243.062222
## 2006 214.972222 357.012222
## 2007 725.912222 672.402222
## 2008 913.522222 1048.802222
## 2009
#Graficamos e
plot(e,type="o",col=2)
abline(h=0)
#Gráfica de la descomposición de la serie
x11()
par(mfrow=c(4,1))
plot(turi.ts,type="o")
plot(media.ts,type="o",col=2)
plot(S.ts,type="o",col=2)
plot(e,type="o",col=2)
# Otra forma de representar los indices estacionales
par(mfrow=c(1,1))
mes = c("Ene","Feb","Mar","Abr","May","Jun","Jul","Ago","Sep","Oct","Nov","Dic")
barplot(S,names.arg = mes, col=4)
# CONCLUIMOS QUE LOS DATOS DE TURI SON DATOS QUE
# DEMUESTRAN TENDENCIA Y ESTACIONALIDAD EXISTENTE A DIFERENCIA DE LA
# HETEROCEDASTICIDAD, POR LO QUE CONCLUIMOS QUE ES UN MODELO ADITIVO.
##################
### 4) CONSUMO DE ELECTRICIDAD
#Parte descriptiva de la serie
dir()
## [1] "1series.R" "consumo_electricidad.txt"
## [3] "consumo_electricidad.xlsx" "pib.txt"
## [5] "pib.xlsx" "TAREA1_1.R"
## [7] "TAREA2.docx" "TAREA2.R"
## [9] "temperatura.txt" "temperatura.xlsx"
## [11] "trabajo1" "turismo.txt"
## [13] "turismo.xlsx"
elect = scan("consumo_electricidad.txt")
##Análisis decriptivo.....
# serie temporal
elect.ts = ts(elect,start = 2000,frequency = 12)
elect.ts
## Jan Feb Mar Apr May Jun Jul Aug Sep
## 2000 75.533 75.024 72.947 69.811 67.804 73.162 81.122 86.421 85.798
## 2001 85.695 81.578 78.054 72.566 71.734 79.732 91.697 94.773 94.320
## 2002 83.739 80.576 77.050 73.966 73.012 81.041 90.403 94.673 90.148
## 2003 89.136 86.206 81.837 77.760 74.842 83.008 93.989 98.180 94.415
## 2004 97.942 90.724 82.648 78.088 76.488 82.068 95.790 99.684 95.143
## 2005 105.375 99.711 88.156 80.281 78.864 88.671 105.138 106.845 100.767
## 2006 106.422 104.208 97.310 83.240 80.622 92.330 106.899 109.496 107.283
## 2007 112.423 109.361 99.408 88.140 84.519 91.417 103.317 110.878 104.487
## 2008 107.688 105.925 101.233 90.213 84.395 94.489 115.731 124.046 115.964
## 2009 119.915 110.311 100.285 91.822 90.929 103.145 121.240 121.576 110.906
## 2010 124.095 115.397 105.329 97.986 92.588 101.217 116.419 121.657 113.925
## 2011 116.482 110.072 103.264 99.387 92.598 101.527 122.676 133.074 127.263
## 2012 130.901 118.090 111.427 101.836 100.429 111.874 127.023 128.801 122.384
## 2013 129.151 125.792 113.307 105.109 103.790 114.842 129.434 132.974 129.496
## 2014 137.844 123.437 115.899 106.145 105.996 123.369 143.430 142.656 131.786
## 2015 138.454 127.738 120.965 112.278 114.758 130.500 149.936 154.880 136.738
## 2016 147.962 137.064 126.937 115.675 112.734 130.974 154.311 163.515 142.403
## 2017 145.160 136.406 136.795 122.313 120.288 137.174 155.210 156.275 146.453
## 2018 159.351 133.724 132.316 124.356 124.982 141.135 164.193 161.930 157.541
## 2019 158.979 140.144 134.461 126.017 132.277 151.830 168.905 167.990 156.686
## 2020 155.304 143.774 135.572 128.986 128.259 138.712 162.140 161.237 150.608
## 2021 159.252 145.954 142.766 131.609 128.008 147.238 178.050 180.157 162.824
## 2022 172.551 154.892 145.585 134.411 133.658 160.009 184.177 176.497 161.385
## 2023 166.851 152.844 147.832 134.953 139.297 161.298 187.612 200.784 173.314
## 2024 181.999 167.028 158.059 142.814 147.563 170.916 190.014 191.705 173.104
## 2025 183.999 162.667 154.453 145.006 144.930 165.968 199.880 195.381 181.628
## 2026 180.019 159.204 161.568 148.342 157.140 185.747 214.889 215.600 198.664
## 2027 192.757 163.510 168.586 155.289 159.033 186.526 222.768 221.462 196.582
## 2028 194.218 172.659 167.933 157.044 172.471 196.529 219.287 227.702 205.348
## 2029 217.787 184.573 180.025 166.841 172.338 197.597 224.453 236.616 205.923
## 2030 207.323 180.982 182.135 173.319 180.291 208.030 242.225 242.243 217.163
## 2031 225.104 202.916 193.334 174.732 185.602 203.964 245.195 254.228 221.165
## 2032 229.922 207.913 195.917 180.561 193.574 222.073 247.093 243.509 224.615
## Oct Nov Dec
## 2000 75.293 72.894 77.951
## 2001 80.388 76.629 77.967
## 2002 78.196 75.661 84.041
## 2003 78.832 76.972 85.682
## 2004 82.580 83.289 95.148
## 2005 88.350 82.118 93.418
## 2006 91.907 86.215 97.085
## 2007 90.911 88.954 98.213
## 2008 96.911 91.040 102.989
## 2009 98.366 95.193 107.249
## 2010 98.843 96.162 107.581
## 2011 103.414 99.085 113.692
## 2012 106.745 105.318 115.738
## 2013 110.398 108.001 125.935
## 2014 115.498 110.942 128.472
## 2015 119.445 114.889 129.736
## 2016 123.500 119.645 135.355
## 2017 127.264 124.284 148.463
## 2018 135.451 127.591 140.730
## 2019 135.433 133.603 145.781
## 2020 136.519 132.570 152.213
## 2021 139.946 136.302 153.933
## 2022 142.385 137.728 154.310
## 2023 149.609 147.200 163.995
## 2024 151.053 150.035 167.048
## 2025 167.508 155.347 173.153
## 2026 170.550 155.703 172.218
## 2027 169.378 158.246 177.606
## 2028 176.979 170.200 196.285
## 2029 178.276 167.473 183.939
## 2030 191.893 176.253 198.094
## 2031 192.445 182.248 211.100
## 2032 198.691 187.896 216.703
plot(elect.ts,type="o")
#Identicando las características
#Tendencia
# test de Mann-Kendall
#H0:No existe tendencia monótona
library(Kendall)
resultado <- MannKendall(elect.ts)
print(resultado)
## tau = 0.796, 2-sided pvalue =< 2.22e-16
#pvalue =< 2.22e-16---Si
#Estacionalidad
#H0: No existe estacionalidad de la serie
estacion = cycle(elect.ts)
# test de Kruskal-Wallis
resultado <- kruskal.test(elect.ts ~ estacion)
print(resultado)
##
## Kruskal-Wallis rank sum test
##
## data: elect.ts by estacion
## Kruskal-Wallis chi-squared = 32.189, df = 11, p-value = 0.0007112
#p-value = 0.0007112 --- Si
#Heterocedasticidad
#H0: No existe heterocedastidad de la serie
estacion = cycle(elect.ts)
#prueba de Levene
library(car)
resultado <- leveneTest(elect.ts ~ as.factor(estacion))
print(resultado)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 11 1.7211 0.0668 .
## 384
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#p-value 0.0668 --- Si (alfa=0.1 o >0.7)
#CUENTA CON LAS TRES CARACTERISTICAS SEGUN EL VALOR DE SU P-VALUE
#otras pruebas para heterocedasticidad
#El a proponer es: x_t = T_t x S_t x e_t, donde e_t ----> 1 Modelo multiplicativo
# Descomponer la serie según el modelo propuesto
elect.descomp = decompose(elect.ts,type = "multiplicative")
names(elect.descomp)
## [1] "x" "seasonal" "trend" "random" "figure" "type"
#Tendencia
Tn=elect.descomp$trend
#Estacional
S=elect.descomp$seasonal
#Irregular
e=elect.descomp$random
#graficando
par(mfrow=c(4,1))
plot(elect.ts,type="o")
plot(Tn,col=2,ylab="Tendencia")
plot(S,col=2,ylab="Estacionalidad")
plot(e,col=2,ylab="Iregular")
#Presentacion de los indices estacionales
Is = elect.descomp$figure;Is
## [1] 1.0999011 1.0062294 0.9530559 0.8770732 0.8759204 0.9893462 1.1385004
## [8] 1.1632918 1.0759193 0.9305372 0.8919358 0.9982893
mes = c("Ene","Feb","Mar","Abr","May","Jun","Jul","Ago","Sep","Oct","Nov","Dic")
par(mfrow=c(1,1))
barplot(Is,names.arg = mes, col=4)
# CONCLUIMOS QUE LOS DATOS DE ELECTRICIDAD SON DATOS QUE
# DEMUESTRAN TENDENCIA, ESTACIONALIDAD Y HETEROCEDASTICIDAD
# EXISTENTE POR LO QUE CONCLUIMOS QUE ES UN MODELO MULTIPLICATIVO.
# NOTA: MODELO ADITIVO, SE SUMAN LOS COMPONENTES Y EL MODELO
# MULTIPLICATIVO, SE MULTIPLICAN LOS TRES COMPONENTES.