# --- 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 ---
# Agricultura, ganadería, silvicultura y pesca
bcm_data <- read_sav("Balanza_Comercial_de_Mercancías_según_CIIU_Rev._4._ValoresOriginal.sav")
head(bcm_data, 10)# A tibble: 10 × 5
Concepto BCM YEAR_ MONTH_ DATE_
<chr> <dbl> <dbl> <dbl> <chr>
1 2000-01 48.3 2000 1 JAN 2000
2 2000-02 56.3 2000 2 FEB 2000
3 2000-03 40.9 2000 3 MAR 2000
4 2000-04 46.8 2000 4 APR 2000
5 2000-05 34.0 2000 5 MAY 2000
6 2000-06 25.7 2000 6 JUN 2000
7 2000-07 24.5 2000 7 JUL 2000
8 2000-08 23.4 2000 8 AUG 2000
9 2000-09 14.3 2000 9 SEP 2000
10 2000-10 11.8 2000 10 OCT 2000# --- Crear el objeto de serie temporal (ts) ---
# Frecuencia mensual (12)
bcm_ts <- ts(bcm_data$BCM, start = c(2000, 1), frequency = 12)
# --- Visualizar la serie ---
plot(bcm_ts, main="Balanza_Comercial_de_Mercancías_según_CIIU_Rev._4._Valores (2000-2025)",
ylab="BCM", xlab="Año")
El gráfico representa lo que es la evolución entre los años 2000 y 2025. La serie es estacional, con picos recurrentes, pero muestra una caída inicial en (2000-2005), un gran evento atípico en el año 2010-2012, y luego una estabilización con fluctuaciones regulares hasta 2025.
# --- 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_modelBCM <- auto.arima(bcm_ts,
d = 1, D = 1,
stepwise = FALSE,
approximation = FALSE,
trace = TRUE)
ARIMA(0,1,0)(0,1,0)[12] : 1832.281
ARIMA(0,1,0)(0,1,1)[12] : 1755.318
ARIMA(0,1,0)(0,1,2)[12] : 1753.438
ARIMA(0,1,0)(1,1,0)[12] : 1789.467
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] : 1767.02
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] : 1826.18
ARIMA(0,1,1)(0,1,1)[12] : 1755.221
ARIMA(0,1,1)(0,1,2)[12] : 1753.517
ARIMA(0,1,1)(1,1,0)[12] : 1785.834
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] : 1764.48
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] : 1824.666
ARIMA(0,1,2)(0,1,1)[12] : 1751.568
ARIMA(0,1,2)(0,1,2)[12] : 1749.526
ARIMA(0,1,2)(1,1,0)[12] : 1784.809
ARIMA(0,1,2)(1,1,1)[12] : 1748.692
ARIMA(0,1,2)(1,1,2)[12] : 1750.472
ARIMA(0,1,2)(2,1,0)[12] : 1759.108
ARIMA(0,1,2)(2,1,1)[12] : Inf
ARIMA(0,1,3)(0,1,0)[12] : 1825.785
ARIMA(0,1,3)(0,1,1)[12] : 1753.418
ARIMA(0,1,3)(0,1,2)[12] : 1751.328
ARIMA(0,1,3)(1,1,0)[12] : 1786.152
ARIMA(0,1,3)(1,1,1)[12] : 1750.342
ARIMA(0,1,3)(2,1,0)[12] : 1760.775
ARIMA(0,1,4)(0,1,0)[12] : 1827.212
ARIMA(0,1,4)(0,1,1)[12] : 1750.875
ARIMA(0,1,4)(1,1,0)[12] : 1784.496
ARIMA(0,1,5)(0,1,0)[12] : 1829.271
ARIMA(1,1,0)(0,1,0)[12] : 1824.92
ARIMA(1,1,0)(0,1,1)[12] : 1754.704
ARIMA(1,1,0)(0,1,2)[12] : 1753.016
ARIMA(1,1,0)(1,1,0)[12] : 1785.007
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] : 1763.352
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] : 1826.582
ARIMA(1,1,1)(0,1,1)[12] : 1755.549
ARIMA(1,1,1)(0,1,2)[12] : 1753.753
ARIMA(1,1,1)(1,1,0)[12] : 1786.671
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] : 1764.079
ARIMA(1,1,1)(2,1,1)[12] : Inf
ARIMA(1,1,2)(0,1,0)[12] : Inf
ARIMA(1,1,2)(0,1,1)[12] : 1753.563
ARIMA(1,1,2)(0,1,2)[12] : 1751.504
ARIMA(1,1,2)(1,1,0)[12] : 1786.691
ARIMA(1,1,2)(1,1,1)[12] : 1750.622
ARIMA(1,1,2)(2,1,0)[12] : 1761.02
ARIMA(1,1,3)(0,1,0)[12] : Inf
ARIMA(1,1,3)(0,1,1)[12] : 1754.573
ARIMA(1,1,3)(1,1,0)[12] : Inf
ARIMA(1,1,4)(0,1,0)[12] : Inf
ARIMA(2,1,0)(0,1,0)[12] : 1826.147
ARIMA(2,1,0)(0,1,1)[12] : 1753.334
ARIMA(2,1,0)(0,1,2)[12] : 1751.264
ARIMA(2,1,0)(1,1,0)[12] : 1786.157
ARIMA(2,1,0)(1,1,1)[12] : 1750.285
ARIMA(2,1,0)(1,1,2)[12] : 1752.695
ARIMA(2,1,0)(2,1,0)[12] : 1761.837
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] : 1755.279
ARIMA(2,1,1)(0,1,2)[12] : 1753.209
ARIMA(2,1,1)(1,1,0)[12] : 1787.894
ARIMA(2,1,1)(1,1,1)[12] : 1752.197
ARIMA(2,1,1)(2,1,0)[12] : 1763.432
ARIMA(2,1,2)(0,1,0)[12] : Inf
ARIMA(2,1,2)(0,1,1)[12] : Inf
ARIMA(2,1,2)(1,1,0)[12] : 1785.314
ARIMA(2,1,3)(0,1,0)[12] : Inf
ARIMA(3,1,0)(0,1,0)[12] : 1825.718
ARIMA(3,1,0)(0,1,1)[12] : 1754.905
ARIMA(3,1,0)(0,1,2)[12] : 1752.835
ARIMA(3,1,0)(1,1,0)[12] : 1786.349
ARIMA(3,1,0)(1,1,1)[12] : 1751.713
ARIMA(3,1,0)(2,1,0)[12] : 1762.103
ARIMA(3,1,1)(0,1,0)[12] : 1827.108
ARIMA(3,1,1)(0,1,1)[12] : 1755.506
ARIMA(3,1,1)(1,1,0)[12] : 1787.106
ARIMA(3,1,2)(0,1,0)[12] : Inf
ARIMA(4,1,0)(0,1,0)[12] : 1826.598
ARIMA(4,1,0)(0,1,1)[12] : 1750.317
ARIMA(4,1,0)(1,1,0)[12] : 1784.775
ARIMA(4,1,1)(0,1,0)[12] : Inf
ARIMA(5,1,0)(0,1,0)[12] : 1828.232
Best model: ARIMA(0,1,2)(1,1,1)[12] # Mostrar AIC y BIC
aic_valueBCM <- AIC(auto_modelBCM)
bic_valueBCM <- BIC(auto_modelBCM)
cat("AIC:", aic_valueBCM, "\n")AIC: 1748.485 cat("BIC:", bic_valueBCM, "\n")BIC: 1766.92 Para ARIMA (0,1,2) que es la parte no estacional:
AR(0) : no tiene un término autorregresivo.
d=1 : una diferencia no estacional.
MA(2) : hay 2 términos de media móvil.
Para SARIMA (2,1,0)[12] que es la parte estacional con periodo 12 (mensual):
SAR(1) : un término autorregresivo estacionale.
D=1 : una diferencia estacional.
SMA(1) : hay un término estacional de media móvil.
AIC: 1748.485 y BIC: 1766.92
# --- Mostrar el modelo seleccionado ---
print(auto_modelBCM)Series: bcm_ts
ARIMA(0,1,2)(1,1,1)[12]
Coefficients:
ma1 ma2 sar1 sma1
-0.0948 0.1528 0.2758 -0.8750
s.e. 0.0597 0.0627 0.1001 0.0861
sigma^2 = 20.68: log likelihood = -869.24
AIC=1748.48 AICc=1748.69 BIC=1766.92# graficar la serie temporal
TSstudio::ts_plot(bcm_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_automaticBCM2 <- auto.arima(bcm_ts,
stepwise = FALSE,
approximation = FALSE,
trace = TRUE)
ARIMA(0,0,0)(0,1,0)[12] : 2165.51
ARIMA(0,0,0)(0,1,0)[12] with drift : 2167.014
ARIMA(0,0,0)(0,1,1)[12] : 2137.583
ARIMA(0,0,0)(0,1,1)[12] with drift : 2139.187
ARIMA(0,0,0)(0,1,2)[12] : 2138.697
ARIMA(0,0,0)(0,1,2)[12] with drift : 2140.346
ARIMA(0,0,0)(1,1,0)[12] : 2142.49
ARIMA(0,0,0)(1,1,0)[12] with drift : 2144
ARIMA(0,0,0)(1,1,1)[12] : Inf
ARIMA(0,0,0)(1,1,1)[12] with drift : Inf
ARIMA(0,0,0)(1,1,2)[12] : Inf
ARIMA(0,0,0)(1,1,2)[12] with drift : Inf
ARIMA(0,0,0)(2,1,0)[12] : 2141.364
ARIMA(0,0,0)(2,1,0)[12] with drift : 2142.94
ARIMA(0,0,0)(2,1,1)[12] : Inf
ARIMA(0,0,0)(2,1,1)[12] with drift : Inf
ARIMA(0,0,0)(2,1,2)[12] : Inf
ARIMA(0,0,0)(2,1,2)[12] with drift : Inf
ARIMA(0,0,1)(0,1,0)[12] : 1980.955
ARIMA(0,0,1)(0,1,0)[12] with drift : 1982.604
ARIMA(0,0,1)(0,1,1)[12] : 1939.309
ARIMA(0,0,1)(0,1,1)[12] with drift : 1941.058
ARIMA(0,0,1)(0,1,2)[12] : 1938.749
ARIMA(0,0,1)(0,1,2)[12] with drift : 1940.413
ARIMA(0,0,1)(1,1,0)[12] : 1949.286
ARIMA(0,0,1)(1,1,0)[12] with drift : 1950.93
ARIMA(0,0,1)(1,1,1)[12] : Inf
ARIMA(0,0,1)(1,1,1)[12] with drift : Inf
ARIMA(0,0,1)(1,1,2)[12] : Inf
ARIMA(0,0,1)(1,1,2)[12] with drift : Inf
ARIMA(0,0,1)(2,1,0)[12] : 1945.455
ARIMA(0,0,1)(2,1,0)[12] with drift : 1947.167
ARIMA(0,0,1)(2,1,1)[12] : Inf
ARIMA(0,0,1)(2,1,1)[12] with drift : Inf
ARIMA(0,0,1)(2,1,2)[12] : Inf
ARIMA(0,0,1)(2,1,2)[12] with drift : Inf
ARIMA(0,0,2)(0,1,0)[12] : 1911.418
ARIMA(0,0,2)(0,1,0)[12] with drift : 1913.036
ARIMA(0,0,2)(0,1,1)[12] : 1858.794
ARIMA(0,0,2)(0,1,1)[12] with drift : 1860.53
ARIMA(0,0,2)(0,1,2)[12] : 1852.201
ARIMA(0,0,2)(0,1,2)[12] with drift : Inf
ARIMA(0,0,2)(1,1,0)[12] : 1879.928
ARIMA(0,0,2)(1,1,0)[12] with drift : 1881.553
ARIMA(0,0,2)(1,1,1)[12] : Inf
ARIMA(0,0,2)(1,1,1)[12] with drift : Inf
ARIMA(0,0,2)(1,1,2)[12] : Inf
ARIMA(0,0,2)(1,1,2)[12] with drift : Inf
ARIMA(0,0,2)(2,1,0)[12] : 1867.572
ARIMA(0,0,2)(2,1,0)[12] with drift : 1869.267
ARIMA(0,0,2)(2,1,1)[12] : Inf
ARIMA(0,0,2)(2,1,1)[12] with drift : Inf
ARIMA(0,0,3)(0,1,0)[12] : 1853.968
ARIMA(0,0,3)(0,1,0)[12] with drift : 1855.71
ARIMA(0,0,3)(0,1,1)[12] : 1795.99
ARIMA(0,0,3)(0,1,1)[12] with drift : 1797.8
ARIMA(0,0,3)(0,1,2)[12] : 1791.783
ARIMA(0,0,3)(0,1,2)[12] with drift : 1793.159
ARIMA(0,0,3)(1,1,0)[12] : 1819.153
ARIMA(0,0,3)(1,1,0)[12] with drift : 1820.877
ARIMA(0,0,3)(1,1,1)[12] : Inf
ARIMA(0,0,3)(1,1,1)[12] with drift : Inf
ARIMA(0,0,3)(2,1,0)[12] : 1802.793
ARIMA(0,0,3)(2,1,0)[12] with drift : 1804.594
ARIMA(0,0,4)(0,1,0)[12] : 1843.343
ARIMA(0,0,4)(0,1,0)[12] with drift : 1845.136
ARIMA(0,0,4)(0,1,1)[12] : 1774.542
ARIMA(0,0,4)(0,1,1)[12] with drift : 1776.405
ARIMA(0,0,4)(1,1,0)[12] : 1803.21
ARIMA(0,0,4)(1,1,0)[12] with drift : 1805.001
ARIMA(0,0,5)(0,1,0)[12] : 1807.955
ARIMA(0,0,5)(0,1,0)[12] with drift : 1809.741
ARIMA(1,0,0)(0,1,0)[12] : 1818.879
ARIMA(1,0,0)(0,1,0)[12] with drift : 1820.684
ARIMA(1,0,0)(0,1,1)[12] : 1748.094
ARIMA(1,0,0)(0,1,1)[12] with drift : 1749.904
ARIMA(1,0,0)(0,1,2)[12] : 1745.401
ARIMA(1,0,0)(0,1,2)[12] with drift : 1747.103
ARIMA(1,0,0)(1,1,0)[12] : 1778.993
ARIMA(1,0,0)(1,1,0)[12] with drift : 1780.778
ARIMA(1,0,0)(1,1,1)[12] : Inf
ARIMA(1,0,0)(1,1,1)[12] with drift : Inf
ARIMA(1,0,0)(1,1,2)[12] : Inf
ARIMA(1,0,0)(1,1,2)[12] with drift : Inf
ARIMA(1,0,0)(2,1,0)[12] : 1758.674
ARIMA(1,0,0)(2,1,0)[12] with drift : 1760.494
ARIMA(1,0,0)(2,1,1)[12] : Inf
ARIMA(1,0,0)(2,1,1)[12] with drift : Inf
ARIMA(1,0,0)(2,1,2)[12] : Inf
ARIMA(1,0,0)(2,1,2)[12] with drift : Inf
ARIMA(1,0,1)(0,1,0)[12] : 1818.826
ARIMA(1,0,1)(0,1,0)[12] with drift : 1820.633
ARIMA(1,0,1)(0,1,1)[12] : 1749.986
ARIMA(1,0,1)(0,1,1)[12] with drift : 1751.804
ARIMA(1,0,1)(0,1,2)[12] : 1747.37
ARIMA(1,0,1)(0,1,2)[12] with drift : 1749.089
ARIMA(1,0,1)(1,1,0)[12] : 1779.892
ARIMA(1,0,1)(1,1,0)[12] with drift : 1781.679
ARIMA(1,0,1)(1,1,1)[12] : Inf
ARIMA(1,0,1)(1,1,1)[12] with drift : Inf
ARIMA(1,0,1)(1,1,2)[12] : Inf
ARIMA(1,0,1)(1,1,2)[12] with drift : Inf
ARIMA(1,0,1)(2,1,0)[12] : 1759.698
ARIMA(1,0,1)(2,1,0)[12] with drift : 1761.517
ARIMA(1,0,1)(2,1,1)[12] : Inf
ARIMA(1,0,1)(2,1,1)[12] with drift : Inf
ARIMA(1,0,2)(0,1,0)[12] : 1813.474
ARIMA(1,0,2)(0,1,0)[12] with drift : 1815.292
ARIMA(1,0,2)(0,1,1)[12] : 1741.649
ARIMA(1,0,2)(0,1,1)[12] with drift : 1743.483
ARIMA(1,0,2)(0,1,2)[12] : 1738.639
ARIMA(1,0,2)(0,1,2)[12] with drift : 1740.325
ARIMA(1,0,2)(1,1,0)[12] : 1775.036
ARIMA(1,0,2)(1,1,0)[12] with drift : 1776.84
ARIMA(1,0,2)(1,1,1)[12] : 1737.597
ARIMA(1,0,2)(1,1,1)[12] with drift : Inf
ARIMA(1,0,2)(2,1,0)[12] : 1749.464
ARIMA(1,0,2)(2,1,0)[12] with drift : 1751.312
ARIMA(1,0,3)(0,1,0)[12] : 1810.279
ARIMA(1,0,3)(0,1,0)[12] with drift : 1812.139
ARIMA(1,0,3)(0,1,1)[12] : 1739.679
ARIMA(1,0,3)(0,1,1)[12] with drift : 1741.558
ARIMA(1,0,3)(1,1,0)[12] : 1771.314
ARIMA(1,0,3)(1,1,0)[12] with drift : 1773.162
ARIMA(1,0,4)(0,1,0)[12] : 1809.896
ARIMA(1,0,4)(0,1,0)[12] with drift : 1811.775
ARIMA(2,0,0)(0,1,0)[12] : 1818.1
ARIMA(2,0,0)(0,1,0)[12] with drift : 1819.902
ARIMA(2,0,0)(0,1,1)[12] : 1749.914
ARIMA(2,0,0)(0,1,1)[12] with drift : 1751.729
ARIMA(2,0,0)(0,1,2)[12] : 1747.323
ARIMA(2,0,0)(0,1,2)[12] with drift : 1749.044
ARIMA(2,0,0)(1,1,0)[12] : 1779.514
ARIMA(2,0,0)(1,1,0)[12] with drift : 1781.296
ARIMA(2,0,0)(1,1,1)[12] : Inf
ARIMA(2,0,0)(1,1,1)[12] with drift : Inf
ARIMA(2,0,0)(1,1,2)[12] : Inf
ARIMA(2,0,0)(1,1,2)[12] with drift : Inf
ARIMA(2,0,0)(2,1,0)[12] : Inf
ARIMA(2,0,0)(2,1,0)[12] with drift : Inf
ARIMA(2,0,0)(2,1,1)[12] : Inf
ARIMA(2,0,0)(2,1,1)[12] with drift : Inf
ARIMA(2,0,1)(0,1,0)[12] : 1819.157
ARIMA(2,0,1)(0,1,0)[12] with drift : 1820.971
ARIMA(2,0,1)(0,1,1)[12] : 1750.866
ARIMA(2,0,1)(0,1,1)[12] with drift : 1752.687
ARIMA(2,0,1)(0,1,2)[12] : 1748.252
ARIMA(2,0,1)(0,1,2)[12] with drift : 1749.983
ARIMA(2,0,1)(1,1,0)[12] : 1780.762
ARIMA(2,0,1)(1,1,0)[12] with drift : 1782.557
ARIMA(2,0,1)(1,1,1)[12] : Inf
ARIMA(2,0,1)(1,1,1)[12] with drift : Inf
ARIMA(2,0,1)(2,1,0)[12] : 1759.722
ARIMA(2,0,1)(2,1,0)[12] with drift : 1761.544
ARIMA(2,0,2)(0,1,0)[12] : 1806.942
ARIMA(2,0,2)(0,1,0)[12] with drift : 1808.792
ARIMA(2,0,2)(0,1,1)[12] : 1739.264
ARIMA(2,0,2)(0,1,1)[12] with drift : 1741.145
ARIMA(2,0,2)(1,1,0)[12] : 1771.202
ARIMA(2,0,2)(1,1,0)[12] with drift : 1773.046
ARIMA(2,0,3)(0,1,0)[12] : Inf
ARIMA(2,0,3)(0,1,0)[12] with drift : Inf
ARIMA(3,0,0)(0,1,0)[12] : 1815.614
ARIMA(3,0,0)(0,1,0)[12] with drift : 1817.433
ARIMA(3,0,0)(0,1,1)[12] : 1742.887
ARIMA(3,0,0)(0,1,1)[12] with drift : 1744.73
ARIMA(3,0,0)(0,1,2)[12] : 1739.411
ARIMA(3,0,0)(0,1,2)[12] with drift : 1741.056
ARIMA(3,0,0)(1,1,0)[12] : 1777.066
ARIMA(3,0,0)(1,1,0)[12] with drift : 1778.873
ARIMA(3,0,0)(1,1,1)[12] : Inf
ARIMA(3,0,0)(1,1,1)[12] with drift : Inf
ARIMA(3,0,0)(2,1,0)[12] : 1752.327
ARIMA(3,0,0)(2,1,0)[12] with drift : 1754.182
ARIMA(3,0,1)(0,1,0)[12] : Inf
ARIMA(3,0,1)(0,1,0)[12] with drift : Inf
ARIMA(3,0,1)(0,1,1)[12] : 1742.859
ARIMA(3,0,1)(0,1,1)[12] with drift : 1744.731
ARIMA(3,0,1)(1,1,0)[12] : 1774.929
ARIMA(3,0,1)(1,1,0)[12] with drift : 1776.766
ARIMA(3,0,2)(0,1,0)[12] : Inf
ARIMA(3,0,2)(0,1,0)[12] with drift : Inf
ARIMA(4,0,0)(0,1,0)[12] : 1807.017
ARIMA(4,0,0)(0,1,0)[12] with drift : 1808.877
ARIMA(4,0,0)(0,1,1)[12] : 1740.177
ARIMA(4,0,0)(0,1,1)[12] with drift : 1742.063
ARIMA(4,0,0)(1,1,0)[12] : 1770.361
ARIMA(4,0,0)(1,1,0)[12] with drift : 1772.212
ARIMA(4,0,1)(0,1,0)[12] : 1808.084
ARIMA(4,0,1)(0,1,0)[12] with drift : 1809.953
ARIMA(5,0,0)(0,1,0)[12] : 1808.602
ARIMA(5,0,0)(0,1,0)[12] with drift : 1810.477
Best model: ARIMA(1,0,2)(1,1,1)[12] # Mostrar AIC y BIC
aic_valueBCM2 <- AIC(auto_model_fully_automaticBCM2)
bic_valueBCM2 <- BIC(auto_model_fully_automaticBCM2)
cat("AIC:", aic_valueBCM2, "\n") # Cat() función principal es imprimir texto y valoresAIC: 1737.306 cat("BIC:", bic_valueBCM2, "\n")BIC: 1759.448 Parte no estacional (1,0,2)
AR(1) : la serie depende de un valore anterior.
d=0 : no se aplicó ninguna diferencia para lograr estacionariedad.
MA(2) : la serie depende también de dos errores aleatorios en el período anterior.
Parte estacional (1,1,1) [12]
SAR(1) y D=1 : hay una parte autorregresiva estacional y una 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 1737.306 y BIC es de 1759.448
# --- Mostrar el modelo seleccionado ---
print(auto_model_fully_automaticBCM2)Series: bcm_ts
ARIMA(1,0,2)(1,1,1)[12]
Coefficients:
ar1 ma1 ma2 sar1 sma1
0.8387 -0.0212 0.2063 0.2786 -0.8850
s.e. 0.0409 0.0677 0.0624 0.0894 0.0719
sigma^2 = 19.32: log likelihood = -862.65
AIC=1737.31 AICc=1737.6 BIC=1759.45modeloBCM <- tso(bcm_ts, maxit.oloop = 10)modeloBCMSeries: bcm_ts
Regression with ARIMA(1,0,2)(1,1,1)[12] errors
Coefficients:
ar1 ma1 ma2 sar1 sma1 AO100 LS132 TC135
0.8710 -0.0937 0.1911 0.2104 -0.7481 13.4701 16.2717 17.6293
s.e. 0.0424 0.0691 0.0678 0.1606 0.1349 2.7663 3.8430 3.5365
sigma^2 = 16.09: log likelihood = -830.96
AIC=1679.92 AICc=1680.55 BIC=1713.13
Outliers:
type ind time coefhat tstat
1 AO 100 2008:04 13.47 4.869
2 LS 132 2010:12 16.27 4.234
3 TC 135 2011:03 17.63 4.985La fue ajustada con un modelo SARIMA estacional que es mensual.
El modelo detectó un fuerte componente autoregresivo (AR1=0.87) y un efecto estacional de media móvil (sma1=-0.75).
Identificó tres outliers importantes: uno puntual (impulso)(AO100), un cambio de nivel permanente (escalon) (LS132) y un cambio temporal (escalon) (TC135).
plot(modeloBCM)
Este gráfico muestra que entre 2009 y 2012 hubo valores con anomalias importantes en el comercio de mercancías, que generaron un pico muy por encima del patrón estacional normal. El modelo los identifica y ajusta, revelando que el resto de la serie sigue un ciclo bastante regular y más estable.
En la parte de 2008–2012 aparecen tres puntos rojos, que corresponden a valores extremadamente altos respecto al comportamiento habitual de la serie.
La línea azul suaviza estos picos, mostrando cómo se vería la serie si se eliminara el impacto de esos valores atípicos.
# Crear una secuencia de números de fila para la condición
filasBCM <- 1:nrow(bcm_data)
# AO100: efecto puntual solo en la observación 100
bcm_data$AO100 <- ifelse(filasBCM == 100, 1, 0)
# LS132: cambio permanente a partir de la observación 132
bcm_data$LS132 <- ifelse(filasBCM >= 132, 1, 0)
# TC135: cambio transitorio que decae (ejemplo con decaimiento geométrico 0.7)
bcm_data$TC135 <- ifelse(filasBCM >= 135, 0.7^(filasBCM - 135), 0)print(head(bcm_data))# A tibble: 6 × 8
Concepto BCM YEAR_ MONTH_ DATE_ AO100 LS132 TC135
<chr> <dbl> <dbl> <dbl> <chr> <dbl> <dbl> <dbl>
1 2000-01 48.3 2000 1 JAN 2000 0 0 0
2 2000-02 56.3 2000 2 FEB 2000 0 0 0
3 2000-03 40.9 2000 3 MAR 2000 0 0 0
4 2000-04 46.8 2000 4 APR 2000 0 0 0
5 2000-05 34.0 2000 5 MAY 2000 0 0 0
6 2000-06 25.7 2000 6 JUN 2000 0 0 0library(forecast)
serie1BCM=ts(bcm_data,start = c(2000,1),frequency = 12)library(tsoutliers)
plot(serie1BCM)
Un outlier aditivo (AO): un valor anómalo puntual.
Un cambio de nivel (LS): la serie se elevó de forma permanente después de 2011.
Un cambio transitorio (TC): un efecto fuerte pero de corta duración, que se disipó.
Entre 2010–2012 ocurrieron eventos extraordinarios que generaron: un pico aislado (AO), un salto que se corrigió rápido (TC), y un aumento de nivel que se mantuvo después (LS).
Tras ajustar estos efectos, la serie revela un patrón estacional más estable.
# Modelo llamado modeloBCM con ARIMA (1,0,2) (1,1,1) con AIC= 1679.92 BIC= 1713.13
#Interviniendo el outler 17
modelo1bcm=Arima(bcm_data$BCM,
order = c(1,0,2),
seasonal=list(order=c(1,1,1),period=12),
xreg=cbind(bcm_data$AO100))
#Interviniendo el outler 71
modelo2bcm=Arima(bcm_data$BCM,
order = c(1,0,2),
seasonal=list(order=c(1,1,1),period=12),
xreg=cbind(bcm_data$LS132))
#Interviniendo el outler 169
modelo3bcm=Arima(bcm_data$BCM,
order = c(1,0,2),
seasonal=list(order=c(1,1,1),period=12),
xreg=cbind(bcm_data$TC135))
#Interviniendo el outler 17, 71,
modelo4bcm=Arima(bcm_data$BCM,
order = c(1,0,2),
seasonal=list(order=c(1,1,1),period=12),
xreg=cbind(bcm_data$AO100, bcm_data$LS132))
#Interviniendo el outler 71, 169,
modelo5bcm=Arima(bcm_data$BCM,
order = c(1,0,2),
seasonal=list(order=c(1,1,1),period=12),
xreg=cbind(bcm_data$LS132, bcm_data$TC135))
#Interviniendo el outler 71, 169,
modelo6bcm=Arima(bcm_data$BCM,
order = c(1,0,2),
seasonal=list(order=c(1,1,1),period=12),
xreg=cbind(bcm_data$AO100, bcm_data$LS132, bcm_data$TC135))modelo1bcmSeries: bcm_data$BCM
Regression with ARIMA(1,0,2)(1,1,1)[12] errors
Coefficients:
ar1 ma1 ma2 sar1 sma1 xreg
0.8383 -0.0093 0.2350 0.2682 -0.8600 13.1417
s.e. 0.0409 0.0665 0.0628 0.1107 0.0946 2.9132
sigma^2 = 18.26: log likelihood = -852.96
AIC=1719.92 AICc=1720.31 BIC=1745.76modelo2bcmSeries: bcm_data$BCM
Regression with ARIMA(1,0,2)(1,1,1)[12] errors
Coefficients:
ar1 ma1 ma2 sar1 sma1 xreg
0.8672 -0.0511 0.1958 0.1437 -0.7649 16.2192
s.e. 0.0416 0.0669 0.0652 0.1152 0.0955 4.0284
sigma^2 = 18.57: log likelihood = -854.1
AIC=1722.19 AICc=1722.58 BIC=1748.02modelo3bcmSeries: bcm_data$BCM
Regression with ARIMA(1,0,2)(1,1,1)[12] errors
Coefficients:
ar1 ma1 ma2 sar1 sma1 xreg
0.8299 -0.0426 0.1681 0.3616 -0.9087 18.6842
s.e. 0.0442 0.0706 0.0643 0.0814 0.0630 3.7836
sigma^2 = 17.88: log likelihood = -850.89
AIC=1715.79 AICc=1716.18 BIC=1741.62modelo4bcmSeries: bcm_data$BCM
Regression with ARIMA(1,0,2)(1,1,1)[12] errors
Coefficients:
ar1 ma1 ma2 sar1 sma1 xreg1 xreg2
0.8589 -0.0277 0.2327 0.0422 -0.6666 13.9046 16.9422
s.e. 0.0420 0.0661 0.0666 0.1302 0.1153 2.8423 3.7387
sigma^2 = 17.36: log likelihood = -842.84
AIC=1701.68 AICc=1702.18 BIC=1731.21modelo5bcmSeries: bcm_data$BCM
Regression with ARIMA(1,0,2)(1,1,1)[12] errors
Coefficients:
ar1 ma1 ma2 sar1 sma1 xreg1 xreg2
0.8778 -0.1106 0.1566 0.2700 -0.8130 15.7695 18.2142
s.e. 0.0429 0.0700 0.0683 0.1094 0.0839 4.0006 3.6503
sigma^2 = 17.22: log likelihood = -842.35
AIC=1700.69 AICc=1701.19 BIC=1730.22modelo6bcmSeries: bcm_data$BCM
Regression with ARIMA(1,0,2)(1,1,1)[12] errors
Coefficients:
ar1 ma1 ma2 sar1 sma1 xreg1 xreg2 xreg3
0.8710 -0.0937 0.1911 0.2104 -0.7481 13.4701 16.2717 17.6293
s.e. 0.0424 0.0691 0.0678 0.1606 0.1349 2.7663 3.8430 3.5365
sigma^2 = 16.09: log likelihood = -830.96
AIC=1679.92 AICc=1680.55 BIC=1713.13Al 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 = 1679.92 y BIC= 1713.13, 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(modelo6bcm)
z test of coefficients:
Estimate Std. Error z value Pr(>|z|)
ar1 0.871002 0.042435 20.5257 < 2.2e-16 ***
ma1 -0.093728 0.069120 -1.3560 0.175091
ma2 0.191118 0.067766 2.8203 0.004798 **
sar1 0.210441 0.160595 1.3104 0.190067
sma1 -0.748068 0.134859 -5.5470 2.906e-08 ***
xreg1 13.470066 2.766349 4.8693 1.120e-06 ***
xreg2 16.271670 3.842955 4.2342 2.294e-05 ***
xreg3 17.629266 3.536540 4.9849 6.200e-07 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Los coeficientes que son más relevantes son: ar1, ma2, sma1 que estructuran lo que es la dinámica temporal. xreg1, xreg2, xreg3 explican variaciones adicionales que son significativas. ma1 y sar1 no son significativos.
checkresiduals(modelo6bcm)
Ljung-Box test
data: Residuals from Regression with ARIMA(1,0,2)(1,1,1)[12] errors
Q* = 18.853, df = 5, p-value = 0.002047
Model df: 5. 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 0.002047, esto es menor que 0.05 por lo que rechazamos la hipotesis nula por lo que los residuos muestran autocorrelación significativa.
Los residuos cumplen las condiciones de un buen modelo:
No presentan autocorrelación es decir que la estructura de la serie fue bien capturada.
Son aproximadamente normales por lo que se puede confiar en las inferencias y pronósticos.
Solo se observan leves desviaciones en las colas, pero no afectan de manera importante la validez del modelo.
# resumen de métricas de desempeño del modelo ARIMA aplicado al conjunto de entrenamiento
accuracy(modelo6bcm) ME RMSE MAE MPE MAPE MASE
Training set -0.384886 3.878805 2.897928 -5.795887 18.98328 0.6149693
ACF1
Training set -0.01060677library(forecast)
xreg_futurebcm <- cbind(AO100 = bcm_data$AO100, LS132 = bcm_data$LS132,TC135 = bcm_data$TC135)
prediccionesbcm <- forecast(modelo6bcm, h = 12, xreg = xreg_futurebcm)Warning in forecast.forecast_ARIMA(modelo6bcm, h = 12, xreg = xreg_futurebcm):
xreg contains different column names from the xreg used in training. Please
check that the regressors are in the same order.prediccionesbcm Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
309 -5.1968448 -1.033744e+01 -0.05625256 -13.0587021 2.665013
310 -8.6883458 -1.519918e+01 -2.17751634 -18.6458002 1.269109
311 -10.6657260 -1.855917e+01 -2.77228538 -22.7377018 1.406250
312 -8.4284968 -1.722709e+01 0.37009422 -21.8847805 5.027787
313 -1.9202383 -1.134772e+01 7.50724365 -16.3383277 12.497851
314 3.0402215 -6.837692e+00 12.91813460 -12.0667429 18.147186
315 10.1956760 -1.070215e-02 20.40205413 -5.4136324 25.804984
316 7.5101164 -2.938564e+00 17.95879699 -8.4697616 23.489994
317 8.4804950 -2.148323e+00 19.10931294 -7.7748794 24.735869
318 9.5680672 -1.195400e+00 20.33153458 -6.8932355 26.029370
319 7.1325573 -3.731948e+00 17.99706251 -9.4832696 23.748384
320 -1.0561449 -1.199668e+01 9.88438973 -17.7882487 15.675959
321 -5.8086222 -1.729486e+01 5.67761656 -23.3753084 11.758064
322 -8.6271984 -2.045556e+01 3.20116798 -26.7171238 9.462727
323 -10.4943596 -2.267643e+01 1.68771418 -29.1252336 8.136514
324 -8.0377006 -2.048141e+01 4.40600633 -27.0687080 10.993307
325 -1.5799906 -1.421857e+01 11.05859033 -20.9090323 17.749051
326 3.4079987 -9.376441e+00 16.19243857 -16.1441148 22.960112
327 9.5340490 -3.359945e+00 22.42804331 -10.1856136 29.253712
328 7.0977266 -5.878764e+00 20.07421690 -12.7481026 26.943556
329 8.3359029 -4.702824e+00 21.37463014 -11.6051095 28.276915
330 9.0800047 -4.005741e+00 22.16575021 -10.9329160 29.092925
331 6.7095717 -6.411732e+00 19.83087495 -13.3577300 26.776873
332 -0.9325395 -1.408075e+01 12.21567531 -21.0409989 19.175920
333 -5.7592324 -1.914820e+01 7.62973225 -26.2358868 14.717422
334 -8.4591767 -2.200165e+01 5.08329851 -29.1706052 12.252252
335 -10.3231578 -2.402966e+01 3.38333996 -31.2854371 10.639122
336 -7.8377545 -2.166739e+01 5.99188039 -28.9883560 13.312847
337 -1.4058660 -1.532819e+01 12.51645979 -22.6982258 19.886494
338 3.5746915 -1.041754e+01 17.56692719 -17.8245863 24.973969
339 9.4725943 -4.572446e+00 23.51763461 -12.0074413 30.952630
340 7.0786883 -7.006280e+00 21.16365656 -14.4624118 28.619788
341 8.3644811 -5.750703e+00 22.47966514 -13.2228300 29.951792
342 9.0286911 -5.109373e+00 23.16675512 -12.5936119 30.650994
343 6.6653231 -7.490074e+00 20.82072021 -14.9834885 28.314135
344 -0.8675378 -1.503607e+01 13.30099483 -22.5364384 20.801363
345 -5.7148782 -2.005383e+01 8.62407564 -27.6444158 16.214659
346 -8.3942384 -2.284117e+01 6.05269395 -30.4889148 13.700438
347 -10.2613660 -2.482694e+01 4.30421152 -32.5374945 12.014762
348 -7.7732373 -2.242818e+01 6.88170899 -30.1860435 14.639569
349 -1.3496773 -1.607206e+01 13.37270615 -23.8656199 21.166265
350 3.6267948 -1.114654e+01 18.40013395 -18.9670776 26.220667
351 9.4744900 -5.337389e+00 24.28636941 -13.1783248 32.127305
352 7.0875973 -7.753454e+00 21.92864838 -15.6098316 29.785026
353 8.3817445 -6.481399e+00 23.24488828 -14.3494723 31.112961
354 9.0276909 -5.852192e+00 23.90757332 -13.7291254 31.784507
355 6.6645457 -8.228023e+00 21.55711427 -16.1116724 29.440764
356 -0.8464254 -1.574861e+01 14.05576023 -23.6373515 21.944501
357 -5.6990698 -2.075036e+01 9.35222342 -28.7180364 17.319897
358 -8.3749334 -2.352040e+01 6.77053578 -31.5379298 14.788063
359 -10.2434506 -2.549358e+01 5.00668146 -33.5665150 13.079614
360 -7.7553820 -2.308444e+01 7.57367531 -31.1991521 15.688388
361 -1.3341266 -1.672279e+01 14.05453683 -24.8690565 22.200803
362 3.6410051 -1.179272e+01 19.07473500 -19.9628478 27.244858
363 9.4777159 -5.990116e+00 24.94554759 -14.1782913 33.133723
364 7.0919344 -8.401718e+00 22.58558724 -16.6035627 30.787432
365 8.3875221 -7.125691e+00 23.90073525 -15.3378900 32.112934
366 9.0293484 -6.498688e+00 24.55738453 -14.7187334 32.777430
367 6.6660092 -8.873263e+00 22.20528118 -17.0992565 30.431275
368 -0.8405653 -1.638836e+01 14.70722533 -24.6188591 22.937729
369 -5.6945087 -2.138213e+01 9.99311602 -29.6866604 18.297643
370 -8.3697958 -2.414568e+01 7.40609210 -32.4969342 15.757343
371 -10.2387441 -2.611309e+01 5.63559750 -34.5164545 14.038966
372 -7.7508089 -2.369944e+01 8.19781865 -32.1421299 16.640512
373 -1.3301437 -1.733490e+01 14.67461044 -25.8073029 23.147016
374 3.6446143 -1.240259e+01 19.69181776 -20.8974655 28.186694
375 9.4789337 -6.600399e+00 25.55826634 -15.1122834 34.070151
376 7.0933166 -9.010348e+00 23.19698108 -17.5351129 31.721746
377 8.3891468 -7.732952e+00 24.51124606 -16.2674762 33.045770
378 9.0300534 -7.106017e+00 25.16612401 -15.6479370 33.708044
379 6.6666273 -9.480035e+00 22.81328921 -18.0275610 31.360816
380 -0.8390619 -1.699375e+01 15.31563029 -25.5455316 23.867408
381 -5.6933136 -2.198189e+01 10.59526595 -30.6045462 19.217919
382 -8.3685096 -2.474161e+01 8.00459500 -33.4090123 16.671993
383 -10.2375751 -2.670508e+01 6.22993214 -35.4224541 14.947304
384 -7.7496910 -2.428846e+01 8.78907480 -33.0435507 17.544169
385 -1.3291701 -1.792179e+01 15.26345151 -26.7053950 24.047055
386 3.6454918 -1.298787e+01 20.27885458 -21.7930413 29.084025
387 9.4792927 -7.184912e+00 26.14349715 -16.0064086 34.964994
388 7.0936969 -9.593867e+00 23.78126116 -18.4277302 32.615124
389 8.3895667 -8.315698e+00 25.09483090 -17.1589303 33.938064
390 9.0302696 -7.688410e+00 25.74894938 -16.5387446 34.599284
391 6.6668166 -1.006203e+01 23.39566676 -18.9177520 32.251385
392 -0.8386940 -1.757526e+01 15.89786775 -26.4350565 24.757668
393 -5.6930172 -2.255868e+01 11.17264430 -31.4868206 20.100786
394 -8.3681999 -2.531539e+01 8.57899407 -34.2866964 17.550297
395 -10.2372951 -2.727560e+01 6.80101099 -36.2951355 15.820545
396 -7.7494262 -2.485653e+01 9.35767793 -33.9124841 18.413632
397 -1.3289394 -1.848805e+01 15.83017388 -27.5715386 24.913660
398 3.6456990 -1.355277e+01 20.84416391 -22.6570834 29.948481
399 9.4793879 -7.748871e+00 26.70764682 -16.8689604 35.827736
400 7.0937940 -1.015703e+01 24.34462170 -19.2890701 33.476658
401 8.3896699 -8.878260e+00 25.65759951 -18.0193495 34.798689
402 9.0303281 -8.250565e+00 26.31122073 -17.3985166 35.459173
403 6.6668677 -1.062385e+01 23.95758816 -19.7770074 33.110743
404 -0.8386068 -1.813678e+01 16.45956580 -27.2938789 25.616665
405 -5.6929463 -2.311602e+01 11.73012714 -32.3392376 20.953345
406 -8.3681273 -2.587011e+01 9.13385629 -35.1351013 18.398847
407 -10.2372297 -2.782743e+01 7.35296790 -37.1391153 16.664656
408 5.7207016 -1.193613e+01 23.37752822 -21.2830845 32.724488
409 -1.3288859 -1.903609e+01 16.37832124 -28.4097224 25.751950
410 3.6457468 -1.409959e+01 21.39107959 -23.4933976 30.784891
411 9.4794117 -8.294790e+00 27.25361362 -17.7038845 36.662708
412 7.0938177 -1.070225e+01 24.88988995 -20.1229261 34.310562
413 8.3896944 -9.422952e+00 26.20234050 -18.8523968 35.631786
414 9.0303428 -8.794867e+00 26.85555227 -18.2309625 36.291648
415 6.6668806 -1.116785e+01 24.50161523 -20.6089923 33.942753
416 -0.8385866 -1.868054e+01 17.00337095 -28.1255059 26.448333
417 -5.6929297 -2.365600e+01 12.27013954 -33.1650734 21.779214
418 -8.3681106 -2.640772e+01 9.67150117 -35.9573159 19.221095
419 -10.2372147 -2.836242e+01 7.88798921 -37.9573219 17.482893
420 -7.7493508 -2.593922e+01 10.44051845 -35.5683551 20.069654
421 -1.3288737 -1.956765e+01 16.90990052 -29.2226719 26.564924
422 3.6457577 -1.463003e+01 21.92154633 -24.3046489 31.596164
423 9.4794174 -8.824402e+00 27.78323675 -18.5138587 37.472693
424 7.0938233 -1.123123e+01 25.41887955 -20.9319317 35.119578
425 8.3897001 -9.951451e+00 26.73085116 -19.6606697 36.440070
426 9.0303464 -9.323005e+00 27.38369826 -19.0386830 37.099376
427 6.6668837 -1.169572e+01 25.02948620 -21.4162934 34.750061
428 -0.8385820 -1.920820e+01 17.53103541 -28.9324874 27.255323
429 -5.6929259 -2.418020e+01 12.79434492 -33.9667668 22.580915
430 -8.3681068 -2.692976e+01 10.19354376 -36.7557016 20.019488
431 -10.2372113 -2.888206e+01 8.40763387 -38.7520412 18.277619
432 -7.7493476 -2.645706e+01 10.95836585 -36.3603264 20.861631
433 -1.3288710 -2.008414e+01 17.42639658 -30.0125775 27.354835
434 3.6457602 -1.514550e+01 22.43702422 -25.0929982 32.384519
435 9.4794187 -9.339108e+00 28.29794535 -19.3010342 38.259872
436 7.0938246 -1.174536e+01 25.93300760 -21.7182194 35.905869
437 8.3897015 -1.046514e+01 27.24454013 -20.4462859 37.225689
438 9.0303473 -9.836360e+00 27.89705441 -19.8237913 37.884486
439 6.6668844 -1.220882e+01 25.54259053 -22.2010169 35.534786
440 15.4330892 -3.449441e+00 34.31561948 -13.4452487 44.311427
441 10.5787451 -8.418262e+00 29.57575207 -18.4746699 39.632160
442 7.9035642 -1.116583e+01 26.97296253 -21.2605638 37.067692
443 23.6637260 4.513339e+00 42.81411299 -5.6242634 52.951715
444 20.8628097 1.651209e+00 40.07441054 -8.5187982 50.244418
445 23.5811403 4.323230e+00 42.83905086 -5.8712923 53.033573
446 25.9642693 6.671300e+00 45.25723837 -3.5417808 55.470319
447 29.9838760 1.066435e+01 49.30339970 0.4372143 59.530538
448 26.3284459 6.988801e+00 45.66809072 -3.2489885 55.905880
449 26.7354375 7.380542e+00 46.09033315 -2.8653211 56.336196
450 26.7538635 7.387406e+00 46.12032117 -2.8645775 56.372305
451 23.9548469 4.579622e+00 43.33007136 -5.6770019 53.586696
452 16.1444940 -3.237379e+00 35.52636668 -13.4975224 45.786510
453 11.0767284 -8.416689e+00 30.57014559 -18.7358804 40.889337
454 8.2521526 -1.131182e+01 27.81612429 -21.6683601 38.172665
455 6.2784716 -1.336445e+01 25.92139280 -23.7627840 36.319727
456 8.6931316 -1.100947e+01 28.39573648 -21.4394022 38.825665
457 15.0623657 -4.685397e+00 34.81012883 -15.1392318 45.263963
458 20.0011270 2.191735e-01 39.78308061 -10.2527602 50.255014
459 25.8096765 6.001824e+00 45.61752905 -4.4838199 56.103173
460 23.4065062 3.579028e+00 43.23398439 -6.9170049 53.730017
461 24.6900797 4.847726e+00 44.53243379 -5.6561821 55.036342
462 25.3221131 5.468481e+00 45.17574525 -5.0413971 55.685623
463 22.9526216 3.090438e+00 42.81480554 -7.4239674 53.329211
464 15.4429363 -4.425733e+00 35.31160553 -14.9435712 45.829444
465 10.5856381 -9.391858e+00 30.56313389 -19.9673052 41.138581
466 7.9083894 -1.213796e+01 27.95473602 -22.7498522 38.566631
467 6.0378373 -1.408557e+01 26.16124110 -24.7382530 36.813928
468 8.5246876 -1.165698e+01 28.70635417 -22.3405078 39.389883
469 14.9444549 -5.281300e+00 35.17021013 -15.9881684 45.877078
470 19.9185895 -3.405495e-01 40.17772848 -11.0650898 50.902269
471 25.7519002 5.467471e+00 46.03632891 -5.2704565 56.774257
472 23.3660628 3.062469e+00 43.66965649 -7.6856041 54.417730
473 24.6617693 4.343648e+00 44.97989032 -6.4121152 55.735654
474 25.3022958 4.973161e+00 45.63143095 -5.7884334 56.393025
475 22.9387495 2.601263e+00 43.27623647 -8.1647527 54.042252
476 15.4332258 -4.910595e+00 35.77704657 -15.6799631 46.546415
477 10.5788407 -9.871278e+00 31.02895967 -20.6969172 41.854599
478 7.9036312 -1.261375e+01 28.42101506 -23.4749995 39.282262
479 6.0345066 -1.455817e+01 26.62718504 -25.4592773 37.528291
480 8.5223562 -1.212726e+01 29.17197331 -23.0585080 40.103220
481 14.9428229 -5.749886e+00 35.63553170 -16.7039444 46.589590
482 19.9174471 -8.078934e-01 40.64278752 -11.7792259 51.614120
483 25.7511005 5.001038e+00 46.50116248 -5.9833808 57.485582
484 23.3655030 2.596706e+00 44.13430030 -8.3976314 55.128637
485 24.6613775 3.878378e+00 45.44437689 -7.1234772 56.446232
486 25.3020215 4.508254e+00 46.09578884 -6.4993013 57.103344
487 22.9385575 2.136625e+00 43.74049010 -8.8752530 54.752368
488 15.4330914 -5.375034e+00 36.24121643 -16.3901896 47.256372
489 10.5787467 -1.033332e+01 31.49080988 -21.4034941 42.560987
490 7.9035654 -1.307428e+01 28.88141233 -24.1792829 39.986414
491 6.0344605 -1.501703e+01 27.08595520 -26.1610223 38.229943
492 8.5223239 -1.258487e+01 29.62951964 -23.7583463 40.802994
493 14.9428003 -6.206555e+00 36.09215542 -17.4023472 47.287948
494 19.9174313 -1.263852e+00 41.09871452 -12.4765460 52.311409
495 25.7510894 4.545616e+00 46.95656269 -6.6798833 58.182062
496 23.3654953 2.141689e+00 44.58930181 -9.0935157 55.824506
497 24.6613721 3.423668e+00 45.89907646 -7.8188939 57.141638
498 25.3020177 4.053776e+00 46.55025960 -7.1943639 57.798399
499 22.9385548 1.682322e+00 44.19478743 -9.5700476 55.447157
500 15.4330896 -5.829203e+00 36.69538225 -17.0847810 47.950960
501 10.5787454 -1.078528e+01 31.94276679 -22.0947059 43.252197
502 7.9035645 -1.352485e+01 29.33198220 -24.8683724 40.675501
503 6.0344599 -1.546606e+01 27.53498202 -26.8477511 38.916671
504 8.5223235 -1.303274e+01 30.07738633 -24.4433004 41.487947
505 14.9428000 -6.653548e+00 36.53914795 -18.0859641 47.971564
506 19.9174310 -1.710185e+00 41.54504728 -13.1591536 52.994016
507 25.7510893 4.099782e+00 47.40239685 -7.3617282 58.863907
508 23.3654952 1.696232e+00 45.03475883 -9.7747837 56.505774
509 24.6613720 2.978496e+00 46.34424799 -8.4997252 57.822469
510 25.3020177 3.608820e+00 46.99521491 -7.8748645 58.478900
511 22.9385548 1.237531e+00 44.63957892 -10.2502975 56.127407
512 15.4330895 -6.273871e+00 37.14004957 -17.7648410 48.631020
513 10.5787453 -1.122787e+01 32.38535983 -22.7715935 43.929084
514 7.9035645 -1.396614e+01 29.77327205 -25.5432670 41.350396
515 6.0344599 -1.590590e+01 27.97482167 -27.5204279 39.589348
516 8.5223235 -1.347149e+01 30.51613529 -25.1143091 42.158956
517 14.9428000 -7.091475e+00 36.97707486 -18.7557155 48.641315
518 19.9174310 -2.147492e+00 41.98235360 -13.8279560 53.662818
519 25.7510893 3.662944e+00 47.83923414 -8.0298132 59.531992
520 23.3654952 1.259749e+00 45.47124128 -10.4423260 57.173316
521 24.6613720 2.542282e+00 46.78046183 -9.1668567 58.489601
522 25.3020177 3.172810e+00 47.43122530 -8.5416848 59.145720
523 22.9385548 8.016745e-01 45.07543515 -10.9168821 56.793992
524 15.4330895 -6.709610e+00 37.57578896 -18.4312469 49.297426
525 10.5787453 -1.166166e+01 32.81914684 -23.4350135 44.592504
526 7.9035645 -1.439870e+01 30.20583192 -26.2048102 42.011939
527 6.0344599 -1.633710e+01 28.40601546 -28.1798819 40.248802
528 8.5223235 -1.390165e+01 30.94630131 -25.7721912 42.816838
529 14.9428000 -7.520866e+00 37.40646604 -19.4124126 49.298013
530 19.9174310 -2.576298e+00 42.41115975 -14.4837584 54.318620
531 25.7510893 3.234580e+00 48.26759804 -8.6849393 60.187118
532 23.3654952 8.317198e-01 45.89927059 -11.0969404 57.827931
533 24.6613720 2.114506e+00 47.20823782 -9.8210836 59.143828
534 25.3020177 2.745226e+00 47.85880942 -9.1956183 59.799654
535 22.9385548 3.742357e-01 45.50287387 -11.5705932 57.447703
536 15.4330895 -7.136938e+00 38.00311748 -19.0847895 49.950969
537 10.5787453 -1.208714e+01 33.24463343 -24.0857391 45.243230
538 7.9035645 -1.482303e+01 30.63016028 -26.8537644 42.660893
539 6.0344599 -1.676013e+01 28.82905404 -28.8268635 40.895783
540 8.5223235 -1.432372e+01 31.36836920 -26.4176884 43.462335
541 14.9428000 -7.942202e+00 37.82780198 -20.0567904 49.942390
542 19.9174310 -2.997081e+00 42.83194293 -15.1272907 54.962153
543 25.7510893 2.814215e+00 48.68796332 -9.3278325 60.830011
544 23.3654952 4.116707e-01 46.31931966 -11.7393500 58.470340
545 24.6613720 1.694697e+00 47.62804747 -10.4631271 59.785871
546 25.3020177 2.325598e+00 48.27843771 -9.8373844 60.441420
547 22.9385548 -4.525511e-02 45.92236473 -12.2121491 58.089259
548 15.4330895 -7.556325e+00 38.42250417 -19.7261861 50.592365
549 10.5787453 -1.250479e+01 33.66227857 -24.7244722 45.881963
550 7.9035645 -1.523958e+01 31.04670991 -27.4908221 43.297951
551 6.0344599 -1.717546e+01 29.24438333 -29.4620549 41.530975
552 8.5223235 -1.473813e+01 31.78277981 -27.0514747 44.096122
553 14.9428000 -8.355920e+00 38.24151969 -20.6895170 50.575117
554 19.9174310 -3.410275e+00 43.24513729 -15.7592169 55.594079
555 25.7510893 2.401417e+00 49.10076196 -9.9591535 61.461332
556 23.3654952 -8.284926e-04 46.73181885 -12.3702131 59.101203
557 24.6613720 1.282424e+00 48.04031992 -11.0936434 60.416387
558 25.3020177 1.913497e+00 48.69053839 -10.4676380 61.071673
559 22.9385548 -4.572256e-01 46.33433524 -12.8422037 58.719313
560 15.4330895 -7.968197e+00 38.83437601 -20.3560897 51.222269
561 10.5787453 -1.291501e+01 34.07250047 -25.3518525 46.509343
562 7.9035645 -1.564876e+01 31.45589353 -28.1166145 43.923743
563 6.0344599 -1.758349e+01 29.65241005 -30.0860779 42.154998
564 8.5223235 -1.514529e+01 32.18993537 -27.6741654 44.718812
565 14.9428000 -8.762418e+00 38.64801805 -21.3112026 51.196803
566 19.9174310 -3.816277e+00 43.65113919 -16.3801433 56.215005
567 25.7510893 1.995790e+00 49.50638844 -10.5795057 62.081684
568 23.3654952 -4.061708e-01 47.13716120 -12.9901307 59.721121
569 24.6613720 8.772969e-01 48.44544712 -11.7132320 61.035976
570 25.3020177 1.508533e+00 49.09550260 -11.0869773 61.691013
571 22.9385548 -8.620663e-01 46.73917593 -13.4613541 59.338464
572 15.4330895 -8.372944e+00 39.23912307 -20.9750969 51.841276
573 10.5787453 -1.331819e+01 34.47568142 -25.9684645 47.125955
574 7.9035645 -1.605096e+01 31.85808864 -28.7317188 44.538848
575 6.0344599 -1.798459e+01 30.05350636 -30.6995018 42.768422
576 8.5223235 -1.554556e+01 32.59020407 -28.2863236 45.330970
577 14.9428000 -9.162062e+00 39.04766230 -21.9224057 51.808006
578 19.9174310 -4.215450e+00 44.05031164 -16.9906249 56.825487
579 25.7510893 1.596974e+00 49.90520408 -11.1894416 62.691620
580 23.3654952 -8.047164e-01 47.53570679 -13.5996536 60.330644
581 24.6613720 4.789558e-01 48.84378820 -12.3224421 61.645186
582 25.3020177 1.110347e+00 49.49368873 -11.6959505 62.299986
583 22.9385548 -1.260135e+00 47.13724464 -14.0701476 59.947257
584 15.4330895 -8.770924e+00 39.63710276 -21.5837543 52.449933
585 10.5787453 -1.371468e+01 34.87217197 -26.5748445 47.732335
586 7.9035645 -1.644651e+01 32.25364151 -29.3366647 45.143794
587 6.0344599 -1.837909e+01 30.44801386 -31.3028489 43.371769
588 8.5223235 -1.593928e+01 32.98392400 -28.8884662 45.933113
589 14.9428000 -9.555188e+00 39.44078788 -22.5236394 52.409239
590 19.9174310 -4.608126e+00 44.44298812 -17.5911717 57.426034
591 25.7510893 1.204638e+00 50.29754086 -11.7894689 63.291647
592 23.3654952 -1.196796e+00 47.92778646 -14.1992877 60.930278
593 24.6613720 8.707083e-02 49.23567315 -12.9217784 62.244522
594 25.3020177 7.186092e-01 49.88542615 -12.2950611 62.899097
595 22.9385548 -1.651761e+00 47.52887024 -14.6690873 60.546197
596 15.4330895 -9.162465e+00 40.02864360 -22.1825644 53.048743
597 10.5787453 -1.410480e+01 35.26229454 -27.1714855 48.328976
598 7.9035645 -1.683574e+01 32.64287075 -29.9319395 45.739068
599 6.0344599 -1.876733e+01 30.83624694 -31.8966002 43.965520
600 8.5223235 -1.632676e+01 33.37140643 -29.4810695 46.525716
601 14.9428000 -9.942104e+00 39.82770374 -23.1153762 53.000976
602 19.9174310 -4.994614e+00 44.82947579 -18.1822536 58.017116
603 25.7510893 8.184739e-01 50.68370465 -12.3800555 63.882234
604 23.3654952 -1.582715e+00 48.31370507 -14.7894993 61.520490
605 24.6613720 -2.986621e-01 49.62140607 -13.5117060 62.834450
606 25.3020177 3.330170e-01 50.27101838 -12.8847736 63.488809
607 22.9385548 -2.037246e+00 47.91435584 -15.2586366 61.135746
608 15.4330895 -9.547869e+00 40.41404835 -22.7719901 53.638169
609 10.5787453 -1.448886e+01 35.64634644 -27.7588422 48.916333
610 7.9035645 -1.721894e+01 33.02607030 -30.5179926 46.325122
611 6.0344599 -1.914958e+01 31.21849580 -32.4811994 44.550119
612 8.5223235 -1.670829e+01 33.75293876 -30.0645728 47.109220
613 14.9428000 -1.032310e+01 40.20869515 -23.6980522 53.583652
614 19.9174310 -5.375196e+00 45.21005837 -18.7643044 58.599167
615 25.7510893 4.382006e-01 51.06397795 -12.9616333 64.463812
616 23.3654952 -1.962754e+00 48.69374424 -15.3707190 62.101709summary(prediccionesbcm)
Forecast method: Regression with ARIMA(1,0,2)(1,1,1)[12] errors
Model Information:
Series: bcm_data$BCM
Regression with ARIMA(1,0,2)(1,1,1)[12] errors
Coefficients:
ar1 ma1 ma2 sar1 sma1 xreg1 xreg2 xreg3
0.8710 -0.0937 0.1911 0.2104 -0.7481 13.4701 16.2717 17.6293
s.e. 0.0424 0.0691 0.0678 0.1606 0.1349 2.7663 3.8430 3.5365
sigma^2 = 16.09: log likelihood = -830.96
AIC=1679.92 AICc=1680.55 BIC=1713.13
Error measures:
ME RMSE MAE MPE MAPE MASE
Training set -0.384886 3.878805 2.897928 -5.795887 18.98328 0.6149693
ACF1
Training set -0.01060677
Forecasts:
Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
309 -5.1968448 -1.033744e+01 -0.05625256 -13.0587021 2.665013
310 -8.6883458 -1.519918e+01 -2.17751634 -18.6458002 1.269109
311 -10.6657260 -1.855917e+01 -2.77228538 -22.7377018 1.406250
312 -8.4284968 -1.722709e+01 0.37009422 -21.8847805 5.027787
313 -1.9202383 -1.134772e+01 7.50724365 -16.3383277 12.497851
314 3.0402215 -6.837692e+00 12.91813460 -12.0667429 18.147186
315 10.1956760 -1.070215e-02 20.40205413 -5.4136324 25.804984
316 7.5101164 -2.938564e+00 17.95879699 -8.4697616 23.489994
317 8.4804950 -2.148323e+00 19.10931294 -7.7748794 24.735869
318 9.5680672 -1.195400e+00 20.33153458 -6.8932355 26.029370
319 7.1325573 -3.731948e+00 17.99706251 -9.4832696 23.748384
320 -1.0561449 -1.199668e+01 9.88438973 -17.7882487 15.675959
321 -5.8086222 -1.729486e+01 5.67761656 -23.3753084 11.758064
322 -8.6271984 -2.045556e+01 3.20116798 -26.7171238 9.462727
323 -10.4943596 -2.267643e+01 1.68771418 -29.1252336 8.136514
324 -8.0377006 -2.048141e+01 4.40600633 -27.0687080 10.993307
325 -1.5799906 -1.421857e+01 11.05859033 -20.9090323 17.749051
326 3.4079987 -9.376441e+00 16.19243857 -16.1441148 22.960112
327 9.5340490 -3.359945e+00 22.42804331 -10.1856136 29.253712
328 7.0977266 -5.878764e+00 20.07421690 -12.7481026 26.943556
329 8.3359029 -4.702824e+00 21.37463014 -11.6051095 28.276915
330 9.0800047 -4.005741e+00 22.16575021 -10.9329160 29.092925
331 6.7095717 -6.411732e+00 19.83087495 -13.3577300 26.776873
332 -0.9325395 -1.408075e+01 12.21567531 -21.0409989 19.175920
333 -5.7592324 -1.914820e+01 7.62973225 -26.2358868 14.717422
334 -8.4591767 -2.200165e+01 5.08329851 -29.1706052 12.252252
335 -10.3231578 -2.402966e+01 3.38333996 -31.2854371 10.639122
336 -7.8377545 -2.166739e+01 5.99188039 -28.9883560 13.312847
337 -1.4058660 -1.532819e+01 12.51645979 -22.6982258 19.886494
338 3.5746915 -1.041754e+01 17.56692719 -17.8245863 24.973969
339 9.4725943 -4.572446e+00 23.51763461 -12.0074413 30.952630
340 7.0786883 -7.006280e+00 21.16365656 -14.4624118 28.619788
341 8.3644811 -5.750703e+00 22.47966514 -13.2228300 29.951792
342 9.0286911 -5.109373e+00 23.16675512 -12.5936119 30.650994
343 6.6653231 -7.490074e+00 20.82072021 -14.9834885 28.314135
344 -0.8675378 -1.503607e+01 13.30099483 -22.5364384 20.801363
345 -5.7148782 -2.005383e+01 8.62407564 -27.6444158 16.214659
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593 24.6613720 8.707083e-02 49.23567315 -12.9217784 62.244522
594 25.3020177 7.186092e-01 49.88542615 -12.2950611 62.899097
595 22.9385548 -1.651761e+00 47.52887024 -14.6690873 60.546197
596 15.4330895 -9.162465e+00 40.02864360 -22.1825644 53.048743
597 10.5787453 -1.410480e+01 35.26229454 -27.1714855 48.328976
598 7.9035645 -1.683574e+01 32.64287075 -29.9319395 45.739068
599 6.0344599 -1.876733e+01 30.83624694 -31.8966002 43.965520
600 8.5223235 -1.632676e+01 33.37140643 -29.4810695 46.525716
601 14.9428000 -9.942104e+00 39.82770374 -23.1153762 53.000976
602 19.9174310 -4.994614e+00 44.82947579 -18.1822536 58.017116
603 25.7510893 8.184739e-01 50.68370465 -12.3800555 63.882234
604 23.3654952 -1.582715e+00 48.31370507 -14.7894993 61.520490
605 24.6613720 -2.986621e-01 49.62140607 -13.5117060 62.834450
606 25.3020177 3.330170e-01 50.27101838 -12.8847736 63.488809
607 22.9385548 -2.037246e+00 47.91435584 -15.2586366 61.135746
608 15.4330895 -9.547869e+00 40.41404835 -22.7719901 53.638169
609 10.5787453 -1.448886e+01 35.64634644 -27.7588422 48.916333
610 7.9035645 -1.721894e+01 33.02607030 -30.5179926 46.325122
611 6.0344599 -1.914958e+01 31.21849580 -32.4811994 44.550119
612 8.5223235 -1.670829e+01 33.75293876 -30.0645728 47.109220
613 14.9428000 -1.032310e+01 40.20869515 -23.6980522 53.583652
614 19.9174310 -5.375196e+00 45.21005837 -18.7643044 58.599167
615 25.7510893 4.382006e-01 51.06397795 -12.9616333 64.463812
616 23.3654952 -1.962754e+00 48.69374424 -15.3707190 62.101709plot(prediccionesbcm)
autoplot(prediccionesbcm)
library(TSstudio)Warning: package 'TSstudio' was built under R version 4.3.3TSstudio::ts_plot(serie1BCM)