What, if anything, did anyone do to 'test' their data before trying to fit a model? The postings mention checking it for a few things (none of which I understood, so I can't recall offhand) before beginning to attempt to fit a model. So, I'm talking like, before even taking first differences or anything involving the autocorrelation function...
Where do we start? The textbook and postings discuss many items; is there a specific order?
Rachel: The order depends on the goals of your project and the results of previous steps. We suggest some common steps, though you vary them for your project.
Jacob: How would one start?
Rachel: Start by graphing the data. The type of graph depends on the question. To examine if monthly interest rates have a long-term drift, use a 12 month moving average. This eliminates seasonality, smooths random fluctuations, and highlights long-term trends. To examine if the stochasticity changes over time, we don’t use a moving average.
Jacob: The graph is just visual; shouldn’t we use statistical tests?
Rachel: We start with graphs. To test for random walks, we graph the interest rates and their first differences. We graph the sample autocorrelations (form a correlogram) which shows the pattern. For seasonality, we graph the interest rates and the correlogram.
Jacob: After forming the graphs and charts, do we construct an ARIMA model?
Rachel: We first see if we should separate the time series into intervals. We focus on means, drifts, and variances in each period.
Jacob: How do we know how to choose the periods?
Rachel: Choose them initially by examining the graphs, and then calculate the mean, drift, and variance of each period.
Jacob: Do we examine if the differences in the means, drifts, and variances are statistically significant?
Rachel: One might do this. The tests for statistically significant differences are not on the time series syllabus, and they are not required for the student project.
Jacob: If the means and drifts differ, must we use separate ARIMA models?
Rachel: Not necessarily. The means and drifts may differ for the original series, but not for the first or second differences. In some cases the drift may differ by time period, but the ARIMA model may help explain (and predict) the changing drift.
Jacob: What else should we examine in each project?
Rachel: We check for seasonality. We examine the correlogram, and if we observe spikes at 12 month periods, we use a seasonal ARIMA parameter and compare the models with and without the seasonal parameter. If we don’t observe spikes, we don’t need the statistical tests.
Jacob: Do we always use the Durbin-Watson statistic, Bartlett’s test, and the Box-Pierce Q statistic?
Rachel: If the student project selects one ARIMA model from a choice of two or more models, we examine these tests. In almost all student projects, at least one or two of these tests are used.