STATISTICS: Time Series Models?

Question

I'm trying to build a basic, "nested" time series model. Using all of my data doesn't have practical use.

I want to focus ONLY on a non-linear, simple Moving Average (MA) Model. If you were asked to determine, statistically, the best MA (10 day, 100 day, 1000 day etc.) to choose for purposes of analyzing your continuous data on a daily basis, what statistical test(s) would you run each day to determine which MA to use for the next day--SPECIFICALLY, for constructing "Prediction Interval Bands" (95%, 99% etc.) for outliers around the MA.

Here are some of the things I've attempted. I calculate the Skew for each time period to find a skew closest to 0. I also calculate the "Kurtosis" to find the time period with a kurtosis closest to 0. Also, I calculate the Confidence Interval (CI) around each MA and find the MA with the narrowest 99.99% CI, in percentage terms. The narrowest CI, however, isn't always the MA with the best skew & kurtosis. Thoughts?

Answer 1

Try using odd-numbered MA's and offsetting them by (n-1)/2. This is the amount the moving average lags the original data, and it should minimize your skew and kurtosis. You can do it with even-numbered MA's as well, but your plots end up halfway between data points and you have to interpolate to run all your calculations.