(2) Settings under "Tools -> Options -> Data -> Quote currencies (FX) in" are "HalfPip", as required by my FOREX broker.
If I round the values for the PSAR to the full tick and change that setting under Options -> Data to (the full) "Pip", then I get exactly your values (CSAR data).
For intraday data, I prefer not to round the PSAR, as this may lead to a significant distortion of the original idea on smaller timeframe charts. What I can do, is to add an option to round the value to the full tick. This option could be switched on and off. However, it would be ridiculous to introduce a multiplier for the TickSize to compensate for the half pip settings of some brokers.
The difference between the dataseries can be explained and is only caused by rounding issues.
I noticed the 2006 discrepancy by accident, but I'll bet my left one that there many more. Discrepancies of only 2 pips are very difficult to spot visually. Hence my suggestion that we use Excel to find them, which will take me about 5 minutes if you can get me your plot values in a text file. For all we know, there could be discrepancies of a lot more than 2 pips.
I tend to agree that there is little point to adding a rounding parameter, however I would only take this position if I fully understood the impact this would have on actual trading results, ie. does it degrade the effectiveness of the indicator? Unlikely but possible.
I rounded the numbers only to ensure that my PSAR followed all Wilder's rules, not because I believe rounding is better. My next step is to conduct testing to see whether the PSAR can be improved. Wilder did not have the benefit of the computing power that we have, so there could be room for significant improvement.
If I look at Wilder's book, he has computed everything manually. Obviously, he did it in a way that was easy for him. Rounding the results was quite natural to avoid some work. Rounding did not affect the result a lot, as it was applied to daily data only.
Also I believe that he used the exponential moving average for the average ture range, because it is easier to calculate via a recursive formula than a simple moving average. I believe he did not care about the moving average type. Using a Butterworth filter or a Hull moving average was out of question.
If course the idea can be modulated. The basic idea behind the PSAR is to
-> increase the acceleration when price moves into the direction of the trade (new extreme point)
-> maintain the acceleration when price consolidates
This idea can be enhanced. For example I do not see any reason to maintain a high acceleration factor during a longer consolidation. I would rather decrease the acceleration factor to avoid that the stopline hits the consolidation. Decreasing the acceleration factor should be done carefully and at a much slower pace than increasing it. In the end this should only have an impact on longer consolidations.
It is also possible to bring volatility into the equation, that is adjust acceleration and deceleration factor according to the "gain = difference between two consecutive extreme points" or the average bar size.
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