Follow the Rachael/Jacob discussion in http://www.neas-seminars.com/discussions/shwmessage.aspx?ForumID=174&MessageID=4771, this walks you through the different types of tests and when they are useful to perform (i.e. Q-test, DW, etc.)
My steps are:
1. Calculate deviations and first differences and plot.
[NEAS: Graph the time series and check for drifts and seasonality. For drifts, compute moving averages. Use 12 month moving averages for monthly rates. A drift appears as a consistent upward or downward trend. A fluctuating trend may be stochasticity, not trend. For seasonality, the correlogram is a better graph. Sales volumes show large year-end changes; we need a correlogram to see slight seasonality in interest rates.
Compute deviations and see if the mean or variance is changing. If the means, drifts, or variances differ by time period, we may need to separate the time series into eras to construct ARIMA models. If the deviations are below zero on one side of the graph and above zero on the other side, the mean is changing. If the average size of the deviations changes, the variance is changing.
Several types of models are common; they have distinct graphs and correlograms. White noise shows no pattern. For white noise, examine the graph of the deviations. The devations should appear as random fluctuations about zero. The average deviation size may vary over time, suggesting a change in the variance or conditional heteroscedasticity. White noise may have a positive mean, but no trends or cycles.
A random walk takes several forms. A random walk with no drift means that an upward movement in one month is equally likely to be followed by another upward movement as by a downward movement. A trend (drift) does not negate a random walk, but we may have to detrend the rates or take first differences.]
2. Calculate the autocorrelation function and plot vis-a-vis correllogram (SP?). If the autocorrelation function tends to zero your series may be stationary. There are few ways to test (ie using tests above). I then took first differences and calculated the autocorrelation function. This showed positive signs of being stationary - this was confirmed by calculating and plotting the autocorrelation function for the second difference (the autocorrelation function tended to zero quickly and remained there with some stability).
[NEAS: The sample autocorrelation function and correlogram are powerful tools. Weak seasonality may be obscured in a scatterplot of the interest rates but may show up in the correlogram. Autoregressive, moving average, and ARMA models have distinct sample autocorrelation functions. Check for geometric decay (autoregressive), spikes (moving average), or both.]
3. Since I am comparing two models (seasonality adjustment vs no seasonality) I calculated a 6-month diffence and a difference of the 6-month differences and plotted their autocorrelation functions.
[NEAS: Start with a 12 month difference, even if you see a six month autocorrelation.]
4. I calculated the DW and Q stats.
[NEAS: On the write-up, be sure to state the hypothesis and what the test shows.]
5. That's were I've got to for now.
My idea for completion is to plot my two fitted models against actual data and see which one replicates (ie fits) the best and perhaps do some forecsasts using the data.
Does the above sound reasonable to everyone? Input/criticism would be appreciated.
JR