ANALISIS DE INTERVENCION SERIES TEMPORALES 1

# --- Cargar librerías ---
# 'forecast' para auto.arima y 'tsoutlier' para el análisis de intervención.
library(forecast)

Registered S3 method overwritten by 'quantmod':
  method            from
  as.zoo.data.frame zoo 

library(tsoutliers)

# --- Cargar los datos ---
# Asegúrate de que el archivo 'ipi.csv' esté en tu directorio de trabajo
ipi_data <- read.csv("ipi.csv")

# --- Crear el objeto de serie temporal (ts) ---
# Frecuencia mensual (12), comenzando en enero de 1988
ipi_ts <- ts(ipi_data$Ipi, start = c(1988, 1), frequency = 12)

# --- Visualizar la serie (opcional) ---
plot(ipi_ts, main="Índice de Producción Industrial de España (1988-2000)", 
     ylab="IPI", xlab="Año")

# --- Encontrar el mejor modelo ARIMA automáticamente ---
# Forzamos la diferenciación (d=1, D=1) que sabemos que es necesaria.
# 'stepwise=FALSE' y 'approximation=FALSE' hacen la búsqueda más exhaustiva.
auto_model <- auto.arima(ipi_ts, 
                         d = 1, D = 1, 
                         stepwise = FALSE, 
                         approximation = FALSE, 
                         trace = TRUE)

 ARIMA(0,1,0)(0,1,0)[12]                    : 900.2247
 ARIMA(0,1,0)(0,1,1)[12]                    : Inf
 ARIMA(0,1,0)(0,1,2)[12]                    : Inf
 ARIMA(0,1,0)(1,1,0)[12]                    : 894.3355
 ARIMA(0,1,0)(1,1,1)[12]                    : Inf
 ARIMA(0,1,0)(1,1,2)[12]                    : Inf
 ARIMA(0,1,0)(2,1,0)[12]                    : 893.8956
 ARIMA(0,1,0)(2,1,1)[12]                    : Inf
 ARIMA(0,1,0)(2,1,2)[12]                    : Inf
 ARIMA(0,1,1)(0,1,0)[12]                    : 833.0983
 ARIMA(0,1,1)(0,1,1)[12]                    : Inf
 ARIMA(0,1,1)(0,1,2)[12]                    : Inf
 ARIMA(0,1,1)(1,1,0)[12]                    : 824.0026
 ARIMA(0,1,1)(1,1,1)[12]                    : Inf
 ARIMA(0,1,1)(1,1,2)[12]                    : Inf
 ARIMA(0,1,1)(2,1,0)[12]                    : 821.245
 ARIMA(0,1,1)(2,1,1)[12]                    : Inf
 ARIMA(0,1,1)(2,1,2)[12]                    : Inf
 ARIMA(0,1,2)(0,1,0)[12]                    : 817.4068
 ARIMA(0,1,2)(0,1,1)[12]                    : 784.5567
 ARIMA(0,1,2)(0,1,2)[12]                    : Inf
 ARIMA(0,1,2)(1,1,0)[12]                    : 806.5752
 ARIMA(0,1,2)(1,1,1)[12]                    : Inf
 ARIMA(0,1,2)(1,1,2)[12]                    : Inf
 ARIMA(0,1,2)(2,1,0)[12]                    : 803.0354
 ARIMA(0,1,2)(2,1,1)[12]                    : Inf
 ARIMA(0,1,3)(0,1,0)[12]                    : 814.8034
 ARIMA(0,1,3)(0,1,1)[12]                    : 785.6049
 ARIMA(0,1,3)(0,1,2)[12]                    : Inf
 ARIMA(0,1,3)(1,1,0)[12]                    : 806.2374
 ARIMA(0,1,3)(1,1,1)[12]                    : Inf
 ARIMA(0,1,3)(2,1,0)[12]                    : 802.7037
 ARIMA(0,1,4)(0,1,0)[12]                    : 815.8123
 ARIMA(0,1,4)(0,1,1)[12]                    : 782.9063
 ARIMA(0,1,4)(1,1,0)[12]                    : 806.1415
 ARIMA(0,1,5)(0,1,0)[12]                    : 816.5685
 ARIMA(1,1,0)(0,1,0)[12]                    : 852.0131
 ARIMA(1,1,0)(0,1,1)[12]                    : Inf
 ARIMA(1,1,0)(0,1,2)[12]                    : Inf
 ARIMA(1,1,0)(1,1,0)[12]                    : 844.6964
 ARIMA(1,1,0)(1,1,1)[12]                    : Inf
 ARIMA(1,1,0)(1,1,2)[12]                    : Inf
 ARIMA(1,1,0)(2,1,0)[12]                    : 845.1071
 ARIMA(1,1,0)(2,1,1)[12]                    : Inf
 ARIMA(1,1,0)(2,1,2)[12]                    : Inf
 ARIMA(1,1,1)(0,1,0)[12]                    : 827.2804
 ARIMA(1,1,1)(0,1,1)[12]                    : Inf
 ARIMA(1,1,1)(0,1,2)[12]                    : Inf
 ARIMA(1,1,1)(1,1,0)[12]                    : 816.8771
 ARIMA(1,1,1)(1,1,1)[12]                    : Inf
 ARIMA(1,1,1)(1,1,2)[12]                    : Inf
 ARIMA(1,1,1)(2,1,0)[12]                    : 814.3057
 ARIMA(1,1,1)(2,1,1)[12]                    : Inf
 ARIMA(1,1,2)(0,1,0)[12]                    : 815.8987
 ARIMA(1,1,2)(0,1,1)[12]                    : 786.2131
 ARIMA(1,1,2)(0,1,2)[12]                    : Inf
 ARIMA(1,1,2)(1,1,0)[12]                    : 807.1787
 ARIMA(1,1,2)(1,1,1)[12]                    : Inf
 ARIMA(1,1,2)(2,1,0)[12]                    : 803.8889
 ARIMA(1,1,3)(0,1,0)[12]                    : 815.3334
 ARIMA(1,1,3)(0,1,1)[12]                    : 784.3122
 ARIMA(1,1,3)(1,1,0)[12]                    : 805.8862
 ARIMA(1,1,4)(0,1,0)[12]                    : 817.5082
 ARIMA(2,1,0)(0,1,0)[12]                    : 816.0084
 ARIMA(2,1,0)(0,1,1)[12]                    : 776.2589
 ARIMA(2,1,0)(0,1,2)[12]                    : Inf
 ARIMA(2,1,0)(1,1,0)[12]                    : 800.6987
 ARIMA(2,1,0)(1,1,1)[12]                    : Inf
 ARIMA(2,1,0)(1,1,2)[12]                    : Inf
 ARIMA(2,1,0)(2,1,0)[12]                    : 796.0987
 ARIMA(2,1,0)(2,1,1)[12]                    : Inf
 ARIMA(2,1,1)(0,1,0)[12]                    : 817.8815
 ARIMA(2,1,1)(0,1,1)[12]                    : 778.3021
 ARIMA(2,1,1)(0,1,2)[12]                    : Inf
 ARIMA(2,1,1)(1,1,0)[12]                    : 802.8097
 ARIMA(2,1,1)(1,1,1)[12]                    : Inf
 ARIMA(2,1,1)(2,1,0)[12]                    : 797.9891
 ARIMA(2,1,2)(0,1,0)[12]                    : 819.6413
 ARIMA(2,1,2)(0,1,1)[12]                    : 780.3933
 ARIMA(2,1,2)(1,1,0)[12]                    : 804.9004
 ARIMA(2,1,3)(0,1,0)[12]                    : 817.5025
 ARIMA(3,1,0)(0,1,0)[12]                    : 817.9676
 ARIMA(3,1,0)(0,1,1)[12]                    : 778.3153
 ARIMA(3,1,0)(0,1,2)[12]                    : Inf
 ARIMA(3,1,0)(1,1,0)[12]                    : 802.8148
 ARIMA(3,1,0)(1,1,1)[12]                    : Inf
 ARIMA(3,1,0)(2,1,0)[12]                    : Inf
 ARIMA(3,1,1)(0,1,0)[12]                    : 819.9239
 ARIMA(3,1,1)(0,1,1)[12]                    : 780.4253
 ARIMA(3,1,1)(1,1,0)[12]                    : 803.5572
 ARIMA(3,1,2)(0,1,0)[12]                    : 817.7509
 ARIMA(4,1,0)(0,1,0)[12]                    : 818.942
 ARIMA(4,1,0)(0,1,1)[12]                    : 780.3523
 ARIMA(4,1,0)(1,1,0)[12]                    : 804.8222
 ARIMA(4,1,1)(0,1,0)[12]                    : 821.1184
 ARIMA(5,1,0)(0,1,0)[12]                    : 821.091



 Best model: ARIMA(2,1,0)(0,1,1)[12]                    

# --- Mostrar el modelo seleccionado ---
print(auto_model)

Series: ipi_ts 
ARIMA(2,1,0)(0,1,1)[12] 

Coefficients:
          ar1      ar2     sma1
      -0.8655  -0.5546  -0.8323
s.e.   0.0717   0.0727   0.0971

sigma^2 = 11.57:  log likelihood = -383.98
AIC=775.97   AICc=776.26   BIC=787.82

TSstudio::ts_plot(ipi_ts)

# --- Dejar que auto.arima() determine d y D automáticamente ---
# Al omitir 'd' y 'D', la función usará pruebas estadísticas.
# 'trace=TRUE' nos mostrará lo que está haciendo.
auto_model_fully_automatic <- auto.arima(ipi_ts, 
                                           stepwise = FALSE, 
                                           approximation = FALSE, 
                                           trace = TRUE)

 ARIMA(0,1,0)(0,1,0)[12]                    : 900.2247
 ARIMA(0,1,0)(0,1,1)[12]                    : Inf
 ARIMA(0,1,0)(0,1,2)[12]                    : Inf
 ARIMA(0,1,0)(1,1,0)[12]                    : 894.3355
 ARIMA(0,1,0)(1,1,1)[12]                    : Inf
 ARIMA(0,1,0)(1,1,2)[12]                    : Inf
 ARIMA(0,1,0)(2,1,0)[12]                    : 893.8956
 ARIMA(0,1,0)(2,1,1)[12]                    : Inf
 ARIMA(0,1,0)(2,1,2)[12]                    : Inf
 ARIMA(0,1,1)(0,1,0)[12]                    : 833.0983
 ARIMA(0,1,1)(0,1,1)[12]                    : Inf
 ARIMA(0,1,1)(0,1,2)[12]                    : Inf
 ARIMA(0,1,1)(1,1,0)[12]                    : 824.0026
 ARIMA(0,1,1)(1,1,1)[12]                    : Inf
 ARIMA(0,1,1)(1,1,2)[12]                    : Inf
 ARIMA(0,1,1)(2,1,0)[12]                    : 821.245
 ARIMA(0,1,1)(2,1,1)[12]                    : Inf
 ARIMA(0,1,1)(2,1,2)[12]                    : Inf
 ARIMA(0,1,2)(0,1,0)[12]                    : 817.4068
 ARIMA(0,1,2)(0,1,1)[12]                    : 784.5567
 ARIMA(0,1,2)(0,1,2)[12]                    : Inf
 ARIMA(0,1,2)(1,1,0)[12]                    : 806.5752
 ARIMA(0,1,2)(1,1,1)[12]                    : Inf
 ARIMA(0,1,2)(1,1,2)[12]                    : Inf
 ARIMA(0,1,2)(2,1,0)[12]                    : 803.0354
 ARIMA(0,1,2)(2,1,1)[12]                    : Inf
 ARIMA(0,1,3)(0,1,0)[12]                    : 814.8034
 ARIMA(0,1,3)(0,1,1)[12]                    : 785.6049
 ARIMA(0,1,3)(0,1,2)[12]                    : Inf
 ARIMA(0,1,3)(1,1,0)[12]                    : 806.2374
 ARIMA(0,1,3)(1,1,1)[12]                    : Inf
 ARIMA(0,1,3)(2,1,0)[12]                    : 802.7037
 ARIMA(0,1,4)(0,1,0)[12]                    : 815.8123
 ARIMA(0,1,4)(0,1,1)[12]                    : 782.9063
 ARIMA(0,1,4)(1,1,0)[12]                    : 806.1415
 ARIMA(0,1,5)(0,1,0)[12]                    : 816.5685
 ARIMA(1,1,0)(0,1,0)[12]                    : 852.0131
 ARIMA(1,1,0)(0,1,1)[12]                    : Inf
 ARIMA(1,1,0)(0,1,2)[12]                    : Inf
 ARIMA(1,1,0)(1,1,0)[12]                    : 844.6964
 ARIMA(1,1,0)(1,1,1)[12]                    : Inf
 ARIMA(1,1,0)(1,1,2)[12]                    : Inf
 ARIMA(1,1,0)(2,1,0)[12]                    : 845.1071
 ARIMA(1,1,0)(2,1,1)[12]                    : Inf
 ARIMA(1,1,0)(2,1,2)[12]                    : Inf
 ARIMA(1,1,1)(0,1,0)[12]                    : 827.2804
 ARIMA(1,1,1)(0,1,1)[12]                    : Inf
 ARIMA(1,1,1)(0,1,2)[12]                    : Inf
 ARIMA(1,1,1)(1,1,0)[12]                    : 816.8771
 ARIMA(1,1,1)(1,1,1)[12]                    : Inf
 ARIMA(1,1,1)(1,1,2)[12]                    : Inf
 ARIMA(1,1,1)(2,1,0)[12]                    : 814.3057
 ARIMA(1,1,1)(2,1,1)[12]                    : Inf
 ARIMA(1,1,2)(0,1,0)[12]                    : 815.8987
 ARIMA(1,1,2)(0,1,1)[12]                    : 786.2131
 ARIMA(1,1,2)(0,1,2)[12]                    : Inf
 ARIMA(1,1,2)(1,1,0)[12]                    : 807.1787
 ARIMA(1,1,2)(1,1,1)[12]                    : Inf
 ARIMA(1,1,2)(2,1,0)[12]                    : 803.8889
 ARIMA(1,1,3)(0,1,0)[12]                    : 815.3334
 ARIMA(1,1,3)(0,1,1)[12]                    : 784.3122
 ARIMA(1,1,3)(1,1,0)[12]                    : 805.8862
 ARIMA(1,1,4)(0,1,0)[12]                    : 817.5082
 ARIMA(2,1,0)(0,1,0)[12]                    : 816.0084
 ARIMA(2,1,0)(0,1,1)[12]                    : 776.2589
 ARIMA(2,1,0)(0,1,2)[12]                    : Inf
 ARIMA(2,1,0)(1,1,0)[12]                    : 800.6987
 ARIMA(2,1,0)(1,1,1)[12]                    : Inf
 ARIMA(2,1,0)(1,1,2)[12]                    : Inf
 ARIMA(2,1,0)(2,1,0)[12]                    : 796.0987
 ARIMA(2,1,0)(2,1,1)[12]                    : Inf
 ARIMA(2,1,1)(0,1,0)[12]                    : 817.8815
 ARIMA(2,1,1)(0,1,1)[12]                    : 778.3021
 ARIMA(2,1,1)(0,1,2)[12]                    : Inf
 ARIMA(2,1,1)(1,1,0)[12]                    : 802.8097
 ARIMA(2,1,1)(1,1,1)[12]                    : Inf
 ARIMA(2,1,1)(2,1,0)[12]                    : 797.9891
 ARIMA(2,1,2)(0,1,0)[12]                    : 819.6413
 ARIMA(2,1,2)(0,1,1)[12]                    : 780.3933
 ARIMA(2,1,2)(1,1,0)[12]                    : 804.9004
 ARIMA(2,1,3)(0,1,0)[12]                    : 817.5025
 ARIMA(3,1,0)(0,1,0)[12]                    : 817.9676
 ARIMA(3,1,0)(0,1,1)[12]                    : 778.3153
 ARIMA(3,1,0)(0,1,2)[12]                    : Inf
 ARIMA(3,1,0)(1,1,0)[12]                    : 802.8148
 ARIMA(3,1,0)(1,1,1)[12]                    : Inf
 ARIMA(3,1,0)(2,1,0)[12]                    : Inf
 ARIMA(3,1,1)(0,1,0)[12]                    : 819.9239
 ARIMA(3,1,1)(0,1,1)[12]                    : 780.4253
 ARIMA(3,1,1)(1,1,0)[12]                    : 803.5572
 ARIMA(3,1,2)(0,1,0)[12]                    : 817.7509
 ARIMA(4,1,0)(0,1,0)[12]                    : 818.942
 ARIMA(4,1,0)(0,1,1)[12]                    : 780.3523
 ARIMA(4,1,0)(1,1,0)[12]                    : 804.8222
 ARIMA(4,1,1)(0,1,0)[12]                    : 821.1184
 ARIMA(5,1,0)(0,1,0)[12]                    : 821.091



 Best model: ARIMA(2,1,0)(0,1,1)[12]                    

# --- Mostrar el modelo seleccionado ---
print(auto_model_fully_automatic)

Series: ipi_ts 
ARIMA(2,1,0)(0,1,1)[12] 

Coefficients:
          ar1      ar2     sma1
      -0.8655  -0.5546  -0.8323
s.e.   0.0717   0.0727   0.0971

sigma^2 = 11.57:  log likelihood = -383.98
AIC=775.97   AICc=776.26   BIC=787.82

modelo=tso(ipi_ts)

modelo

Series: ipi_ts 
Regression with ARIMA(3,0,0)(0,1,1)[12] errors 

Coefficients:
         ar1     ar2     ar3     sma1   LS112
      0.1130  0.3012  0.5474  -0.7995  8.1588
s.e.  0.0732  0.0699  0.0741   0.0941  2.2547

sigma^2 = 10.81:  log likelihood = -379.61
AIC=771.21   AICc=771.83   BIC=789.03

Outliers:
  type ind    time coefhat tstat
1   LS 112 1997:04   8.159 3.619

plot(modelo)

# Crear una secuencia de números de fila para la condición
filas <- 1:nrow(ipi_data)

# Si el número de fila es mayor o igual a 112, pone 1, de lo contrario, pone 0.
ipi_data$LS <- ifelse(filas==112, 1, 0)

print(head(ipi_data))

    Ipi YEAR_ MONTH_    DATE_ LS
1  90.2  1988      1 JAN 1988  0
2  96.5  1988      2 FEB 1988  0
3 103.4  1988      3 MAR 1988  0
4  95.0  1988      4 APR 1988  0
5 101.2  1988      5 MAY 1988  0
6 100.3  1988      6 JUN 1988  0

library(forecast)
serie1=ts(ipi_data,start = c(1988,1),frequency = 12)

library(tsoutliers)
plot(serie1)

modelo1=Arima(ipi_data$Ipi,order = c(2,1,0),seasonal=list(order=c(0,1,1),period=12),xreg=ipi_data$LS)

modelo1

Series: ipi_data$Ipi 
Regression with ARIMA(2,1,0)(0,1,1)[12] errors 

Coefficients:
          ar1      ar2     sma1    xreg
      -0.8458  -0.5306  -0.7581  9.8846
s.e.   0.0743   0.0757   0.0900  2.6975

sigma^2 = 10.94:  log likelihood = -377.58
AIC=765.15   AICc=765.59   BIC=779.97

library(lmtest)

Cargando paquete requerido: zoo

Adjuntando el paquete: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric

coeftest(modelo1)

z test of coefficients:

      Estimate Std. Error  z value  Pr(>|z|)    
ar1  -0.845761   0.074322 -11.3798 < 2.2e-16 ***
ar2  -0.530613   0.075658  -7.0133 2.327e-12 ***
sma1 -0.758086   0.089998  -8.4234 < 2.2e-16 ***
xreg  9.884645   2.697483   3.6644 0.0002479 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

checkresiduals(modelo1)

    Ljung-Box test

data:  Residuals from Regression with ARIMA(2,1,0)(0,1,1)[12] errors
Q* = 16.054, df = 7, p-value = 0.02463

Model df: 3.   Total lags used: 10

accuracy(modelo1)

                      ME     RMSE      MAE        MPE     MAPE      MASE
Training set -0.05596506 3.122571 2.393593 -0.0926248 2.328203 0.1995626
                   ACF1
Training set 0.02109753

predicciones=forecast(modelo1,12,xreg = ipi_data$LS)
predicciones

    Point Forecast     Lo 80     Hi 80     Lo 95     Hi 95
157      120.62522 116.38487 124.86557 114.14016 127.11028
158      123.76441 119.47393 128.05489 117.20268 130.32613
159      128.15330 123.62852 132.67808 121.23325 135.07335
160      119.81261 114.55497 125.07025 111.77175 127.85347
161      129.28476 123.88903 134.68050 121.03270 137.53683
162      130.10541 124.41943 135.79140 121.40945 138.80138
163      131.31067 125.25631 137.36504 122.05133 140.57002
164       86.40089  80.15630  92.64548  76.85062  95.95117
165      127.37528 120.86444 133.88612 117.41781 137.33276
166      130.67883 123.90482 137.45285 120.31887 141.03879
167      131.65627 124.67685 138.63569 120.98217 142.33037
168      118.39661 111.18222 125.61099 107.36316 129.43005
169      123.10570 115.35570 130.85570 111.25310 134.95830
170      125.19614 117.21571 133.17656 112.99113 137.40114
171      132.39079 124.12462 140.65695 119.74878 145.03280
172      122.23358 113.61649 130.85067 109.05488 135.41228
173      131.75330 122.89231 140.61429 118.20158 145.30501
174      133.49759 124.36060 142.63458 119.52377 147.47141
175      133.89643 124.47781 143.31506 119.49188 148.30098
176       89.17859  79.51757  98.83962  74.40333 103.95385
177      130.41854 120.50244 140.33464 115.25318 145.58390
178      133.39564 123.23067 143.56062 117.84966 148.94163
179      134.50827 124.11003 144.90650 118.60553 150.41100
180      121.30749 110.67328 131.94169 105.04387 137.57110
181      125.89505 114.77588 137.01421 108.88975 142.90035
182      128.05703 116.68917 139.42488 110.67139 145.44266
183      135.25566 123.60091 146.91040 117.43126 153.08005
184      125.05712 113.05555 137.05870 106.70230 143.41195
185      134.60968 122.34916 146.87021 115.85882 153.36054
186      136.34813 123.80386 148.89239 117.16333 155.53292
187      136.73449 123.89892 149.57006 117.10418 156.36480
188       92.03031  78.93693 105.12368  72.00571 112.05490
189      133.26533 119.90384 146.62681 112.83070 153.69995
190      136.23935 122.61399 149.86471 115.40117 157.07754
191      137.35719 123.48171 151.23268 116.13647 158.57791
192      124.15363 110.02580 138.28146 102.54698 145.76029
193      128.74077 114.14132 143.34023 106.41284 151.06871
194      130.90458 116.03968 145.76949 108.17068 153.63849
195      138.10189 122.93702 153.26675 114.90923 161.29455
196      127.90351 112.38449 143.42253 104.16921 151.63780
197      137.45664 121.66191 153.25137 113.30069 161.61259
198      139.19452 123.10142 155.28761 114.58225 163.80678
199      139.58105 123.18238 155.97973 114.50145 164.66066
200       94.87702  78.20309 111.55095  69.37645 120.37760
201      136.11182 119.15310 153.07055 110.17569 162.04795
202      139.08595 121.84615 156.32576 112.71995 165.45196
203      140.20382 122.69552 157.71212 113.42719 166.98046
204      127.00018 109.22130 144.77907  99.80973 154.19064
205      131.58738 113.33897 149.83579 103.67884 159.49592
206      133.75119 115.21941 152.28296 105.40928 162.09309
207      140.94846 122.10139 159.79554 112.12435 169.77257
208      130.75010 111.53782 149.96239 101.36745 160.13276
209      140.30323 120.79763 159.80884 110.47199 170.13448
210      142.04110 122.22110 161.86111 111.72902 172.35318
211      142.42765 122.28644 162.56886 111.62432 173.23097
212       97.72361  77.28925 118.15798  66.47195 128.97528
213      138.95841 118.22197 159.69486 107.24475 170.67207
214      141.93255 120.89742 162.96767 109.76210 174.10299
215      143.05041 121.72837 164.37246 110.44116 175.65967
216      129.84677 108.23586 151.45769  96.79573 162.89782
217      134.43397 112.35032 156.51762 100.65994 168.20800
218      136.59778 114.21289 158.98266 102.36305 170.83250
219      143.79505 121.07901 166.51110 109.05386 178.53625
220      133.59669 110.50289 156.69050  98.27777 168.91562
221      143.14982 119.74520 166.55445 107.35554 178.94411
222      144.88769 121.15244 168.62295 108.58775 181.18763
223      145.27424 121.20189 169.34659 108.45876 182.08972
224      100.57021  76.18708 124.95333  63.27943 137.86098
225      141.80500 117.10268 166.50732 104.02606 179.58394
226      144.77914 119.76080 169.79747 106.51690 183.04138
227      145.89700 120.57377 171.22024 107.16845 184.62555
228      132.69336 107.06340 158.32333  93.49572 171.89101
229      137.28056 111.17188 163.38924  97.35078 177.21034
230      139.44437 113.01702 165.87171  99.02723 179.86150
231      146.64164 119.86735 173.41594 105.69389 187.58940
232      136.44329 109.27813 163.60845  94.89776 177.98881
233      145.99642 118.50339 173.48944 103.94946 188.04338
234      147.73428 119.89461 175.57396 105.15718 190.31139
235      148.12083 119.92837 176.31329 105.00418 191.23748
236      103.41680  74.89645 131.93715  59.79868 147.03491
237      144.65159 115.79537 173.50782 100.51981 188.78338
238      147.62573 118.43664 176.81481 102.98487 192.26658
239      148.74359 119.23223 178.25496 103.60986 193.87733
240      135.53996 105.70460 165.37531  89.91072 181.16919
241      140.12715 109.80552 170.44878  93.75422 186.50009
242      142.29096 111.63380 172.94811  95.40489 189.17703
243      149.48823 118.46865 180.50782 102.04787 196.92860
244      139.28988 107.86619 170.71356  91.23149 187.34826
245      148.84301 117.07495 180.61107 100.25795 197.42806
246      150.58088 118.45056 182.71119 101.44179 199.71996
247      150.96742 118.46896 183.46588 101.26532 200.66952
248      106.26339  73.42052 139.10626  56.03455 156.49222
249      147.49818 114.30328 180.69308  96.73097 198.26540
250      150.47232 116.92826 184.01637  99.17111 201.77352
251      151.59019 117.70711 185.47326  99.77050 203.40987
252      138.38655 104.16284 172.61025  86.04591 190.72719
253      142.97374 108.25527 177.69221  89.87642 196.07106
254      145.13755 110.06729 180.20780  91.50222 198.77288
255      152.33483 116.88706 187.78259  98.12214 206.54751
256      142.13647 106.27144 178.00150  87.28564 196.98730
257      151.68960 115.46426 187.91494  96.28772 207.09147
258      153.42747 116.82470 190.03023  97.44837 209.40657
259      153.81401 116.82817 190.79985  97.24906 210.37897
260      109.10998  71.76379 146.45617  51.99391 166.22605
261      150.34477 112.63093 188.05861  92.66643 208.02311
262      153.31891 115.24018 191.39764  95.08252 211.55530
263      154.43678 116.00291 192.87064  95.65725 213.21630
264      141.23314 102.44260 180.02367  81.90813 200.55814
265      145.82033 106.52599 185.11468  85.72482 205.91585
266      147.98414 108.32232 187.64596  87.32662 208.64165
267      155.18142 115.12744 195.23540  93.92414 216.43869
268      154.86770 114.38347 195.35193  92.95242 216.78299
269      154.53619 113.67626 195.39611  92.04632 217.02605
270      156.27406 115.02199 197.52612  93.18447 219.36365
271      156.66060 115.01097 198.31024  92.96298 220.35823
272      111.95657  69.93119 153.98194  47.68431 176.22883
273      153.19136 110.78324 195.59949  88.33374 218.04899
274      156.16550 113.37729 198.95371  90.72658 221.60442
275      157.28337 114.12448 200.44225  91.27755 223.28919
276      144.07973 100.54871 187.61075  77.50478 210.65467
277      148.66692 104.62272 192.71113  81.30713 216.02672
278      150.83073 106.40392 195.25754  82.88578 218.77568
279      158.02801 113.19480 202.86121  89.46154 226.59448
280      147.82965 102.55343 193.10586  78.58565 217.07364
281      157.38278 111.71600 203.04956  87.54147 227.22409
282      159.12065 113.04746 205.19383  88.65779 229.58351
283      159.50719 113.02236 205.99203  88.41477 230.59962
284      114.80316  67.92773 161.67859  43.11337 186.49295
285      156.03796 108.76517 203.31074  83.74047 228.33544
286      159.01209 111.34452 206.67966  86.11083 231.91335
287      160.12996 112.07671 208.18320  86.63886 233.62105
288      146.92632  98.48601 195.36663  72.84326 221.00938
289      151.51351 102.55046 200.47657  76.63098 226.39605
290      153.67732 104.31702 203.03762  78.18726 229.16738
291      160.87460 111.09409 210.65510  84.74188 237.00731
292      150.67624 100.44021 200.91227  73.84686 227.50561
293      160.22937 109.58840 210.87034  82.78068 237.67805
294      161.96724 110.90601 213.02847  83.87582 240.05865
295      162.35378 110.86723 213.84034  83.61189 241.09568
296      117.64975  65.75822 169.54128  38.28851 197.01099
297      158.88455 106.58152 211.18758  78.89397 238.87513
298      161.85868 109.14665 214.57072  81.24258 242.47479
299      162.97655 109.86434 216.08876  81.74843 244.20467
300      149.77291  96.25919 203.28663  67.93074 231.61508
301      154.36010 100.31399 208.40622  71.70371 237.01650
302      156.52391 102.06639 210.98143  73.23832 239.80950
303      163.72119 108.83003 218.61235  79.77241 247.66997
304      153.52283  98.16389 208.88177  68.85864 238.18702
305      163.07596 107.29814 218.85378  77.77115 248.38077
306      164.81383 108.60231 221.02535  78.84572 250.78194
307      165.20038 108.55023 221.85052  78.56146 251.83929
308      120.49634  63.42730 177.56538  33.21677 207.77591
309      161.73114 104.23687 219.22540  73.80125 249.66102
310      164.70527 106.78821 222.62233  76.12877 253.28177
311      165.82314 107.49186 224.15441  76.61315 255.03312
312      152.61950  93.87273 211.36627  62.77408 242.46493

summary(predicciones)

Forecast method: Regression with ARIMA(2,1,0)(0,1,1)[12] errors

Model Information:
Series: ipi_data$Ipi 
Regression with ARIMA(2,1,0)(0,1,1)[12] errors 

Coefficients:
          ar1      ar2     sma1    xreg
      -0.8458  -0.5306  -0.7581  9.8846
s.e.   0.0743   0.0757   0.0900  2.6975

sigma^2 = 10.94:  log likelihood = -377.58
AIC=765.15   AICc=765.59   BIC=779.97

Error measures:
                      ME     RMSE      MAE        MPE     MAPE      MASE
Training set -0.05596506 3.122571 2.393593 -0.0926248 2.328203 0.1995626
                   ACF1
Training set 0.02109753

Forecasts:
    Point Forecast     Lo 80     Hi 80     Lo 95     Hi 95
157      120.62522 116.38487 124.86557 114.14016 127.11028
158      123.76441 119.47393 128.05489 117.20268 130.32613
159      128.15330 123.62852 132.67808 121.23325 135.07335
160      119.81261 114.55497 125.07025 111.77175 127.85347
161      129.28476 123.88903 134.68050 121.03270 137.53683
162      130.10541 124.41943 135.79140 121.40945 138.80138
163      131.31067 125.25631 137.36504 122.05133 140.57002
164       86.40089  80.15630  92.64548  76.85062  95.95117
165      127.37528 120.86444 133.88612 117.41781 137.33276
166      130.67883 123.90482 137.45285 120.31887 141.03879
167      131.65627 124.67685 138.63569 120.98217 142.33037
168      118.39661 111.18222 125.61099 107.36316 129.43005
169      123.10570 115.35570 130.85570 111.25310 134.95830
170      125.19614 117.21571 133.17656 112.99113 137.40114
171      132.39079 124.12462 140.65695 119.74878 145.03280
172      122.23358 113.61649 130.85067 109.05488 135.41228
173      131.75330 122.89231 140.61429 118.20158 145.30501
174      133.49759 124.36060 142.63458 119.52377 147.47141
175      133.89643 124.47781 143.31506 119.49188 148.30098
176       89.17859  79.51757  98.83962  74.40333 103.95385
177      130.41854 120.50244 140.33464 115.25318 145.58390
178      133.39564 123.23067 143.56062 117.84966 148.94163
179      134.50827 124.11003 144.90650 118.60553 150.41100
180      121.30749 110.67328 131.94169 105.04387 137.57110
181      125.89505 114.77588 137.01421 108.88975 142.90035
182      128.05703 116.68917 139.42488 110.67139 145.44266
183      135.25566 123.60091 146.91040 117.43126 153.08005
184      125.05712 113.05555 137.05870 106.70230 143.41195
185      134.60968 122.34916 146.87021 115.85882 153.36054
186      136.34813 123.80386 148.89239 117.16333 155.53292
187      136.73449 123.89892 149.57006 117.10418 156.36480
188       92.03031  78.93693 105.12368  72.00571 112.05490
189      133.26533 119.90384 146.62681 112.83070 153.69995
190      136.23935 122.61399 149.86471 115.40117 157.07754
191      137.35719 123.48171 151.23268 116.13647 158.57791
192      124.15363 110.02580 138.28146 102.54698 145.76029
193      128.74077 114.14132 143.34023 106.41284 151.06871
194      130.90458 116.03968 145.76949 108.17068 153.63849
195      138.10189 122.93702 153.26675 114.90923 161.29455
196      127.90351 112.38449 143.42253 104.16921 151.63780
197      137.45664 121.66191 153.25137 113.30069 161.61259
198      139.19452 123.10142 155.28761 114.58225 163.80678
199      139.58105 123.18238 155.97973 114.50145 164.66066
200       94.87702  78.20309 111.55095  69.37645 120.37760
201      136.11182 119.15310 153.07055 110.17569 162.04795
202      139.08595 121.84615 156.32576 112.71995 165.45196
203      140.20382 122.69552 157.71212 113.42719 166.98046
204      127.00018 109.22130 144.77907  99.80973 154.19064
205      131.58738 113.33897 149.83579 103.67884 159.49592
206      133.75119 115.21941 152.28296 105.40928 162.09309
207      140.94846 122.10139 159.79554 112.12435 169.77257
208      130.75010 111.53782 149.96239 101.36745 160.13276
209      140.30323 120.79763 159.80884 110.47199 170.13448
210      142.04110 122.22110 161.86111 111.72902 172.35318
211      142.42765 122.28644 162.56886 111.62432 173.23097
212       97.72361  77.28925 118.15798  66.47195 128.97528
213      138.95841 118.22197 159.69486 107.24475 170.67207
214      141.93255 120.89742 162.96767 109.76210 174.10299
215      143.05041 121.72837 164.37246 110.44116 175.65967
216      129.84677 108.23586 151.45769  96.79573 162.89782
217      134.43397 112.35032 156.51762 100.65994 168.20800
218      136.59778 114.21289 158.98266 102.36305 170.83250
219      143.79505 121.07901 166.51110 109.05386 178.53625
220      133.59669 110.50289 156.69050  98.27777 168.91562
221      143.14982 119.74520 166.55445 107.35554 178.94411
222      144.88769 121.15244 168.62295 108.58775 181.18763
223      145.27424 121.20189 169.34659 108.45876 182.08972
224      100.57021  76.18708 124.95333  63.27943 137.86098
225      141.80500 117.10268 166.50732 104.02606 179.58394
226      144.77914 119.76080 169.79747 106.51690 183.04138
227      145.89700 120.57377 171.22024 107.16845 184.62555
228      132.69336 107.06340 158.32333  93.49572 171.89101
229      137.28056 111.17188 163.38924  97.35078 177.21034
230      139.44437 113.01702 165.87171  99.02723 179.86150
231      146.64164 119.86735 173.41594 105.69389 187.58940
232      136.44329 109.27813 163.60845  94.89776 177.98881
233      145.99642 118.50339 173.48944 103.94946 188.04338
234      147.73428 119.89461 175.57396 105.15718 190.31139
235      148.12083 119.92837 176.31329 105.00418 191.23748
236      103.41680  74.89645 131.93715  59.79868 147.03491
237      144.65159 115.79537 173.50782 100.51981 188.78338
238      147.62573 118.43664 176.81481 102.98487 192.26658
239      148.74359 119.23223 178.25496 103.60986 193.87733
240      135.53996 105.70460 165.37531  89.91072 181.16919
241      140.12715 109.80552 170.44878  93.75422 186.50009
242      142.29096 111.63380 172.94811  95.40489 189.17703
243      149.48823 118.46865 180.50782 102.04787 196.92860
244      139.28988 107.86619 170.71356  91.23149 187.34826
245      148.84301 117.07495 180.61107 100.25795 197.42806
246      150.58088 118.45056 182.71119 101.44179 199.71996
247      150.96742 118.46896 183.46588 101.26532 200.66952
248      106.26339  73.42052 139.10626  56.03455 156.49222
249      147.49818 114.30328 180.69308  96.73097 198.26540
250      150.47232 116.92826 184.01637  99.17111 201.77352
251      151.59019 117.70711 185.47326  99.77050 203.40987
252      138.38655 104.16284 172.61025  86.04591 190.72719
253      142.97374 108.25527 177.69221  89.87642 196.07106
254      145.13755 110.06729 180.20780  91.50222 198.77288
255      152.33483 116.88706 187.78259  98.12214 206.54751
256      142.13647 106.27144 178.00150  87.28564 196.98730
257      151.68960 115.46426 187.91494  96.28772 207.09147
258      153.42747 116.82470 190.03023  97.44837 209.40657
259      153.81401 116.82817 190.79985  97.24906 210.37897
260      109.10998  71.76379 146.45617  51.99391 166.22605
261      150.34477 112.63093 188.05861  92.66643 208.02311
262      153.31891 115.24018 191.39764  95.08252 211.55530
263      154.43678 116.00291 192.87064  95.65725 213.21630
264      141.23314 102.44260 180.02367  81.90813 200.55814
265      145.82033 106.52599 185.11468  85.72482 205.91585
266      147.98414 108.32232 187.64596  87.32662 208.64165
267      155.18142 115.12744 195.23540  93.92414 216.43869
268      154.86770 114.38347 195.35193  92.95242 216.78299
269      154.53619 113.67626 195.39611  92.04632 217.02605
270      156.27406 115.02199 197.52612  93.18447 219.36365
271      156.66060 115.01097 198.31024  92.96298 220.35823
272      111.95657  69.93119 153.98194  47.68431 176.22883
273      153.19136 110.78324 195.59949  88.33374 218.04899
274      156.16550 113.37729 198.95371  90.72658 221.60442
275      157.28337 114.12448 200.44225  91.27755 223.28919
276      144.07973 100.54871 187.61075  77.50478 210.65467
277      148.66692 104.62272 192.71113  81.30713 216.02672
278      150.83073 106.40392 195.25754  82.88578 218.77568
279      158.02801 113.19480 202.86121  89.46154 226.59448
280      147.82965 102.55343 193.10586  78.58565 217.07364
281      157.38278 111.71600 203.04956  87.54147 227.22409
282      159.12065 113.04746 205.19383  88.65779 229.58351
283      159.50719 113.02236 205.99203  88.41477 230.59962
284      114.80316  67.92773 161.67859  43.11337 186.49295
285      156.03796 108.76517 203.31074  83.74047 228.33544
286      159.01209 111.34452 206.67966  86.11083 231.91335
287      160.12996 112.07671 208.18320  86.63886 233.62105
288      146.92632  98.48601 195.36663  72.84326 221.00938
289      151.51351 102.55046 200.47657  76.63098 226.39605
290      153.67732 104.31702 203.03762  78.18726 229.16738
291      160.87460 111.09409 210.65510  84.74188 237.00731
292      150.67624 100.44021 200.91227  73.84686 227.50561
293      160.22937 109.58840 210.87034  82.78068 237.67805
294      161.96724 110.90601 213.02847  83.87582 240.05865
295      162.35378 110.86723 213.84034  83.61189 241.09568
296      117.64975  65.75822 169.54128  38.28851 197.01099
297      158.88455 106.58152 211.18758  78.89397 238.87513
298      161.85868 109.14665 214.57072  81.24258 242.47479
299      162.97655 109.86434 216.08876  81.74843 244.20467
300      149.77291  96.25919 203.28663  67.93074 231.61508
301      154.36010 100.31399 208.40622  71.70371 237.01650
302      156.52391 102.06639 210.98143  73.23832 239.80950
303      163.72119 108.83003 218.61235  79.77241 247.66997
304      153.52283  98.16389 208.88177  68.85864 238.18702
305      163.07596 107.29814 218.85378  77.77115 248.38077
306      164.81383 108.60231 221.02535  78.84572 250.78194
307      165.20038 108.55023 221.85052  78.56146 251.83929
308      120.49634  63.42730 177.56538  33.21677 207.77591
309      161.73114 104.23687 219.22540  73.80125 249.66102
310      164.70527 106.78821 222.62233  76.12877 253.28177
311      165.82314 107.49186 224.15441  76.61315 255.03312
312      152.61950  93.87273 211.36627  62.77408 242.46493

plot(predicciones)

autoplot(predicciones)

library(TSstudio)
TSstudio::ts_plot(serie1)