Okay in the past few posts I jumped the gun a little bit. Errors I made include rushing everything, not explaining anything and not giving my blog readers the love and respect they deserve. What am I talking about? Well before we do anything with a series we have to fit it to some sort of trend (which I did very haphazardly) and preferably the best trend we can find. What kind of criteria determined the best trend? R^2, MSE, F-test, P-values and on and on. Only then, can we go into describing cyclicality and only then can we look at whether our series passes the covariance stationary criteria. In addition to that we have to test for white noise using either the Box-Pierce or the Ljung-Box test.
So there is work to be done, but this will not discourage us! On the contrary this will motivate us to push ahead and conquer new ground.
The forecasting posts will attempt to follow the outline below.
1. Define and talk about trend. Fit the GDP series to several different trends select the best one according to various criteria. Explain the criteria by which we judge the models.
2. Produce and plot point and interval forecasts of our chosen trend model.
3. Discuss seasonality and how to easily deal with it.
4. Characterize the cycle. Discuss white noise, ACF, PACF & more. Model the cycle and select the best one based on some intuition and criteria.
5. Forecast and plot.
6. Discuss & clearly identify the implications and results.