To determine what type of model is best suited to meet your needs, follow these steps:
1.Determine your goal (are you attempting to model the relationship of a variable to other variables? are you trying to model the variable over time?
2.IF you have decided on using a time series analysis for an individual variable, plot the values of the variable over time and look for characteristics that would indicate nonstationarity, such as non-constant variance (heteroskedasticity), non-constant mean, seasonality, or structural change (ie a significant shift in the plotted data at a point in time that seems to divide the data into two or more distinct patterns)
3.If there is no seasonal or structural shift, use a tend model (if the data plot on a straight lien with an upward or downward slope, use a linear trend model, if the data plot in a curve, use a log-linear trend model)
4.Run the trend analysis, compute the residuals, and test for serial correlation using the Durbin Watson test. (if you detect no serial correlation, you can use the model!!!; if you detect serial correlation, you must use another model (AR))
5.IF the data has serial correlation, reexamine the data for stationarity before running an AR model. If it is not stationary, treat the data for use in an AR model as follows:
5a.IF the data has a linear trend, first-difference the data
5b.If the data has an exponential trend, first-difference the natural log of the data
5c.If there is a structural shift in the data, run two separate models as discussed above.
5d.IF the data has a seasonal component, incorporate the seasonality in the AR model as discussed above.
6.After first-differencing in 5 above, if the series is covariance stationary, run an AR(1) model and test for serial correlation and seasonality.
6a.IF there is no remaining serial correlation, you can use the model
6b.If you still detect serial correlation, incorporate lagged values of the variable into the AR model until you have removed any serial correlation.
7.Test for ARCH. Regress the square of the residuals on squares of lagged values of the residuals and test whether the resulting coefficient is significantly different from zero.
7a.IF the coefficient is not significantly different from zero, you can use the model!!!
7b.IF the coefficient is significantly different from zero, ARCH is present. correct using generalized least squares.
8. IF you have developed two statistically reliable models and want to determine which is better at forecasting, calculate their out of sample RMSE.