Simple Linear and Exponential Growth Models – If an analyst looks at a time series plot graph he/she may see patterns exhibiting possible linear or exponential growth relationship to the dependent variable. Serial correlation of the error terms must not be present and the Durbin Watson test can test for this.
Auto-Regressive Models – If serial correlation exists in a simple time series model, the analyst can create an auto-regressive time series with the sample data, where the independent variable is a lagged (prior period) value. The AR model is appropriate where the prior period value is the best predictor for the future period dependent variable value. The D-W test will not work on an AR model, so the analyst needs to examine the error term correlations to check for the presence of serial correlation. A Dickey Fuller test can test for the presence of a unit root in the AR model.
Seasonality –The plot of a time series model may show seasonality; the model may be improved by adding a seasonal lag variable, through the technique of first differencing.
Moving Average and AR Moving Average Models – This model modification may improve on a base AR model.
Auto Regressive Conditional Heteroskedasticity – ARCH must be tested for to ensure that the AR, MA, or ARMA model’s t-scores are not overstated.
Out of Sample Data Testing – If an analyst has several time series models examining a dependent variable, then the forecasted values for each can be compared with actual out of sample data values. The model with the lowest root mean square error (RMSE) is considered to have the best predictive capabilities.
