1. Primera parte

Pronóstico de series temporales, enfoque moderno (estocástico)

Metodología Box-Jenkins

Importacion de la data

library(readxl)
library(forecast)
PIBTPC<- read_excel("~/Econometria/tableExportPIB.xlsx", 
    col_types = c("skip", "numeric"), skip = 5)
## Serie
serie.PIB.ts<- ts(data = PIBTPC, start = c(2009,1),frequency = 4)

Yt_1 <- serie.PIB.ts
serie.PIB.ts %>% 
  autoplot(main = "PIB trimestral precios corrientes SLV 2009-2021",
           xlab = "años/ trimestres",
           ylab = "Indice")

Generacion de Grafica general

library(TSstudio)
library(forecast)

ts_plot(Yt_1,Xtitle= "Años/Meses")

Identificación

Orden de Integración

library(kableExtra)
library(magrittr)
d_1<-ndiffs(Yt_1)
D_1<-nsdiffs(Yt_1)
ordenes_integracion<-c(d_1,D_1)
names(ordenes_integracion)<-c("d","D")
ordenes_integracion %>% kable(caption = "Ordenes de Integracion") %>% kable_material()

Ordenes de Integracion
	x
d	1
D	1

#Gráfico de la serie diferenciada
Yt_1 %>%
  diff(lag=4,diffences=D_1) %>%
  diff(diffences=d_1) %>%
  ts_plot(title= "Yt estacionaria")

Verificar los valores para (p,q) & (P,Q)

Se construyen las funciones de autocorrelación simple y parcial.

Yt_1 %>%
  diff(lag=4,diffences=D) %>%
  diff(diffences=d) %>%
  ts_cor(lag.max = 12)

Estimación del modelo.

Usando forecast

library(forecast)
library(ggthemes)
modelo_estimado_PIB<-Yt_1 %>%
  Arima(order = c(0, 1, 0),
        seasonal = c(1, 1, 1))
summary(modelo_estimado_PIB)

## Series: . 
## ARIMA(0,1,0)(1,1,1)[4] 
## 
## Coefficients:
##          sar1     sma1
##       -0.3980  -0.4550
## s.e.   0.3732   0.3688
## 
## sigma^2 = 77377:  log likelihood = -331.67
## AIC=669.34   AICc=669.9   BIC=674.89
## 
## Training set error measures:
##                    ME     RMSE      MAE          MPE     MAPE      MASE
## Training set 6.530071 258.7683 120.9372 -0.004468918 2.054645 0.3680668
##                     ACF1
## Training set -0.09806694

modelo_estimado_PIB %>% autoplot(type="both")+theme_solarized()

modelo_estimado_PIB %>% check_res(lag.max = 4)

## Warning: Ignoring 4 observations

## Warning: Ignoring 4 observations

## Warning: Ignoring 2 observations

Importacion de PronosticosHW de la practica anterior # Estimación del modelo

library(forecast)

#Estimar el modelo
modeloHW_PIB<-HoltWinters(x = Yt_1,
                      seasonal = "multiplicative",
                      optim.start = c(0.9,0.9,0.9))
modeloHW_PIB

## Holt-Winters exponential smoothing with trend and multiplicative seasonal component.
## 
## Call:
## HoltWinters(x = Yt_1, seasonal = "multiplicative", optim.start = c(0.9,     0.9, 0.9))
## 
## Smoothing parameters:
##  alpha: 0.8742302
##  beta : 0
##  gamma: 0
## 
## Coefficients:
##            [,1]
## a  7429.8128051
## b    48.3963750
## s1    0.9751646
## s2    1.0058150
## s3    0.9783521
## s4    1.0406683

Generar pronostico

#Generar el pronostico:
pronosticosMW_PIB<-forecast(object = modeloHW_PIB,h=4, level=c(0.95))
pronosticosMW_PIB

##         Point Forecast    Lo 95    Hi 95
## 2022 Q1       7292.485 6847.413 7737.557
## 2022 Q2       7570.373 6930.977 8209.768
## 2022 Q3       7411.019 6646.235 8175.804
## 2022 Q4       7933.429 7119.875 8746.982

Continuancion de practica SARIMA

Yt_Sarima_PIB<-modelo_estimado_PIB$fitted
Yt_HW_PIB<-pronosticosMW_PIB$fitted
grafico_comparativo_1<-cbind(Yt_1, Yt_Sarima_PIB,Yt_HW_PIB)
ts_plot(grafico_comparativo_1)

Verificación de sobre ajuste/sub ajuste

library(tsibble)

## 
## Attaching package: 'tsibble'

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, union

library(feasts)

## Loading required package: fabletools

## 
## Attaching package: 'fabletools'

## The following objects are masked from 'package:forecast':
## 
##     accuracy, forecast

library(fable)
library(fabletools)
library(tidyr)

## 
## Attaching package: 'tidyr'

## The following object is masked from 'package:magrittr':
## 
##     extract

library(dplyr)

## 
## Attaching package: 'dplyr'

## The following object is masked from 'package:kableExtra':
## 
##     group_rows

## The following objects are masked from 'package:stats':
## 
##     filter, lag

## The following objects are masked from 'package:base':
## 
##     intersect, setdiff, setequal, union

a<-Yt_1 %>% as_tsibble() %>% 
  model(arima_original=ARIMA(value ~ pdq(0, 1, 0) + PDQ(1, 1, 1)),
        arima_010_011 = ARIMA(value ~ pdq(0, 1, 0) + PDQ(0, 1, 1)),
        arima_010_110 = ARIMA(value ~ pdq(0, 1, 0) + PDQ(1, 1, 0)),
        arima_automatico=ARIMA(value,ic="bic",stepwise = FALSE)
  )
print(a)

## # A mable: 1 x 4
##             arima_original            arima_010_011            arima_010_110
##                    <model>                  <model>                  <model>
## 1 <ARIMA(0,1,0)(1,1,1)[4]> <ARIMA(0,1,0)(0,1,1)[4]> <ARIMA(0,1,0)(1,1,0)[4]>
## # … with 1 more variable: arima_automatico <model>

a %>% pivot_longer(everything(), names_to = "Model name",
                         values_to = "Orders") %>% glance() %>% 
  arrange(AICc) ->tabla
tabla

## # A tibble: 4 × 9
##   `Model name`     .model sigma2 log_lik   AIC  AICc   BIC ar_roots  ma_roots 
##   <chr>            <chr>   <dbl>   <dbl> <dbl> <dbl> <dbl> <list>    <list>   
## 1 arima_010_011    Orders 75930.   -332.  668.  669.  672. <cpl [0]> <cpl [4]>
## 2 arima_010_110    Orders 78594.   -333.  669.  670.  673. <cpl [4]> <cpl [0]>
## 3 arima_original   Orders 77377.   -332.  669.  670.  675. <cpl [4]> <cpl [4]>
## 4 arima_automatico Orders 62738.   -334.  676.  677.  683. <cpl [1]> <cpl [4]>

Validación Cruzada (Cross Validated)

library(forecast)
library(dplyr)
library(tsibble)
library(fable)
library(fabletools)

#convertimos
Yt<-Yt_1 %>% 
  as_tsibble() %>% 
  rename(PIB=value)

#generador de la dta (roja)
data.cross.validation.PIB<-Yt %>% 
  as_tsibble() %>% 
  stretch_tsibble(.init = 20,.step = 1)

#generador de pronostico (verde) y simulacion 
TSCV<-data.cross.validation.PIB %>% 
model(ARIMA(PIB ~ pdq(0, 1, 0) + PDQ(1, 1, 1))) %>% 
forecast(h=1) %>% accuracy(Yt)

## Warning: The future dataset is incomplete, incomplete out-of-sample data will be treated as missing. 
## 1 observation is missing at 2022 Q1

print(TSCV)

## # A tibble: 1 × 10
##   .model                  .type    ME  RMSE   MAE   MPE  MAPE  MASE RMSSE   ACF1
##   <chr>                   <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl>
## 1 ARIMA(PIB ~ pdq(0, 1, … Test   30.1  370.  197. 0.228  3.21 0.600 0.780 0.0422

2. Segunda Parte IPC

Pronóstico de series temporales, enfoque moderno (estocástico) Metodología Box-Jenkins

Importar la data

library(readxl)
library(forecast)
IPC<- read_excel("~/Econometria/tableExportIPC.xlsx",col_types=c("skip","numeric"), 
    skip = 5)
## Serie
serie.IPC.ts<- ts(data =IPC, start = c(2009,1),
                frequency = 12)
Yt.2 <- serie.IPC.ts
serie.IPC.ts %>% 
  autoplot(main = "IPC general SLV 2009-2022 (mayo)",
           xlab = "años/ trimestres",
           ylab = "Indice")

Generacion de Grafica general

library(TSstudio)
library(forecast)

ts_plot(Yt.2,Xtitle= "Años/Meses")

Identificación

Orden de Integración

library(kableExtra)
library(magrittr)
d_3<-ndiffs(Yt.2)
D_3<-nsdiffs(Yt.2)
ordenes_integracion<-c(d_3,D_3)
names(ordenes_integracion)<-c("d","D")
ordenes_integracion %>% kable(caption = "Ordenes de Integracion") %>% kable_material()

Ordenes de Integracion
	x
d	1
D	0

#Gráfico de la serie diferenciada
Yt.2 %>%
  diff(lag=12,diffences=D_3) %>%
  diff(diffences=d_3) %>%
  ts_plot(title= "Yt estacionaria")

Verificar los valores para (p,q) & (P,Q)

Se construyen las funciones de autocorrelación simple y parcial.

Yt.2 %>%
  diff(lag=12,diffences=D_2) %>%
  diff(diffences=d_2) %>%
  ts_cor(lag.max = 36)

Estimación del modelo.

Usando forecast

library(forecast)
library(ggthemes)
modelo_estimado_IPC<-Yt.2 %>%
  Arima(order = c(1, 1, 1),
        seasonal = c(1, 0, 2))
summary(modelo_estimado_IPC)

## Series: . 
## ARIMA(1,1,1)(1,0,2)[12] 
## 
## Coefficients:
##          ar1      ma1    sar1    sma1     sma2
##       0.9414  -0.7965  0.0702  0.0478  -0.0678
## s.e.  0.0810   0.1355  0.6798  0.6773   0.1110
## 
## sigma^2 = 0.224:  log likelihood = -105.16
## AIC=222.31   AICc=222.86   BIC=240.76
## 
## Training set error measures:
##                     ME     RMSE       MAE        MPE      MAPE      MASE
## Training set 0.0566041 0.464391 0.3076996 0.05030787 0.2821278 0.1667415
##                    ACF1
## Training set 0.08593583

#grafico de las raices (estabilidad/convertibilidad)
modelo_estimado_IPC %>% autoplot(type="both")+theme_solarized()

#verificacion
modelo_estimado_IPC %>% check_res(lag.max = 36)

## Warning: Ignoring 36 observations

## Warning: Ignoring 34 observations

## Warning: Ignoring 4 observations

Estimación del modelo

library(forecast)

#Estimar el modelo
modeloHW_IPC<-HoltWinters(x = Yt.2,
                      seasonal = "multiplicative",
                      optim.start = c(0.9,0.9,0.9))
modeloHW_IPC

## Holt-Winters exponential smoothing with trend and multiplicative seasonal component.
## 
## Call:
## HoltWinters(x = Yt.2, seasonal = "multiplicative", optim.start = c(0.9,     0.9, 0.9))
## 
## Smoothing parameters:
##  alpha: 0.8353873
##  beta : 0.07612657
##  gamma: 1
## 
## Coefficients:
##            [,1]
## a   122.7690242
## b     0.4801476
## s1    1.0043291
## s2    1.0021040
## s3    0.9986014
## s4    0.9975846
## s5    0.9989586
## s6    0.9984650
## s7    0.9959074
## s8    0.9975598
## s9    1.0007205
## s10   1.0041558
## s11   1.0048925
## s12   1.0053839

Generar pronostico

pronosticosMW_IPC<-forecast(object = modeloHW_IPC,h=12, level=c(0.95,0.70))
pronosticosMW_IPC

##          Point Forecast    Lo 95    Hi 95    Lo 70    Hi 70
## Jun 2022       123.7827 122.6365 124.9289 123.1766 124.3888
## Jul 2022       123.9896 122.4499 125.5294 123.1754 124.8038
## Aug 2022       124.0357 122.1459 125.9256 123.0364 125.0351
## Sep 2022       124.3884 122.1648 126.6120 123.2126 125.5643
## Oct 2022       125.0394 122.4870 127.5918 123.6897 126.3891
## Nov 2022       125.4570 122.5842 128.3298 123.9379 126.9762
## Dec 2022       125.6139 122.4280 128.7997 123.9292 127.2985
## Jan 2023       126.3012 122.7897 129.8128 124.4443 128.1582
## Feb 2023       127.1819 123.3369 131.0269 125.1487 129.2152
## Mar 2023       128.1007 123.9171 132.2842 125.8884 130.3129
## Apr 2023       128.6771 124.1616 133.1927 126.2893 131.0650
## May 2023       129.2228 123.9338 134.5118 126.4259 132.0196

Grafico de Comparacion

Yt_Sarima_IPC<-modelo_estimado_IPC$fitted
Yt_HW_IPC<-pronosticosMW_IPC$fitted
grafico_comparativo_2_IPC<-cbind(Yt.2, Yt_Sarima_IPC,Yt_HW_IPC)
ts_plot(grafico_comparativo_2_IPC)

Verificación de sobre ajuste/sub ajuste

library(tsibble)
library(feasts)
library(fable)
library(fabletools)
library(tidyr)
library(dplyr)
#generando modelo automatico
a_3<-Yt.2 %>% as_tsibble() %>% 
  model(arima_original=ARIMA(value ~ pdq(1, 1, 1) + PDQ(1, 0, 2)),
        arima_010_011 = ARIMA(value ~ pdq(1, 1, 1) + PDQ(0, 0, 2)),
        arima_010_110 = ARIMA(value ~ pdq(1, 1, 1) + PDQ(1, 0, 1)),
        arima_automatico=ARIMA(value,ic="bic",stepwise = FALSE)
  )
print(a_3)

## # A mable: 1 x 4
##                       arima_original                      arima_010_011
##                              <model>                            <model>
## 1 <ARIMA(1,1,1)(1,0,2)[12] w/ drift> <ARIMA(1,1,1)(0,0,2)[12] w/ drift>
## # … with 2 more variables: arima_010_110 <model>, arima_automatico <model>

#ordenar  
a_3 %>% pivot_longer(everything(), names_to = "Model name",
                         values_to = "Orders") %>% glance() %>% 
  arrange(AICc) ->tabla_3
tabla_3

## # A tibble: 4 × 9
##   `Model name`     .model sigma2 log_lik   AIC  AICc   BIC ar_roots   ma_roots  
##   <chr>            <chr>   <dbl>   <dbl> <dbl> <dbl> <dbl> <list>     <list>    
## 1 arima_010_011    Orders  0.218   -103.  218.  218.  236. <cpl [1]>  <cpl [25]>
## 2 arima_010_110    Orders  0.219   -103.  218.  219.  237. <cpl [13]> <cpl [13]>
## 3 arima_original   Orders  0.219   -103.  220.  221.  241. <cpl [13]> <cpl [25]>
## 4 arima_automatico Orders  0.225   -105.  223.  224.  241. <cpl [27]> <cpl [0]>

Validación Cruzada (Cross Validated)

library(forecast)
library(dplyr)
library(tsibble)
library(fable)
library(fabletools)

#convertimos
Yt<-Yt.2 %>% as_tsibble() %>% rename(IPC=value)

#generador de la dta (roja)
data.cross.validation.IPC<-Yt %>% 
  as_tsibble() %>% 
  stretch_tsibble(.init = 60,.step = 1)

#generador de pronostico (verde) y simulacion 
TSCV_3<-data.cross.validation.IPC %>% 
model(ARIMA(IPC ~ pdq(0, 1, 0) + PDQ(1, 1, 1))) %>% 
forecast(h=1) %>% accuracy(Yt)

## Warning: The future dataset is incomplete, incomplete out-of-sample data will be treated as missing. 
## 1 observation is missing at 2022 jun.

print(TSCV_3)

## # A tibble: 1 × 10
##   .model                 .type     ME  RMSE   MAE    MPE  MAPE  MASE RMSSE  ACF1
##   <chr>                  <chr>  <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>
## 1 ARIMA(IPC ~ pdq(0, 1,… Test  0.0284 0.473 0.333 0.0200 0.296 0.181 0.173 0.324

3. Tercera Parte

Pronóstico de series temporales, enfoque moderno (estocástico) Metodología Box-Jenkins

Importamos la data

library(readxl)
library(forecast)
HCB <- read_excel("~/Econometria/tableExportHCB.xlsx",col_type= c("skip", "numeric"),
             skip = 7)
## Serie
serie.HCB.ts<- ts(data = HCB, start = c(2017,1),
                frequency = 12)
Yt_4<-serie.HCB.ts
serie.HCB.ts %>% 
  autoplot(main = "Importación de Hidrocarburos SLV 2017-2022 (mayo)",
           xlab = "años/ trimestres",
           ylab = "Indice")

library(TSstudio)
library(forecast)

ts_plot(Yt_4,Xtitle= "Años/Meses")

Identificación

Orden de Integración

library(kableExtra)
library(magrittr)
d_4<-ndiffs(Yt_4)
D_4<-nsdiffs(Yt_4)
ordenes_integracion<-c(d_4,D_4)
names(ordenes_integracion)<-c("d","D")
ordenes_integracion %>% kable(caption = "Ordenes de Integracion") %>% kable_material()

Ordenes de Integracion
	x
d	0
D	0

#Gráfico de la serie diferenciada
Yt_4 %>%
  diff(lag=12,diffences=D_4) %>%
  diff(diffences=d_4) %>%
  ts_plot(title= "Yt estacionaria")

Verificar los valores para (p,q) & (P,Q)

Yt_4 %>%
  diff(lag=12,diffences=D_4) %>%
  diff(diffences=d_4) %>%
  ts_cor(lag.max = 36)

Estimación del modelo.

Usando forecast

library(forecast)
library(ggthemes)
modelo_estimado_HCB<-Yt_4 %>%
  Arima(order = c(1, 0, 1),
        seasonal = c(1, 0, 0))

summary(modelo_estimado_HCB)

## Series: . 
## ARIMA(1,0,1)(1,0,0)[12] with non-zero mean 
## 
## Coefficients:
##          ar1      ma1     sar1        mean
##       0.6652  -0.4851  -0.2022  215790.730
## s.e.  0.2952   0.3398   0.1519    5147.504
## 
## sigma^2 = 1.042e+09:  log likelihood = -741.69
## AIC=1493.39   AICc=1494.44   BIC=1504.1
## 
## Training set error measures:
##                     ME     RMSE      MAE       MPE     MAPE      MASE
## Training set -428.6553 31240.12 25005.59 -2.421527 12.06669 0.6217076
##                      ACF1
## Training set -0.007961808

#grafico de las raices (estabilidad/convertibilidad)
modelo_estimado_HCB %>% autoplot(type="both")+theme_solarized()

#verificacion
modelo_estimado_HCB %>% check_res(lag.max = 36)

## Warning: Ignoring 36 observations

## Warning: Ignoring 34 observations

## Warning: Ignoring 4 observations

library(forecast)

#Estimar el modelo
modeloHW_M_HC<-HoltWinters(x = Yt_4,
                      seasonal = "multiplicative",
                      optim.start = c(0.9,0.9,0.9))
modeloHW_M_HC

## Holt-Winters exponential smoothing with trend and multiplicative seasonal component.
## 
## Call:
## HoltWinters(x = Yt_4, seasonal = "multiplicative", optim.start = c(0.9,     0.9, 0.9))
## 
## Smoothing parameters:
##  alpha: 0.1580326
##  beta : 0
##  gamma: 0.4946113
## 
## Coefficients:
##             [,1]
## a   2.501763e+05
## b   1.683628e+03
## s1  9.111372e-01
## s2  8.894296e-01
## s3  8.823914e-01
## s4  8.896954e-01
## s5  9.398533e-01
## s6  1.039846e+00
## s7  9.375516e-01
## s8  9.546773e-01
## s9  9.615739e-01
## s10 1.097096e+00
## s11 9.326123e-01
## s12 8.393040e-01

#Generar el pronostico:
pronosticosMW_M_HC<-forecast(object = modeloHW_M_HC,h=12, level=c(0.95, 0.90))
pronosticosMW_M_HC

##          Point Forecast    Lo 95    Hi 95    Lo 90    Hi 90
## Apr 2022       229478.9 182755.6 276202.2 190267.5 268690.3
## May 2022       225509.1 177130.5 273887.7 184908.5 266109.7
## Jun 2022       225210.3 175204.2 275216.3 183243.9 267176.6
## Jul 2022       228572.3 176863.3 280281.4 185176.7 271967.9
## Aug 2022       243040.8 189049.4 297032.2 197729.8 288351.8
## Sep 2022       270649.0 213366.1 327932.0 222575.6 318722.4
## Oct 2022       245602.6 188944.1 302261.0 198053.3 293151.9
## Nov 2022       251696.2 193221.1 310171.3 202622.3 300770.0
## Dec 2022       255133.4 195092.9 315173.9 204745.8 305520.9
## Jan 2023       292938.5 227754.8 358122.3 238234.6 347642.4
## Feb 2023       250589.4 188983.5 312195.2 198888.1 302290.6
## Mar 2023       226930.8 188989.5 264872.2 195089.4 258772.2

#Gráfico comparativo
#Gráfico comparativo
Yt_Sarima_M_HC<-modelo_estimado_HCB$fitted
Yt_HW_M_HC<-pronosticosMW_M_HC$fitted
grafico_comparativo_4<-cbind(Yt_4, Yt_Sarima_M_HC,Yt_HW_M_HC)
ts_plot(grafico_comparativo_4)

Verificación de sobre ajuste/sub ajuste

library(tsibble)
library(feasts)
library(fable)
library(fabletools)
library(tidyr)
library(dplyr)

#generando modelo automatico
a_4<-Yt_4 %>% as_tsibble() %>% 
  model(arima_original=ARIMA(value ~ pdq(1, 0, 1) + PDQ(1, 0, 0)),
        arima_010_011 = ARIMA(value ~ pdq(1, 1, 1) + PDQ(1, 0, 0)),
        arima_010_110 = ARIMA(value ~ pdq(1, 0, 1) + PDQ(1, 1, 0)),
        arima_automatico=ARIMA(value,ic="bic",stepwise = FALSE) 
        #modelo automatico 
  )

## Warning: It looks like you're trying to fully specify your ARIMA model but have not said if a constant should be included.
## You can include a constant using `ARIMA(y~1)` to the formula or exclude it by adding `ARIMA(y~0)`.

## Warning: 1 error encountered for arima_010_011
## [1] Could not find an appropriate ARIMA model.
## This is likely because automatic selection does not select models with characteristic roots that may be numerically unstable.
## For more details, refer to https://otexts.com/fpp3/arima-r.html#plotting-the-characteristic-roots

print(a_4)

## # A mable: 1 x 4
##                      arima_original arima_010_011             arima_010_110
##                             <model>       <model>                   <model>
## 1 <ARIMA(1,0,1)(1,0,0)[12] w/ mean>  <NULL model> <ARIMA(1,0,1)(1,1,0)[12]>
## # … with 1 more variable: arima_automatico <model>

#ordenar  
a_4 %>% pivot_longer(everything(), names_to = "Model name",
                         values_to = "Orders") %>% glance() %>% 
  arrange(AICc) ->tabla_4
tabla_4

## # A tibble: 3 × 9
##   `Model name`     .model     sigma2 log_lik   AIC  AICc   BIC ar_roots ma_roots
##   <chr>            <chr>       <dbl>   <dbl> <dbl> <dbl> <dbl> <list>   <list>  
## 1 arima_010_110    Orders     1.47e9   -612. 1232. 1233. 1240. <cpl>    <cpl>   
## 2 arima_automatico Orders     1.10e9   -745. 1493. 1494. 1498. <cpl>    <cpl>   
## 3 arima_original   Orders     1.04e9   -742. 1493. 1494. 1504. <cpl>    <cpl>

Validación Cruzada (Cross Validated)

library(forecast)
library(dplyr)
library(tsibble)
library(fable)
library(fabletools)

#convertimos
Yt<-Yt_4 %>% 
  as_tsibble() %>% 
  rename(M_HC= value)

#generador de la dta (roja)
data.cross.validation.M_HC<-Yt %>% 
  as_tsibble() %>% 
  stretch_tsibble(.init = 60,.step = 1)

#generador de pronostico (verde) y simulacion 
TSCV_4<-data.cross.validation.M_HC %>% 
model(ARIMA(M_HC ~ pdq(0, 1, 0) + PDQ(1, 1, 1))) %>% 
forecast(h=1) %>% accuracy(Yt)

## Warning: The future dataset is incomplete, incomplete out-of-sample data will be treated as missing. 
## 1 observation is missing at 2022 abr.

print(TSCV_4)

## # A tibble: 1 × 10
##   .model              .type      ME   RMSE    MAE   MPE  MAPE  MASE RMSSE   ACF1
##   <chr>               <chr>   <dbl>  <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl>
## 1 ARIMA(M_HC ~ pdq(0… Test  -35010. 41442. 35010. -16.9  16.9 0.870 0.839 -0.194

Modelo SIMAR PIB

Diana Carolina Villatoro Romero

2022-07-10

1. Primera parte

Identificación

Verificar los valores para (p,q) & (P,Q)

Estimación del modelo.

Generar pronostico

Continuancion de practica SARIMA

Verificación de sobre ajuste/sub ajuste

Validación Cruzada (Cross Validated)

2. Segunda Parte IPC

Identificación

Verificar los valores para (p,q) & (P,Q)

Estimación del modelo.

Estimación del modelo

Generar pronostico

Grafico de Comparacion

Verificación de sobre ajuste/sub ajuste

Validación Cruzada (Cross Validated)

3. Tercera Parte

Identificación

Verificar los valores para (p,q) & (P,Q)

Estimación del modelo.

Verificación de sobre ajuste/sub ajuste

Validación Cruzada (Cross Validated)