7.2 Model Building Process

The Box-Jenkins model-building strategy. It has th following steps

1. Model Identification

   1. Assessment for stationarity - can be done with ACF correlogram.
      1. If found, then use difference, hence ARIMA
   2. Identify what form of model to be used, e.g., MA, ARMA, ARIMA, or AR. This is done by assessing the time-series’ ACF (see examples on page 357 - 359)

2. Model Specification: This is estimating model parameters

3. Model Checking

   1. Make model diagnostics:
      1. Residuals no autocorelation left in them (hence no serial correlation). Can be checked with Ljung-Box Q stats, visual inspection, or apply DW test to the fitted model. i: No spike in the ACF, must be within \(±2/\sqrt{n}\) confidence interval from 0. Just apply the acf()
      2. Residuals to be independent: adf.test(resid(fit)) where H0: Non stationarity
      3. Residuals to be normally distributed: tseries::jarque.bera.test(resid(fit)), where H0: Normal distribution
      4. No heteroskedasticity - plot(resid(fit)) and apply the Bresuch-Pagan test
   2. If several model. Choose the one with the lowest AIC or BIC, depending on the goal.
      1. if that concludes indecisive result, then choose the simplest model (principle of parsimony)

4. Forecasting with the Model