Abstract
the value of a that gave the smallest average value of the Brier score within the sample of 21 observations. The result was a = .01, which implies little or no serial dependence in the data. To further check the lack of serial dependence I performed a runs test on all 52 observations (probably a good thing to do first). The (approximate) standard normal test statistic was .2, confirming that the data were approximately serially independent. I then calculated successive one-step-ahead forecasts for the remaining 31 observations. The average Brier score for this method in the post-sample period was .75. Next I calculated forecasts based on the Harvey-Fernandes Poisson model (using a computer program provided by Harvey and Fernandes). The average Brier score for the Harvey-Fernandes model for the same 31 observations was also .75. (The Harvey-Fernandes forecasts were not post-sample forecasts-the computer program did not conveniently allow that option-thus, the Brier score of .75 for the Harvey-Fernandes forecasts is probably understated.) I did not construct a reliability diagram because there was little variation in the forecast distribution over time for either method.
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