Model choice and residual analysis

ARIMA Models in R

David Stoffer

Professor of Statistics at the University of Pittsburgh

AIC and BIC

ch2_3.006.png

  • AIC and BIC measure the error and penalize (differently) for adding parameters

  • For example, AIC has $\ k=2$ and BIC has $\ k = log(n)$

  • Goal: find the model with the smallest AIC or BIC

ARIMA Models in R

Model Choice: AR(1) vs. MA(2)

gnpgr <- diff(log(gnp))
sarima(gnpgr, p = 1, d = 0, q = 0)

$AIC                          $BIC
-8.294403                     -9.263748

sarima(gnpgr, p = 0, d = 0, q = 2)

$AIC                          $BIC                                       
-8.297695                     -9.251712

ch2_3.010.png

ARIMA Models in R

Residual Analysis

sarima() includes residual analysis graphic showing:

  1. Standardized residuals
  2. Sample ACF of residuals
  3. Normal Q-Q plot
  4. Q-statistic p-values

ch2_3.016.png

ARIMA Models in R

Bad Residuals

ch2_3.018.png

ARIMA Models in R

Bad Residuals

ch2_3.019.png

ARIMA Models in R

Bad Residuals

ch2_3.020.png

ARIMA Models in R

Bad Residuals

ch2_3.021.png

ARIMA Models in R

Bad Residuals

ch2_3.022.png

ARIMA Models in R

Bad Residuals

ch2_3.023.png

ARIMA Models in R

Bad Residuals

ch2_3.024.png

ARIMA Models in R

Let's practice!

ARIMA Models in R

Preparing Video For Download...