ARIMA diagnostics

ARIMA Models in R

David Stoffer

Professor of Statistics at the University of Pittsburgh

Weekly Oil Prices ARIMA(1, 1, 1)?

ch3_2.003.png

Weekly Oil Prices ARIMA(1, 1, 1)?

ch3_2.004.png

Weekly Oil Prices ARIMA(1, 1, 1)?

oil <- window(oil, end = 2006)
x <- sarima(oil, p = 1, d = 1, q = 1) 
x$ttable

         Estimate     SE t.value p.value
ar1       -0.4987 0.0995 -5.0131  0.0000
ma1        0.7316 0.0734  9.9732  0.0000
constant   0.1091 0.0936  1.1664  0.2443

Weekly Oil Prices ARIMA(1, 1, 1)!

ch3_2.008.png

Overfit: ARIMA(2, 1, 1) and ARIMA(1, 1, 2)

oil_fit1 <- sarima(oil, p = 2, d = 1, q = 1) 
oil_fit1$ttable

         Estimate     SE t.value p.value
ar1       -0.4704 0.1117 -4.2121  0.0000
ar2       -0.0738 0.0652 -1.1319  0.2586
ma1        0.6771 0.0986  6.8696  0.0000
constant   0.1088 0.0878  1.2391  0.2163

oil_fit2 <- sarima(oil, p = 1, d = 1, q = 2) 
oil_fit2$ttable

         Estimate     SE t.value p.value
ar1       -0.3664 0.1816 -2.0178  0.0445
ma1        0.5777 0.1818  3.1777  0.0016
ma2       -0.0836 0.0837 -0.9989  0.3186
constant   0.1088 0.0884  1.2306  0.2194

Let's practice!

ARIMA Models in R