# --- Cargar librerías ---
# 'forecast' para auto.arima y 'tsoutlier' para el análisis de intervención.
library(forecast)Warning: package 'forecast' was built under R version 4.3.3Registered S3 method overwritten by 'quantmod':
method from
as.zoo.data.frame zoo library(tsoutliers)Warning: package 'tsoutliers' was built under R version 4.3.3library(haven)Warning: package 'haven' was built under R version 4.3.2# --- Cargar los datos ---
ipc_data <- read_sav("Índice_De_Precios_al_Consumidor_Original(IPC).sav")
head(ipc_data, 10)# A tibble: 10 × 5
periodo ipc_general YEAR_ MONTH_ DATE_
<dbl> <dbl> <dbl> <dbl> <chr>
1 13479004800 100 2009 12 DEC 2009
2 13481683200 100. 2010 1 JAN 2010
3 13484361600 101. 2010 2 FEB 2010
4 13486780800 101. 2010 3 MAR 2010
5 13489459200 101. 2010 4 APR 2010
6 13492051200 100. 2010 5 MAY 2010
7 13494729600 101. 2010 6 JUN 2010
8 13497321600 101. 2010 7 JUL 2010
9 13500000000 101. 2010 8 AUG 2010
10 13502678400 101. 2010 9 SEP 2010# --- Crear el objeto de serie temporal (ts) ---
# Frecuencia mensual (12)
ipc_ts <- ts(ipc_data$ipc_general, start = c(2009, 12), frequency = 12)
# --- Visualizar la serie ---
plot(ipc_ts, main="Índice_De_Precios_al_Consumidor (IPC) (2009-2025)",
ylab="IPC", xlab="Año")
El grafico nos muestra una tendencia que es de forma creciente, lo que nos indica que los precios han aumentado conforme al tiempo, en otras palabras es que a existico una inflcacion en los precios.
Tmpoco se observan caidas de forma brusca, si no que periodos con mayor o menor crecimiento.
El nivel genarl de precios (IPC) a aumentado de forma sostenida entre los año 2009 y 2025
Existe lo que es una aceleracion notable al rededor del año 2021 y 2022 lo que refleja un periodo de inflacion fuerte
En los años 2024 y 2025 vemos que se estabiliza.
# --- 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(ipc_ts,
d = 1, D = 1,
stepwise = FALSE,
approximation = FALSE,
trace = TRUE)
ARIMA(0,1,0)(0,1,0)[12] : 325.597
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] : 305.6389
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] : 286.4624
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] : 301.7673
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] : 283.5079
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] : 262.5795
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] : 303.0717
ARIMA(0,1,2)(0,1,1)[12] : Inf
ARIMA(0,1,2)(0,1,2)[12] : Inf
ARIMA(0,1,2)(1,1,0)[12] : 285.1454
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] : 263.7744
ARIMA(0,1,2)(2,1,1)[12] : Inf
ARIMA(0,1,3)(0,1,0)[12] : 303.1345
ARIMA(0,1,3)(0,1,1)[12] : Inf
ARIMA(0,1,3)(0,1,2)[12] : Inf
ARIMA(0,1,3)(1,1,0)[12] : 283.9923
ARIMA(0,1,3)(1,1,1)[12] : Inf
ARIMA(0,1,3)(2,1,0)[12] : 262.8816
ARIMA(0,1,4)(0,1,0)[12] : 305.2214
ARIMA(0,1,4)(0,1,1)[12] : Inf
ARIMA(0,1,4)(1,1,0)[12] : 286.1065
ARIMA(0,1,5)(0,1,0)[12] : 304.4877
ARIMA(1,1,0)(0,1,0)[12] : 300.6832
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] : 282.1303
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] : 260.6352
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] : 302.5242
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] : 284.2218
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] : 262.7438
ARIMA(1,1,1)(2,1,1)[12] : Inf
ARIMA(1,1,2)(0,1,0)[12] : 304.4039
ARIMA(1,1,2)(0,1,1)[12] : Inf
ARIMA(1,1,2)(0,1,2)[12] : Inf
ARIMA(1,1,2)(1,1,0)[12] : 283.5358
ARIMA(1,1,2)(1,1,1)[12] : Inf
ARIMA(1,1,2)(2,1,0)[12] : 261.7479
ARIMA(1,1,3)(0,1,0)[12] : 305.2435
ARIMA(1,1,3)(0,1,1)[12] : Inf
ARIMA(1,1,3)(1,1,0)[12] : 286.1176
ARIMA(1,1,4)(0,1,0)[12] : Inf
ARIMA(2,1,0)(0,1,0)[12] : 302.5787
ARIMA(2,1,0)(0,1,1)[12] : Inf
ARIMA(2,1,0)(0,1,2)[12] : Inf
ARIMA(2,1,0)(1,1,0)[12] : 284.2235
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] : Inf
ARIMA(2,1,0)(2,1,1)[12] : Inf
ARIMA(2,1,1)(0,1,0)[12] : Inf
ARIMA(2,1,1)(0,1,1)[12] : Inf
ARIMA(2,1,1)(0,1,2)[12] : Inf
ARIMA(2,1,1)(1,1,0)[12] : Inf
ARIMA(2,1,1)(1,1,1)[12] : Inf
ARIMA(2,1,1)(2,1,0)[12] : Inf
ARIMA(2,1,2)(0,1,0)[12] : 306.1265
ARIMA(2,1,2)(0,1,1)[12] : Inf
ARIMA(2,1,2)(1,1,0)[12] : 285.0538
ARIMA(2,1,3)(0,1,0)[12] : Inf
ARIMA(3,1,0)(0,1,0)[12] : 304.4386
ARIMA(3,1,0)(0,1,1)[12] : Inf
ARIMA(3,1,0)(0,1,2)[12] : Inf
ARIMA(3,1,0)(1,1,0)[12] : 284.2149
ARIMA(3,1,0)(1,1,1)[12] : Inf
ARIMA(3,1,0)(2,1,0)[12] : 264.0858
ARIMA(3,1,1)(0,1,0)[12] : 306.6901
ARIMA(3,1,1)(0,1,1)[12] : Inf
ARIMA(3,1,1)(1,1,0)[12] : 285.9126
ARIMA(3,1,2)(0,1,0)[12] : Inf
ARIMA(4,1,0)(0,1,0)[12] : 304.613
ARIMA(4,1,0)(0,1,1)[12] : Inf
ARIMA(4,1,0)(1,1,0)[12] : 285.9764
ARIMA(4,1,1)(0,1,0)[12] : 306.7461
ARIMA(5,1,0)(0,1,0)[12] : 306.715
Best model: ARIMA(1,1,0)(2,1,0)[12] # Mostrar AIC y BIC
aic_value <- AIC(auto_model)
bic_value <- BIC(auto_model)
cat("AIC:", aic_value, "\n")AIC: 260.4013 cat("BIC:", bic_value, "\n")BIC: 273.0832 Para ARIMA (1,1,0) que es la parte no estacional:
AR(1) : un término autorregresivo.
d=1 : una diferencia no estacional.
MA(0) : no hay término de media móvil.
Para SARIMA (2,1,0)[12] que es la parte estacional con periodo 12 (mensual):
SAR(2) : dos términos autorregresivos estacionales.
D=1 : una diferencia estacional.
SMA(0) : no hay término estacional de media móvil.
AIC: 260.4013 y BIC: 273.0832: Ambos valores son relativamente bajos, lo que sugiere que el modelo se ajusta bien a los datos.
# --- Mostrar el modelo seleccionado ---
print(auto_model)Series: ipc_ts
ARIMA(1,1,0)(2,1,0)[12]
Coefficients:
ar1 sar1 sar2
0.3833 -0.4603 -0.3987
s.e. 0.0696 0.0753 0.0769
sigma^2 = 0.2427: log likelihood = -126.2
AIC=260.4 AICc=260.64 BIC=273.08Es la varianza de los residuos (el error del modelo) fue de 0.2427 que indica que, en promedio, el error de predicción es relativamente bajo respecto a la escala de la serie.
Los coeficientes son significativos, ya que indica que esos patrones sí existen en la serie. El valor de AIC/BIC te servirá para contrastarlo con otros modelos y decidir si este es el más adecuado.
AIC = 260.4, AICC = 260.64 y BIC = 273.08
Se usan para comparar los modelos: cuanto más bajo, mejor.
# graficar la serie temporal
TSstudio::ts_plot(ipc_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.
# R encuentra el ARIMA óptimo de manera totalmente automática, sin que tengamoa que especificar d ni D.
auto_model_fully_automatic <- auto.arima(ipc_ts,
stepwise = FALSE,
approximation = FALSE,
trace = TRUE)
ARIMA(0,1,0) : 268.4105
ARIMA(0,1,0) with drift : 248.2887
ARIMA(0,1,0)(0,0,1)[12] : 256.4821
ARIMA(0,1,0)(0,0,1)[12] with drift : 243.7612
ARIMA(0,1,0)(0,0,2)[12] : 258.5093
ARIMA(0,1,0)(0,0,2)[12] with drift : 244.1312
ARIMA(0,1,0)(1,0,0)[12] : 257.6958
ARIMA(0,1,0)(1,0,0)[12] with drift : 245.2457
ARIMA(0,1,0)(1,0,1)[12] : 258.5117
ARIMA(0,1,0)(1,0,1)[12] with drift : 244.9341
ARIMA(0,1,0)(1,0,2)[12] : 260.5987
ARIMA(0,1,0)(1,0,2)[12] with drift : 245.9913
ARIMA(0,1,0)(2,0,0)[12] : 258.7892
ARIMA(0,1,0)(2,0,0)[12] with drift : 243.1204
ARIMA(0,1,0)(2,0,1)[12] : 260.5817
ARIMA(0,1,0)(2,0,1)[12] with drift : 245.2313
ARIMA(0,1,0)(2,0,2)[12] : 262.3834
ARIMA(0,1,0)(2,0,2)[12] with drift : Inf
ARIMA(0,1,1) : 242.9684
ARIMA(0,1,1) with drift : 231.3953
ARIMA(0,1,1)(0,0,1)[12] : 230.2924
ARIMA(0,1,1)(0,0,1)[12] with drift : 223.8091
ARIMA(0,1,1)(0,0,2)[12] : 231.9045
ARIMA(0,1,1)(0,0,2)[12] with drift : 224.175
ARIMA(0,1,1)(1,0,0)[12] : 232.4118
ARIMA(0,1,1)(1,0,0)[12] with drift : 225.9742
ARIMA(0,1,1)(1,0,1)[12] : 231.899
ARIMA(0,1,1)(1,0,1)[12] with drift : 224.6689
ARIMA(0,1,1)(1,0,2)[12] : 234.0051
ARIMA(0,1,1)(1,0,2)[12] with drift : 226.2312
ARIMA(0,1,1)(2,0,0)[12] : 232.5461
ARIMA(0,1,1)(2,0,0)[12] with drift : 223.9232
ARIMA(0,1,1)(2,0,1)[12] : 234.0005
ARIMA(0,1,1)(2,0,1)[12] with drift : 225.9323
ARIMA(0,1,1)(2,0,2)[12] : Inf
ARIMA(0,1,1)(2,0,2)[12] with drift : 228.0083
ARIMA(0,1,2) : 244.4305
ARIMA(0,1,2) with drift : 233.4781
ARIMA(0,1,2)(0,0,1)[12] : 231.5816
ARIMA(0,1,2)(0,0,1)[12] with drift : 225.7814
ARIMA(0,1,2)(0,0,2)[12] : 233.1228
ARIMA(0,1,2)(0,0,2)[12] with drift : 226.1878
ARIMA(0,1,2)(1,0,0)[12] : 233.8445
ARIMA(0,1,2)(1,0,0)[12] with drift : 227.9888
ARIMA(0,1,2)(1,0,1)[12] : 233.1203
ARIMA(0,1,2)(1,0,1)[12] with drift : 226.6588
ARIMA(0,1,2)(1,0,2)[12] : 235.2456
ARIMA(0,1,2)(1,0,2)[12] with drift : 228.2785
ARIMA(0,1,2)(2,0,0)[12] : 233.8313
ARIMA(0,1,2)(2,0,0)[12] with drift : 225.9771
ARIMA(0,1,2)(2,0,1)[12] : 235.239
ARIMA(0,1,2)(2,0,1)[12] with drift : 227.9905
ARIMA(0,1,3) : 239.391
ARIMA(0,1,3) with drift : 231.1031
ARIMA(0,1,3)(0,0,1)[12] : 229.457
ARIMA(0,1,3)(0,0,1)[12] with drift : 225.0055
ARIMA(0,1,3)(0,0,2)[12] : 231.0974
ARIMA(0,1,3)(0,0,2)[12] with drift : 225.7762
ARIMA(0,1,3)(1,0,0)[12] : 231.2124
ARIMA(0,1,3)(1,0,0)[12] with drift : 226.7413
ARIMA(0,1,3)(1,0,1)[12] : 231.1118
ARIMA(0,1,3)(1,0,1)[12] with drift : 226.1594
ARIMA(0,1,3)(2,0,0)[12] : 231.5426
ARIMA(0,1,3)(2,0,0)[12] with drift : 225.5244
ARIMA(0,1,4) : 240.8775
ARIMA(0,1,4) with drift : 233.1605
ARIMA(0,1,4)(0,0,1)[12] : 231.512
ARIMA(0,1,4)(0,0,1)[12] with drift : 227.1581
ARIMA(0,1,4)(1,0,0)[12] : 233.2083
ARIMA(0,1,4)(1,0,0)[12] with drift : 228.8979
ARIMA(0,1,5) : 241.5303
ARIMA(0,1,5) with drift : 234.604
ARIMA(1,1,0) : 239.8036
ARIMA(1,1,0) with drift : 231.2853
ARIMA(1,1,0)(0,0,1)[12] : 227.9753
ARIMA(1,1,0)(0,0,1)[12] with drift : 223.5404
ARIMA(1,1,0)(0,0,2)[12] : 229.4717
ARIMA(1,1,0)(0,0,2)[12] with drift : 224.1526
ARIMA(1,1,0)(1,0,0)[12] : 230.0899
ARIMA(1,1,0)(1,0,0)[12] with drift : 225.6312
ARIMA(1,1,0)(1,0,1)[12] : 229.4881
ARIMA(1,1,0)(1,0,1)[12] with drift : 224.5412
ARIMA(1,1,0)(1,0,2)[12] : 231.5774
ARIMA(1,1,0)(1,0,2)[12] with drift : 226.2447
ARIMA(1,1,0)(2,0,0)[12] : 230.0623
ARIMA(1,1,0)(2,0,0)[12] with drift : 223.9893
ARIMA(1,1,0)(2,0,1)[12] : 231.5578
ARIMA(1,1,0)(2,0,1)[12] with drift : 225.9507
ARIMA(1,1,0)(2,0,2)[12] : 233.6725
ARIMA(1,1,0)(2,0,2)[12] with drift : 227.9758
ARIMA(1,1,1) : 234.6954
ARIMA(1,1,1) with drift : Inf
ARIMA(1,1,1)(0,0,1)[12] : 229.9967
ARIMA(1,1,1)(0,0,1)[12] with drift : 225.5132
ARIMA(1,1,1)(0,0,2)[12] : 231.5444
ARIMA(1,1,1)(0,0,2)[12] with drift : 225.9995
ARIMA(1,1,1)(1,0,0)[12] : 231.884
ARIMA(1,1,1)(1,0,0)[12] with drift : 227.7
ARIMA(1,1,1)(1,0,1)[12] : 231.5675
ARIMA(1,1,1)(1,0,1)[12] with drift : 226.4302
ARIMA(1,1,1)(1,0,2)[12] : 233.6754
ARIMA(1,1,1)(1,0,2)[12] with drift : 228.1057
ARIMA(1,1,1)(2,0,0)[12] : 232.046
ARIMA(1,1,1)(2,0,0)[12] with drift : 225.8393
ARIMA(1,1,1)(2,0,1)[12] : 233.6486
ARIMA(1,1,1)(2,0,1)[12] with drift : 227.8276
ARIMA(1,1,2) : 230.8038
ARIMA(1,1,2) with drift : 229.9601
ARIMA(1,1,2)(0,0,1)[12] : 225.9051
ARIMA(1,1,2)(0,0,1)[12] with drift : 225.1139
ARIMA(1,1,2)(0,0,2)[12] : 226.6804
ARIMA(1,1,2)(0,0,2)[12] with drift : 225.7042
ARIMA(1,1,2)(1,0,0)[12] : 227.2755
ARIMA(1,1,2)(1,0,0)[12] with drift : 226.5852
ARIMA(1,1,2)(1,0,1)[12] : 226.9552
ARIMA(1,1,2)(1,0,1)[12] with drift : 226.1239
ARIMA(1,1,2)(2,0,0)[12] : 226.8006
ARIMA(1,1,2)(2,0,0)[12] with drift : 225.6001
ARIMA(1,1,3) : 230.932
ARIMA(1,1,3) with drift : 230.0292
ARIMA(1,1,3)(0,0,1)[12] : 231.5024
ARIMA(1,1,3)(0,0,1)[12] with drift : 227.1583
ARIMA(1,1,3)(1,0,0)[12] : 228.5755
ARIMA(1,1,3)(1,0,0)[12] with drift : 227.8451
ARIMA(1,1,4) : 232.5778
ARIMA(1,1,4) with drift : 231.7276
ARIMA(2,1,0) : 241.2892
ARIMA(2,1,0) with drift : 233.3728
ARIMA(2,1,0)(0,0,1)[12] : 230.0369
ARIMA(2,1,0)(0,0,1)[12] with drift : 225.5947
ARIMA(2,1,0)(0,0,2)[12] : 231.5664
ARIMA(2,1,0)(0,0,2)[12] with drift : 226.1517
ARIMA(2,1,0)(1,0,0)[12] : 232.0885
ARIMA(2,1,0)(1,0,0)[12] with drift : 227.7297
ARIMA(2,1,0)(1,0,1)[12] : 231.5855
ARIMA(2,1,0)(1,0,1)[12] with drift : 226.56
ARIMA(2,1,0)(1,0,2)[12] : 233.6962
ARIMA(2,1,0)(1,0,2)[12] with drift : 228.2643
ARIMA(2,1,0)(2,0,0)[12] : Inf
ARIMA(2,1,0)(2,0,0)[12] with drift : Inf
ARIMA(2,1,0)(2,0,1)[12] : Inf
ARIMA(2,1,0)(2,0,1)[12] with drift : Inf
ARIMA(2,1,1) : 232.2613
ARIMA(2,1,1) with drift : 231.3886
ARIMA(2,1,1)(0,0,1)[12] : 227.5575
ARIMA(2,1,1)(0,0,1)[12] with drift : 223.0912
ARIMA(2,1,1)(0,0,2)[12] : 229.0463
ARIMA(2,1,1)(0,0,2)[12] with drift : 223.591
ARIMA(2,1,1)(1,0,0)[12] : 229.9432
ARIMA(2,1,1)(1,0,0)[12] with drift : 225.4535
ARIMA(2,1,1)(1,0,1)[12] : 228.577
ARIMA(2,1,1)(1,0,1)[12] with drift : 224.0186
ARIMA(2,1,1)(2,0,0)[12] : Inf
ARIMA(2,1,1)(2,0,0)[12] with drift : 223.4511
ARIMA(2,1,2) : 229.7121
ARIMA(2,1,2) with drift : 228.8456
ARIMA(2,1,2)(0,0,1)[12] : 226.9244
ARIMA(2,1,2)(0,0,1)[12] with drift : 226.0639
ARIMA(2,1,2)(1,0,0)[12] : 227.8908
ARIMA(2,1,2)(1,0,0)[12] with drift : 227.1121
ARIMA(2,1,3) : 231.8138
ARIMA(2,1,3) with drift : 230.9883
ARIMA(3,1,0) : 235.9541
ARIMA(3,1,0) with drift : 230.9239
ARIMA(3,1,0)(0,0,1)[12] : 229.3528
ARIMA(3,1,0)(0,0,1)[12] with drift : 225.8918
ARIMA(3,1,0)(0,0,2)[12] : 231.0812
ARIMA(3,1,0)(0,0,2)[12] with drift : 226.8511
ARIMA(3,1,0)(1,0,0)[12] : 230.5918
ARIMA(3,1,0)(1,0,0)[12] with drift : 227.3192
ARIMA(3,1,0)(1,0,1)[12] : 231.141
ARIMA(3,1,0)(1,0,1)[12] with drift : 227.2345
ARIMA(3,1,0)(2,0,0)[12] : 231.1935
ARIMA(3,1,0)(2,0,0)[12] with drift : 226.4926
ARIMA(3,1,1) : 232.205
ARIMA(3,1,1) with drift : 232.6697
ARIMA(3,1,1)(0,0,1)[12] : 231.0712
ARIMA(3,1,1)(0,0,1)[12] with drift : 227.1181
ARIMA(3,1,1)(1,0,0)[12] : 229.5269
ARIMA(3,1,1)(1,0,0)[12] with drift : 228.8258
ARIMA(3,1,2) : 231.8149
ARIMA(3,1,2) with drift : 230.9889
ARIMA(4,1,0) : 237.7921
ARIMA(4,1,0) with drift : 233.057
ARIMA(4,1,0)(0,0,1)[12] : 231.4276
ARIMA(4,1,0)(0,0,1)[12] with drift : 227.6572
ARIMA(4,1,0)(1,0,0)[12] : 232.704
ARIMA(4,1,0)(1,0,0)[12] with drift : 229.247
ARIMA(4,1,1) : 233.8097
ARIMA(4,1,1) with drift : 232.9414
ARIMA(5,1,0) : 237.1583
ARIMA(5,1,0) with drift : 233.7084
Best model: ARIMA(2,1,1)(0,0,1)[12] with drift # Mostrar AIC y BIC
aic_value <- AIC(auto_model_fully_automatic)
bic_value <- BIC(auto_model_fully_automatic)
cat("AIC:", aic_value, "\n") # Cat() función principal es imprimir texto y valoresAIC: 222.6271 cat("BIC:", bic_value, "\n")BIC: 242.0457 Parte no estacional (2,1,1)
AR(2) : la serie depende de los 2 valores anteriores.
d=1 : se aplicó una diferencia para lograr estacionariedad.
MA(1) : la serie depende también de un error aleatorio en el período anterior.
Parte estacional (0,0,1) [12]
SAR(0) y D=0 : no hay parte autorregresiva estacional ni diferencia estacional.
SMA(1) : hay una media móvil estacional de orden 1 o que depende de un error 12 períodos antes.
[12] : el período estacional es 12 (lo usual en datos mensuales).
El valor de AIC es de 22.6271 y BIC es de 242.0457
# --- Mostrar el modelo seleccionado ---
print(auto_model_fully_automatic)Series: ipc_ts
ARIMA(2,1,1)(0,0,1)[12] with drift
Coefficients:
ar1 ar2 ma1 sma1 drift
-0.5958 0.2747 0.9782 0.2713 0.1584
s.e. 0.0751 0.0731 0.0251 0.0812 0.0577
sigma^2 = 0.1831: log likelihood = -105.31
AIC=222.63 AICc=223.09 BIC=242.05No estacional (2,1,1):
ar1 = -0.5958, ar2 = 0.2747: la serie depende de los dos últimos rezagos.
ma1 = 0.9782: fuerte efecto de la media móvil (error del período anterior).
Estacional (0,0,1)[12]:
sma1 = 0.2713: hay un efecto de error cada 12 períodos (1 año).
with drift:
drift = 0.1584: la serie diferenciada muestra una tendencia positiva suave.
El modelo ARIMA(2,1,1)(0,0,1)[12] describe mucho mejor la serie ipc_ts que el modelo manual que so probó. Por lo tanto, conviene usar el automático para análisis y pronósticos.
modelo=tso(ipc_ts)modeloSeries: ipc_ts
Regression with ARIMA(1,1,0)(2,0,0)[12] errors
Coefficients:
ar1 sar1 sar2 LS17 LS71 TC169
0.5204 0.2259 0.0175 2.5012 2.3887 -0.9304
s.e. 0.0637 0.0803 0.0822 0.2942 0.2879 0.2485
sigma^2 = 0.1071: log likelihood = -54.18
AIC=122.37 AICc=122.99 BIC=145.02
Outliers:
type ind time coefhat tstat
1 LS 17 2011:04 2.5012 8.502
2 LS 71 2015:10 2.3887 8.296
3 TC 169 2023:12 -0.9304 -3.744La serie ipc_ts tiene dependencia en el tiempo (AR(1) + estacionalidad de 12 meses).
La tendencia se eliminó con una diferencia que hicimos.
Existen cambios estructurales permanentes (LS17 y LS71).
Existe un evento transitorio en el período 169 (TC169).
El ajuste es muy bueno (sigma^2 bajo y AIC/BIC reducidos).
plot(modelo)
ORIGINAL AND ADJUSTED SERIES
La línea azul (serie ajustada por el modelo ARIMA con outlers) sigue de cerca la gris(serie original) , lo que indica que el modelo ajusta muy bien la serie.
Cada punto rojo coincide con un salto o cambio importante en la serie. Esto confirma la presencia de los level shifts (LS) y transitory changes (TC) que el modelo identificó.
OUTLIER EFFECTS
Línea roja es la magnitud acumulada de los efectos de los outliers sobre la serie.
Escala vertical es el número de unidades de efecto que cada outlier agrega a la serie.
La línea sube en escalones: cada salto corresponde a un level shift (LS17, LS71).
El pequeño ajuste al final refleja un cambio transitorio (TC169) que no se mantiene, por eso la línea vuelve a estabilizarse.
Este panel muestra cómo los outliers modifican la serie original; sin ellos, el modelo no podría ajustarse tan bien.
# Crear una secuencia de números de fila para la condición
# filas <- 1:189 #189 datos (vector que va de 1 a 189)
filas <- 1:nrow(ipc_data)
# LS17: cambio permanente a partir de la observación 17
ipc_data$LS17 <- ifelse(filas >= 17, 1, 0)
# LS71: cambio permanente a partir de la observación 71
ipc_data$LS71 <- ifelse(filas >= 71, 1, 0)
# TC169: cambio transitorio en la observación 169
# Se marca solo en el punto exacto
ipc_data$TC169 <- ifelse(filas >= 169, 1, 0)print(head(ipc_data))# A tibble: 6 × 8
periodo ipc_general YEAR_ MONTH_ DATE_ LS17 LS71 TC169
<dbl> <dbl> <dbl> <dbl> <chr> <dbl> <dbl> <dbl>
1 13479004800 100 2009 12 DEC 2009 0 0 0
2 13481683200 100. 2010 1 JAN 2010 0 0 0
3 13484361600 101. 2010 2 FEB 2010 0 0 0
4 13486780800 101. 2010 3 MAR 2010 0 0 0
5 13489459200 101. 2010 4 APR 2010 0 0 0
6 13492051200 100. 2010 5 MAY 2010 0 0 0library(forecast)
serie1=ts(ipc_data,start = c(2009,12),frequency = 12)library(tsoutliers)
plot(serie1)
EL LADO IZQUIERDO INDICA:
Las variables que la base de datos más la serie temporal.
período : un contador de observaciones, básicamente el índice de fila (crece linealmente).
ipc_general : la serie original del IPC (sube con el tiempo, y se nota la tendencia + cambios).
YEAR_ : el año correspondiente a cada dato (sube en escalones de 1 en 1 cada 12 meses).
MONTH_ : el mes (ciclo de 1 a 12 que se repite).
EL LADO DERECHO INDICA:
DATE_ : otra variable de fecha en la base, con estacionalidad mensual
LS17 : se activa en el dato 17 y vale 1 en adelante. Representa un cambio permanente en el nivel de la serie a partir de esa observación.
LS71 : se activa en el dato 71 y vale 1 en adelante. Otro cambio permanente, pero más adelante en la serie.
TC169 : vale 1 solo en la observación 169 y 0 en el resto. Representa un cambio transitorio (choque puntual que no dura).
# Modelo llamado modelo con ARIMA (1,1,0) (2,0,0) con AIC= 122.37 BIC= 145.02
#Interviniendo el outler 17
modelo1=Arima(ipc_data$ipc_general,
order = c(1,1,0),
seasonal=list(order=c(2,0,0),period=12),
xreg=cbind(ipc_data$LS17))
#Interviniendo el outler 71
modelo2=Arima(ipc_data$ipc_general,
order = c(1,1,0),
seasonal=list(order=c(2,0,0),period=12),
xreg=cbind(ipc_data$LS71))
#Interviniendo el outler 169
modelo3=Arima(ipc_data$ipc_general,
order = c(1,1,0),
seasonal=list(order=c(2,0,0),period=12),
xreg=cbind(ipc_data$TC169))
#Interviniendo el outler 17, 71,
modelo4=Arima(ipc_data$ipc_general,
order = c(1,1,0),
seasonal=list(order=c(2,0,0),period=12),
xreg=cbind(ipc_data$LS17, ipc_data$LS71))
#Interviniendo el outler 71, 169,
modelo5=Arima(ipc_data$ipc_general,
order = c(1,1,0),
seasonal=list(order=c(2,0,0),period=12),
xreg=cbind(ipc_data$LS71, ipc_data$TC169))
#Interviniendo el outler 71, 169,
modelo6=Arima(ipc_data$ipc_general,
order = c(1,1,0),
seasonal=list(order=c(2,0,0),period=12),
xreg=cbind(ipc_data$LS17, ipc_data$LS71, ipc_data$TC169))modelo1Series: ipc_data$ipc_general
Regression with ARIMA(1,1,0)(2,0,0)[12] errors
Coefficients:
ar1 sar1 sar2 xreg
0.3895 0.2759 -0.0219 2.5289
s.e. 0.0679 0.0741 0.0780 0.3610
sigma^2 = 0.1522: log likelihood = -88.26
AIC=186.52 AICc=186.85 BIC=202.7modelo2Series: ipc_data$ipc_general
Regression with ARIMA(1,1,0)(2,0,0)[12] errors
Coefficients:
ar1 sar1 sar2 xreg
0.4571 0.2733 -0.1201 2.2957
s.e. 0.0649 0.0761 0.0924 0.3480
sigma^2 = 0.1567: log likelihood = -91.15
AIC=192.3 AICc=192.63 BIC=208.48modelo3Series: ipc_data$ipc_general
Regression with ARIMA(1,1,0)(2,0,0)[12] errors
Coefficients:
ar1 sar1 sar2 xreg
0.4107 0.2714 -0.1408 -1.0727
s.e. 0.0671 0.0742 0.0837 0.3837
sigma^2 = 0.1856: log likelihood = -107.1
AIC=224.21 AICc=224.53 BIC=240.39modelo4Series: ipc_data$ipc_general
Regression with ARIMA(1,1,0)(2,0,0)[12] errors
Coefficients:
ar1 sar1 sar2 xreg1 xreg2
0.4935 0.2527 0.0506 2.5363 2.3832
s.e. 0.0646 0.0772 0.0846 0.3057 0.2982
sigma^2 = 0.1144: log likelihood = -60.99
AIC=133.99 AICc=134.45 BIC=153.4modelo5Series: ipc_data$ipc_general
Regression with ARIMA(1,1,0)(2,0,0)[12] errors
Coefficients:
ar1 sar1 sar2 xreg1 xreg2
0.4842 0.2584 -0.1470 2.2972 -1.0985
s.e. 0.0646 0.0773 0.0906 0.3358 0.3369
sigma^2 = 0.1491: log likelihood = -85.99
AIC=183.97 AICc=184.44 BIC=203.39modelo6Series: ipc_data$ipc_general
Regression with ARIMA(1,1,0)(2,0,0)[12] errors
Coefficients:
ar1 sar1 sar2 xreg1 xreg2 xreg3
0.5210 0.2307 0.0253 2.5063 2.3891 -1.0491
s.e. 0.0637 0.0799 0.0820 0.2942 0.2876 0.2837
sigma^2 = 0.1073: log likelihood = -54.37
AIC=122.73 AICc=123.35 BIC=145.39Al tener los 6 modelos creados para analizar cual modelo es el menor valor de AIC y BIC concluimos que el mejor modelo es “modelo6” con un valor de AIC = 122.73 y BIC= 145.39, estos valores de ese modelo es el menor de todos.
library(lmtest)Warning: package 'lmtest' was built under R version 4.3.2Loading required package: zooWarning: package 'zoo' was built under R version 4.3.2
Attaching package: 'zoo'The following objects are masked from 'package:base':
as.Date, as.Date.numericcoeftest(modelo6)
z test of coefficients:
Estimate Std. Error z value Pr(>|z|)
ar1 0.520987 0.063655 8.1846 2.732e-16 ***
sar1 0.230653 0.079908 2.8865 0.0038957 **
sar2 0.025345 0.081978 0.3092 0.7571971
xreg1 2.506267 0.294232 8.5180 < 2.2e-16 ***
xreg2 2.389119 0.287620 8.3065 < 2.2e-16 ***
xreg3 -1.049063 0.283719 -3.6975 0.0002177 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1H0 : el coeficiente = 0 (no hay efecto significativo).
H1: el coeficiente ≠ 0 (sí tiene efecto significativo).
El modelo tiene varios coeficientes altamente significativos
El sar2 no es significativo
checkresiduals(modelo6)
Ljung-Box test
data: Residuals from Regression with ARIMA(1,1,0)(2,0,0)[12] errors
Q* = 10.398, df = 7, p-value = 0.1671
Model df: 3. Total lags used: 10H0: Los residuos son independientes (ruido blanco).
H1: Los residuos muestran autocorrelación significativa.
Si p_value > 0.05, no rechazamos H0.
Como mi p_value fue de 0.1671, esto es mayor que 0.05 por lo que no rechazamos la hipotesis nula por lo que los residuos son independientes y el modelo se ajusta bien y los residuos se estan comportando como ruido blanco.
PARA LOS GRAFICO TENEMOS QUE:
Los residuos no presentan tendencia (el gráfico superior).
No hay autocorrelación significativa (ACF dentro de los límites).
Los residuos siguen aproximadamente una distribución normal (histograma).
# resumen de métricas de desempeño del modelo ARIMA aplicado al conjunto de entrenamiento
accuracy(modelo6) ME RMSE MAE MPE MAPE MASE
Training set 0.04958185 0.3214601 0.2603451 0.04319565 0.2295182 0.7598956
ACF1
Training set -0.03066765library(forecast)
xreg_future <- cbind(LS17 = ipc_data$LS17, LS71 = ipc_data$LS71,TC169 = ipc_data$TC169)
predicciones <- forecast(modelo6, h = 12, xreg = xreg_future)Warning in forecast.forecast_ARIMA(modelo6, h = 12, xreg = xreg_future): xreg
contains different column names from the xreg used in training. Please check
that the regressors are in the same order.predicciones Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
190 126.6526 126.2328 127.0724 126.0105 127.2947
191 126.4766 125.7125 127.2408 125.3079 127.6454
192 126.4036 125.3312 127.4761 124.7634 128.0438
193 126.3274 124.9823 127.6725 124.2703 128.3846
194 126.4277 124.8404 128.0150 124.0001 128.8553
195 126.4080 124.6032 128.2127 123.6478 129.1681
196 126.4476 124.4453 128.4500 123.3853 129.5100
197 126.4642 124.2804 128.6481 123.1243 129.8042
198 126.5021 124.1499 128.8543 122.9047 130.0995
199 126.6080 124.0983 129.1178 122.7697 130.4464
200 126.7166 124.0584 129.3747 122.6513 130.7819
201 126.5928 123.7940 129.3916 122.3124 130.8732
202 126.5073 123.5441 129.4704 121.9756 131.0390
203 126.4570 123.3221 129.5920 121.6625 131.2515
204 126.4374 123.1313 129.7435 121.3811 131.4936
205 126.4142 122.9412 129.8872 121.1027 131.7257
206 128.9550 125.3207 132.5893 123.3968 134.5132
207 128.9484 125.1586 132.7382 123.1524 134.7445
208 128.9621 125.0224 132.9019 122.9368 134.9874
209 128.9670 124.8826 133.0514 122.7204 135.2136
210 128.9793 124.7550 133.2035 122.5188 135.4397
211 129.0143 124.6546 133.3741 122.3467 135.6820
212 129.0503 124.5591 133.5414 122.1817 135.9188
213 129.0095 124.3908 133.6283 121.9457 136.0734
214 128.9819 124.2313 133.7326 121.7164 136.2474
215 128.9659 124.0830 133.8488 121.4981 136.4336
216 128.9595 123.9458 133.9732 121.2918 136.6273
217 128.9522 123.8101 134.0944 121.0880 136.8165
218 128.9627 123.6947 134.2308 120.9060 137.0195
219 128.9607 123.5695 134.3520 120.7155 137.2059
220 128.9649 123.4530 134.4767 120.5352 137.3945
221 128.9664 123.3365 134.5964 120.3562 137.5767
222 128.9702 123.2246 134.7159 120.1830 137.7574
223 128.9810 123.1219 134.8401 120.0203 137.9417
224 128.9920 123.0217 134.9624 119.8612 138.1229
225 128.9795 122.8999 135.0591 119.6816 138.2774
226 128.9710 122.7822 135.1598 119.5060 138.4359
227 128.9660 122.6689 135.2631 119.3355 138.5965
228 128.9640 122.5600 135.3680 119.1699 138.7581
229 128.9618 122.4523 135.4712 119.0064 138.9171
230 128.9651 122.3517 135.5784 118.8508 139.0793
231 128.9644 122.2487 135.6801 118.6937 139.2352
232 128.9657 122.1492 135.7823 118.5408 139.3907
233 128.9662 122.0503 135.8821 118.3892 139.5432
234 128.9674 121.9535 135.9813 118.2405 139.6942
235 128.9708 121.8602 136.0813 118.0961 139.8454
236 128.9742 121.7683 136.1801 117.9537 139.9947
237 128.9703 121.6703 136.2703 117.8059 140.1347
238 128.9676 121.5742 136.3611 117.6604 140.2749
239 128.9661 121.4801 136.4520 117.5173 140.4148
240 128.9655 121.3880 136.5429 117.3768 140.5542
241 128.9648 121.2968 136.6327 117.2377 140.6918
242 128.9658 121.2084 136.7232 117.1019 140.8297
243 128.9656 121.1197 136.8114 116.9664 140.9648
244 128.9660 121.0327 136.8993 116.8330 141.0990
245 128.9661 120.9463 136.9860 116.7008 141.2315
246 128.9665 120.8610 137.0720 116.5702 141.3628
247 128.9676 120.7774 137.1578 116.4417 141.4934
248 128.9686 120.6946 137.2427 116.3146 141.6227
249 128.9674 120.6103 137.3245 116.1864 141.7485
250 128.9666 120.5272 137.4060 116.0596 141.8736
251 128.9661 120.4451 137.4871 115.9343 141.9979
252 128.9659 120.3640 137.5678 115.8105 142.1214
253 128.9657 120.2837 137.6477 115.6877 142.2437
254 128.9660 120.2046 137.7275 115.5665 142.3655
255 128.9660 120.1258 137.8061 115.4461 142.4858
256 128.9661 120.0479 137.8842 115.3269 142.6052
257 128.9661 119.9706 137.9616 115.2087 142.7236
258 128.9662 119.8941 138.0384 115.0915 142.8409
259 128.9666 119.8183 138.1148 114.9756 142.9576
260 131.3560 122.1324 140.5797 117.2497 145.4623
261 131.3556 122.0572 140.6541 117.1349 145.5764
262 131.3554 121.9827 140.7281 117.0211 145.6896
263 131.3552 121.9089 140.8016 116.9083 145.8022
264 131.3552 121.8357 140.8746 116.7964 145.9139
265 131.3551 121.7631 140.9471 116.6854 146.0248
266 131.3552 121.6912 141.0193 116.5753 146.1351
267 131.3552 121.6196 141.0907 116.4660 146.2444
268 131.3552 121.5487 141.1617 116.3575 146.3530
269 131.3552 121.4783 141.2322 116.2497 146.4608
270 131.3553 121.4083 141.3022 116.1427 146.5678
271 131.3554 121.3390 141.3718 116.0366 146.6742
272 131.3555 121.2701 141.4409 115.9312 146.7798
273 131.3554 121.2014 141.5093 115.8263 146.8845
274 131.3553 121.1333 141.5773 115.7221 146.9885
275 131.3552 121.0656 141.6449 115.6186 147.0919
276 131.3552 120.9984 141.7121 115.5158 147.1946
277 131.3552 120.9316 141.7788 115.4137 147.2967
278 131.3552 120.8653 141.8452 115.3122 147.3982
279 131.3552 120.7993 141.9111 115.2114 147.4990
280 131.3552 120.7338 141.9766 115.1112 147.5992
281 131.3552 120.6687 142.0417 115.0116 147.6988
282 131.3552 120.6040 142.1065 114.9127 147.7978
283 131.3553 120.5397 142.1708 114.8143 147.8962
284 131.3553 120.4758 142.2348 114.7166 147.9941
285 131.3553 120.4122 142.2983 114.6193 148.0913
286 131.3552 120.3490 142.3615 114.5226 148.1879
287 131.3552 120.2861 142.4244 114.4264 148.2840
288 131.3552 120.2236 142.4869 114.3309 148.3796
289 131.3552 120.1614 142.5490 114.2358 148.4747
290 131.3552 120.0996 142.6108 114.1413 148.5692
291 131.3552 120.0382 142.6723 114.0473 148.6632
292 131.3552 119.9770 142.7334 113.9538 148.7567
293 131.3552 119.9162 142.7943 113.8608 148.8497
294 131.3552 119.8557 142.8548 113.7683 148.9422
295 131.3552 119.7956 142.9149 113.6762 149.0343
296 131.3553 119.7357 142.9748 113.5847 149.1258
297 131.3552 119.6761 143.0344 113.4936 149.2169
298 131.3552 119.6169 143.0936 113.4030 149.3075
299 131.3552 119.5579 143.1526 113.3128 149.3977
300 131.3552 119.4993 143.2112 113.2231 149.4874
301 131.3552 119.4409 143.2696 113.1338 149.5767
302 131.3552 119.3828 143.3277 113.0450 149.6655
303 131.3552 119.3250 143.3855 112.9565 149.7539
304 131.3552 119.2674 143.4430 112.8686 149.8419
305 131.3552 119.2102 143.5003 112.7810 149.9295
306 131.3552 119.1532 143.5573 112.6938 150.0167
307 131.3552 119.0965 143.6140 112.6071 150.1034
308 131.3552 119.0400 143.6705 112.5207 150.1898
309 131.3552 118.9838 143.7267 112.4347 150.2757
310 131.3552 118.9278 143.7826 112.3492 150.3613
311 131.3552 118.8721 143.8383 112.2640 150.4465
312 131.3552 118.8167 143.8938 112.1792 150.5313
313 131.3552 118.7615 143.9490 112.0947 150.6158
314 131.3552 118.7065 144.0040 112.0106 150.6998
315 131.3552 118.6518 144.0587 111.9269 150.7835
316 131.3552 118.5973 144.1132 111.8436 150.8669
317 131.3552 118.5430 144.1675 111.7606 150.9499
318 131.3552 118.4890 144.2215 111.6780 151.0325
319 131.3552 118.4351 144.2753 111.5957 151.1148
320 131.3552 118.3816 144.3289 111.5137 151.1968
321 131.3552 118.3282 144.3823 111.4321 151.2784
322 131.3552 118.2750 144.4354 111.3508 151.3597
323 131.3552 118.2221 144.4884 111.2698 151.4406
324 131.3552 118.1694 144.5411 111.1892 151.5213
325 131.3552 118.1169 144.5936 111.1089 151.6016
326 131.3552 118.0646 144.6459 111.0289 151.6816
327 131.3552 118.0125 144.6980 110.9492 151.7613
328 131.3552 117.9606 144.7499 110.8698 151.8406
329 131.3552 117.9089 144.8016 110.7908 151.9197
330 131.3552 117.8574 144.8531 110.7120 151.9985
331 131.3552 117.8061 144.9044 110.6335 152.0769
332 131.3552 117.7549 144.9555 110.5554 152.1551
333 131.3552 117.7040 145.0064 110.4775 152.2330
334 131.3552 117.6533 145.0572 110.3999 152.3105
335 131.3552 117.6027 145.1077 110.3226 152.3878
336 131.3552 117.5524 145.1581 110.2456 152.4649
337 131.3552 117.5022 145.2083 110.1689 152.5416
338 131.3552 117.4522 145.2582 110.0924 152.6181
339 131.3552 117.4024 145.3081 110.0162 152.6942
340 131.3552 117.3528 145.3577 109.9403 152.7702
341 131.3552 117.3033 145.4072 109.8647 152.8458
342 131.3552 117.2540 145.4565 109.7893 152.9212
343 131.3552 117.2049 145.5056 109.7142 152.9963
344 131.3552 117.1560 145.5545 109.6393 153.0712
345 131.3552 117.1072 145.6033 109.5647 153.1458
346 131.3552 117.0586 145.6519 109.4904 153.2201
347 131.3552 117.0101 145.7004 109.4163 153.2942
348 131.3552 116.9618 145.7486 109.3424 153.3680
349 131.3552 116.9137 145.7968 109.2688 153.4416
350 131.3552 116.8657 145.8447 109.1955 153.5150
351 131.3552 116.8179 145.8925 109.1224 153.5881
352 131.3552 116.7703 145.9402 109.0495 153.6610
353 131.3552 116.7228 145.9877 108.9769 153.7336
354 131.3552 116.6755 146.0350 108.9045 153.8060
355 131.3552 116.6283 146.0822 108.8323 153.8782
356 131.3552 116.5812 146.1292 108.7604 153.9501
357 131.3552 116.5343 146.1761 108.6886 154.0218
358 130.3062 115.4385 145.1738 107.5681 153.0442
359 130.3062 115.3920 145.2204 107.4968 153.1155
360 130.3062 115.3455 145.2668 107.4258 153.1865
361 130.3062 115.2992 145.3131 107.3550 153.2574
362 130.3062 115.2530 145.3593 107.2844 153.3280
363 130.3062 115.2070 145.4053 107.2140 153.3983
364 130.3062 115.1611 145.4512 107.1438 153.4685
365 130.3062 115.1154 145.4969 107.0739 153.5385
366 130.3062 115.0698 145.5426 107.0041 153.6082
367 130.3062 115.0243 145.5880 106.9346 153.6777
368 130.3062 114.9790 145.6334 106.8653 153.7471
369 130.3062 114.9338 145.6786 106.7961 153.8162
370 130.3062 114.8887 145.7236 106.7272 153.8851
371 130.3062 114.8438 145.7686 106.6585 153.9539
372 130.3062 114.7990 145.8134 106.5900 154.0224
373 130.3062 114.7543 145.8580 106.5216 154.0907
374 130.3062 114.7098 145.9026 106.4535 154.1588
375 130.3062 114.6653 145.9470 106.3856 154.2268
376 130.3062 114.6210 145.9913 106.3178 154.2945
377 130.3062 114.5769 146.0355 106.2503 154.3621
378 130.3062 114.5328 146.0795 106.1829 154.4294La mayoría de los valores pronosticados (Point Forecast) se mantienen relativamente estables alrededor de 126 durante los primeros periodos (190–205).
A partir del periodo 206–259, hay un salto hacia 126–128, lo que indica que el modelo espera un aumento repentino en la serie temporal. Y asi sucesivamente con los demas
La serie pronosticada se mantiene estable al inicio, con una tendencia creciente hacia el final, y los intervalos muestran que la confianza del pronóstico disminuye cuanto más lejos estamos del periodo actual.
summary(predicciones)
Forecast method: Regression with ARIMA(1,1,0)(2,0,0)[12] errors
Model Information:
Series: ipc_data$ipc_general
Regression with ARIMA(1,1,0)(2,0,0)[12] errors
Coefficients:
ar1 sar1 sar2 xreg1 xreg2 xreg3
0.5210 0.2307 0.0253 2.5063 2.3891 -1.0491
s.e. 0.0637 0.0799 0.0820 0.2942 0.2876 0.2837
sigma^2 = 0.1073: log likelihood = -54.37
AIC=122.73 AICc=123.35 BIC=145.39
Error measures:
ME RMSE MAE MPE MAPE MASE
Training set 0.04958185 0.3214601 0.2603451 0.04319565 0.2295182 0.7598956
ACF1
Training set -0.03066765
Forecasts:
Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
190 126.6526 126.2328 127.0724 126.0105 127.2947
191 126.4766 125.7125 127.2408 125.3079 127.6454
192 126.4036 125.3312 127.4761 124.7634 128.0438
193 126.3274 124.9823 127.6725 124.2703 128.3846
194 126.4277 124.8404 128.0150 124.0001 128.8553
195 126.4080 124.6032 128.2127 123.6478 129.1681
196 126.4476 124.4453 128.4500 123.3853 129.5100
197 126.4642 124.2804 128.6481 123.1243 129.8042
198 126.5021 124.1499 128.8543 122.9047 130.0995
199 126.6080 124.0983 129.1178 122.7697 130.4464
200 126.7166 124.0584 129.3747 122.6513 130.7819
201 126.5928 123.7940 129.3916 122.3124 130.8732
202 126.5073 123.5441 129.4704 121.9756 131.0390
203 126.4570 123.3221 129.5920 121.6625 131.2515
204 126.4374 123.1313 129.7435 121.3811 131.4936
205 126.4142 122.9412 129.8872 121.1027 131.7257
206 128.9550 125.3207 132.5893 123.3968 134.5132
207 128.9484 125.1586 132.7382 123.1524 134.7445
208 128.9621 125.0224 132.9019 122.9368 134.9874
209 128.9670 124.8826 133.0514 122.7204 135.2136
210 128.9793 124.7550 133.2035 122.5188 135.4397
211 129.0143 124.6546 133.3741 122.3467 135.6820
212 129.0503 124.5591 133.5414 122.1817 135.9188
213 129.0095 124.3908 133.6283 121.9457 136.0734
214 128.9819 124.2313 133.7326 121.7164 136.2474
215 128.9659 124.0830 133.8488 121.4981 136.4336
216 128.9595 123.9458 133.9732 121.2918 136.6273
217 128.9522 123.8101 134.0944 121.0880 136.8165
218 128.9627 123.6947 134.2308 120.9060 137.0195
219 128.9607 123.5695 134.3520 120.7155 137.2059
220 128.9649 123.4530 134.4767 120.5352 137.3945
221 128.9664 123.3365 134.5964 120.3562 137.5767
222 128.9702 123.2246 134.7159 120.1830 137.7574
223 128.9810 123.1219 134.8401 120.0203 137.9417
224 128.9920 123.0217 134.9624 119.8612 138.1229
225 128.9795 122.8999 135.0591 119.6816 138.2774
226 128.9710 122.7822 135.1598 119.5060 138.4359
227 128.9660 122.6689 135.2631 119.3355 138.5965
228 128.9640 122.5600 135.3680 119.1699 138.7581
229 128.9618 122.4523 135.4712 119.0064 138.9171
230 128.9651 122.3517 135.5784 118.8508 139.0793
231 128.9644 122.2487 135.6801 118.6937 139.2352
232 128.9657 122.1492 135.7823 118.5408 139.3907
233 128.9662 122.0503 135.8821 118.3892 139.5432
234 128.9674 121.9535 135.9813 118.2405 139.6942
235 128.9708 121.8602 136.0813 118.0961 139.8454
236 128.9742 121.7683 136.1801 117.9537 139.9947
237 128.9703 121.6703 136.2703 117.8059 140.1347
238 128.9676 121.5742 136.3611 117.6604 140.2749
239 128.9661 121.4801 136.4520 117.5173 140.4148
240 128.9655 121.3880 136.5429 117.3768 140.5542
241 128.9648 121.2968 136.6327 117.2377 140.6918
242 128.9658 121.2084 136.7232 117.1019 140.8297
243 128.9656 121.1197 136.8114 116.9664 140.9648
244 128.9660 121.0327 136.8993 116.8330 141.0990
245 128.9661 120.9463 136.9860 116.7008 141.2315
246 128.9665 120.8610 137.0720 116.5702 141.3628
247 128.9676 120.7774 137.1578 116.4417 141.4934
248 128.9686 120.6946 137.2427 116.3146 141.6227
249 128.9674 120.6103 137.3245 116.1864 141.7485
250 128.9666 120.5272 137.4060 116.0596 141.8736
251 128.9661 120.4451 137.4871 115.9343 141.9979
252 128.9659 120.3640 137.5678 115.8105 142.1214
253 128.9657 120.2837 137.6477 115.6877 142.2437
254 128.9660 120.2046 137.7275 115.5665 142.3655
255 128.9660 120.1258 137.8061 115.4461 142.4858
256 128.9661 120.0479 137.8842 115.3269 142.6052
257 128.9661 119.9706 137.9616 115.2087 142.7236
258 128.9662 119.8941 138.0384 115.0915 142.8409
259 128.9666 119.8183 138.1148 114.9756 142.9576
260 131.3560 122.1324 140.5797 117.2497 145.4623
261 131.3556 122.0572 140.6541 117.1349 145.5764
262 131.3554 121.9827 140.7281 117.0211 145.6896
263 131.3552 121.9089 140.8016 116.9083 145.8022
264 131.3552 121.8357 140.8746 116.7964 145.9139
265 131.3551 121.7631 140.9471 116.6854 146.0248
266 131.3552 121.6912 141.0193 116.5753 146.1351
267 131.3552 121.6196 141.0907 116.4660 146.2444
268 131.3552 121.5487 141.1617 116.3575 146.3530
269 131.3552 121.4783 141.2322 116.2497 146.4608
270 131.3553 121.4083 141.3022 116.1427 146.5678
271 131.3554 121.3390 141.3718 116.0366 146.6742
272 131.3555 121.2701 141.4409 115.9312 146.7798
273 131.3554 121.2014 141.5093 115.8263 146.8845
274 131.3553 121.1333 141.5773 115.7221 146.9885
275 131.3552 121.0656 141.6449 115.6186 147.0919
276 131.3552 120.9984 141.7121 115.5158 147.1946
277 131.3552 120.9316 141.7788 115.4137 147.2967
278 131.3552 120.8653 141.8452 115.3122 147.3982
279 131.3552 120.7993 141.9111 115.2114 147.4990
280 131.3552 120.7338 141.9766 115.1112 147.5992
281 131.3552 120.6687 142.0417 115.0116 147.6988
282 131.3552 120.6040 142.1065 114.9127 147.7978
283 131.3553 120.5397 142.1708 114.8143 147.8962
284 131.3553 120.4758 142.2348 114.7166 147.9941
285 131.3553 120.4122 142.2983 114.6193 148.0913
286 131.3552 120.3490 142.3615 114.5226 148.1879
287 131.3552 120.2861 142.4244 114.4264 148.2840
288 131.3552 120.2236 142.4869 114.3309 148.3796
289 131.3552 120.1614 142.5490 114.2358 148.4747
290 131.3552 120.0996 142.6108 114.1413 148.5692
291 131.3552 120.0382 142.6723 114.0473 148.6632
292 131.3552 119.9770 142.7334 113.9538 148.7567
293 131.3552 119.9162 142.7943 113.8608 148.8497
294 131.3552 119.8557 142.8548 113.7683 148.9422
295 131.3552 119.7956 142.9149 113.6762 149.0343
296 131.3553 119.7357 142.9748 113.5847 149.1258
297 131.3552 119.6761 143.0344 113.4936 149.2169
298 131.3552 119.6169 143.0936 113.4030 149.3075
299 131.3552 119.5579 143.1526 113.3128 149.3977
300 131.3552 119.4993 143.2112 113.2231 149.4874
301 131.3552 119.4409 143.2696 113.1338 149.5767
302 131.3552 119.3828 143.3277 113.0450 149.6655
303 131.3552 119.3250 143.3855 112.9565 149.7539
304 131.3552 119.2674 143.4430 112.8686 149.8419
305 131.3552 119.2102 143.5003 112.7810 149.9295
306 131.3552 119.1532 143.5573 112.6938 150.0167
307 131.3552 119.0965 143.6140 112.6071 150.1034
308 131.3552 119.0400 143.6705 112.5207 150.1898
309 131.3552 118.9838 143.7267 112.4347 150.2757
310 131.3552 118.9278 143.7826 112.3492 150.3613
311 131.3552 118.8721 143.8383 112.2640 150.4465
312 131.3552 118.8167 143.8938 112.1792 150.5313
313 131.3552 118.7615 143.9490 112.0947 150.6158
314 131.3552 118.7065 144.0040 112.0106 150.6998
315 131.3552 118.6518 144.0587 111.9269 150.7835
316 131.3552 118.5973 144.1132 111.8436 150.8669
317 131.3552 118.5430 144.1675 111.7606 150.9499
318 131.3552 118.4890 144.2215 111.6780 151.0325
319 131.3552 118.4351 144.2753 111.5957 151.1148
320 131.3552 118.3816 144.3289 111.5137 151.1968
321 131.3552 118.3282 144.3823 111.4321 151.2784
322 131.3552 118.2750 144.4354 111.3508 151.3597
323 131.3552 118.2221 144.4884 111.2698 151.4406
324 131.3552 118.1694 144.5411 111.1892 151.5213
325 131.3552 118.1169 144.5936 111.1089 151.6016
326 131.3552 118.0646 144.6459 111.0289 151.6816
327 131.3552 118.0125 144.6980 110.9492 151.7613
328 131.3552 117.9606 144.7499 110.8698 151.8406
329 131.3552 117.9089 144.8016 110.7908 151.9197
330 131.3552 117.8574 144.8531 110.7120 151.9985
331 131.3552 117.8061 144.9044 110.6335 152.0769
332 131.3552 117.7549 144.9555 110.5554 152.1551
333 131.3552 117.7040 145.0064 110.4775 152.2330
334 131.3552 117.6533 145.0572 110.3999 152.3105
335 131.3552 117.6027 145.1077 110.3226 152.3878
336 131.3552 117.5524 145.1581 110.2456 152.4649
337 131.3552 117.5022 145.2083 110.1689 152.5416
338 131.3552 117.4522 145.2582 110.0924 152.6181
339 131.3552 117.4024 145.3081 110.0162 152.6942
340 131.3552 117.3528 145.3577 109.9403 152.7702
341 131.3552 117.3033 145.4072 109.8647 152.8458
342 131.3552 117.2540 145.4565 109.7893 152.9212
343 131.3552 117.2049 145.5056 109.7142 152.9963
344 131.3552 117.1560 145.5545 109.6393 153.0712
345 131.3552 117.1072 145.6033 109.5647 153.1458
346 131.3552 117.0586 145.6519 109.4904 153.2201
347 131.3552 117.0101 145.7004 109.4163 153.2942
348 131.3552 116.9618 145.7486 109.3424 153.3680
349 131.3552 116.9137 145.7968 109.2688 153.4416
350 131.3552 116.8657 145.8447 109.1955 153.5150
351 131.3552 116.8179 145.8925 109.1224 153.5881
352 131.3552 116.7703 145.9402 109.0495 153.6610
353 131.3552 116.7228 145.9877 108.9769 153.7336
354 131.3552 116.6755 146.0350 108.9045 153.8060
355 131.3552 116.6283 146.0822 108.8323 153.8782
356 131.3552 116.5812 146.1292 108.7604 153.9501
357 131.3552 116.5343 146.1761 108.6886 154.0218
358 130.3062 115.4385 145.1738 107.5681 153.0442
359 130.3062 115.3920 145.2204 107.4968 153.1155
360 130.3062 115.3455 145.2668 107.4258 153.1865
361 130.3062 115.2992 145.3131 107.3550 153.2574
362 130.3062 115.2530 145.3593 107.2844 153.3280
363 130.3062 115.2070 145.4053 107.2140 153.3983
364 130.3062 115.1611 145.4512 107.1438 153.4685
365 130.3062 115.1154 145.4969 107.0739 153.5385
366 130.3062 115.0698 145.5426 107.0041 153.6082
367 130.3062 115.0243 145.5880 106.9346 153.6777
368 130.3062 114.9790 145.6334 106.8653 153.7471
369 130.3062 114.9338 145.6786 106.7961 153.8162
370 130.3062 114.8887 145.7236 106.7272 153.8851
371 130.3062 114.8438 145.7686 106.6585 153.9539
372 130.3062 114.7990 145.8134 106.5900 154.0224
373 130.3062 114.7543 145.8580 106.5216 154.0907
374 130.3062 114.7098 145.9026 106.4535 154.1588
375 130.3062 114.6653 145.9470 106.3856 154.2268
376 130.3062 114.6210 145.9913 106.3178 154.2945
377 130.3062 114.5769 146.0355 106.2503 154.3621
378 130.3062 114.5328 146.0795 106.1829 154.4294Aqui observamis lo que es como un resumen de lo que son las predicciones que nos dieron. Utilizamos lo que es el ARIMA (1,1,0) (2,0,0) el cual ocupa el modelo 6 con un AIC = 122.73 y un BIC=145.39
plot(predicciones)
El modelo ARIMA predice que la serie se mantendrá estable en el futuro..
autoplot(predicciones)
El ARIMA está pronosticando estabilidad del IPC
library(TSstudio)Warning: package 'TSstudio' was built under R version 4.3.3TSstudio::ts_plot(serie1)