Hi Joe,
It is possible to build highly effective and accurete WNH Differences filter based on the calculation of Skewness, Kurtosis and the Jarque-Bera value for the differences in the WNH columns.
I am grateful to Midas for his suggestions regarding this possibility.
To see what is the Jarque-Bera test you can go to: http://en.wikipedia.org/wiki/Jarque-Bera_test
The J-B value is the most important of these three parameters, but it depends on Skewness and Kurtosis. To calculate the J-B value we need to know skewness and kurtosis, so these values must be calculated first.
The formula for calculating the J-B value is: (n/6)*(Skewness^2 + ((Kurtosis - 3)^2)/4)
n = the size of the sample.
A sample of data (WNH Differences in a column) needs to be selected for the calculation. By calculating the J-B value for a large sample of data. large fluctuations of the WNH differences would be transformed into usually small, sometimes almost negligible, fluctuations of the Jarque-Bera value. If the sample is large enough, the J-B value tends to have long, smooth trends, which usually change slowly, gradually, not abruptly (exceptions are possible).
I attached a Winzip file with Excel statistics for the Australian Saturday Lotto.
I copied the differences data from the WNH Summary Table to Excel, and then I removed from the copy the data for the period from 03/08/84 to 02/08/86. This was the initial period when the natural course of trends and natural patterns were just developing and the data looked distorted. I did it to avoid errors in the estimation of trends in the small samples of data. For the large samples of data, e.g. the last 800 draws, removing the distorted beginning of the data would be probably unnecessary.
The Excel statistics demonstrate Skewness, Kurtosis and the J-B value in the WNH Differences columns, for the samples of the last 10, 50, 100, 200, 400 draws (for column 0 only) and for the last 800 draws for all columns.
The statistics for the last 800 draws start in the row 803 and are visible in the columns from AB to BH. The first calculation is in AB803 to BH 803 and is related to the data in the columns B to L in the rows from 3 to 802. The next calculation is in the row 804 (the columns AB : BH) and is related to the data in the columns B to L rows 4 to 803. And so on. This way a kind of rolling statistics is created.
When you look at the selected columns of the J-B values in my statistics, the statistics tell you almost exactly the J-B value for the next draw. Unfortunately, there is no 100% certainty that the trend would continue. So it allows for one draw ahead prediction, but this prediction is conditional, and the condition is that the trend must continue. Of course, we can adjust the filter setting to be prepared for small or even large trend changes. And, if there is no established trend, or if there are chaotic changes of the J-B value, you can decide not to use this filter for this column.
The proposed filter would work with each WNH Differences column separately, because there are large differences of trends between columns, so a button to allow the column selection would be necessary.
There should be a spin button for the sample size selection (e.g. from the last 10 draws to all available draws in the history).
There should be 3 radio buttons for the selection of the Skewness or Kurtosis or J-B Value. The buttons should allow for the selection of one of these parameters only. I believe that the J-B Value alone can be used as the basis of this filter. If you want a simple filter you can build it with J-B Value only and the calculation of Skewness and Kurtosis would occur behind the scene.
And there should be a spin button or (3 spin buttons) to allow setting the desired range of Skewness or Kurtosis or J-B Value.
And the typical buttons such as Remove, Leave, Preview and Back-test should be included.
How to use this filter?
Observation of the current trend of the J-B Value or the trend in the Skewness or Kurtosis column (if such is the user's preference) would be necessary for the successful filtering. Simple statistics in Excel would do, but more appropriate would be the creation of new Table with Skewness, Kurtosis and J-B Value in the WNH History (or maybe one of the existing tables could be expanded).
Could you build this filter, Joe ?
Best Regards
Jerzy