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So I am attempting to calculate the Parabolic SAR over FX market data. I understand that the SAR equation is:

SARt = SARt-1 + * [EPt-1 - SARt-1]

with EPt-1 changing depending on if it is a rising or falling SAR but my question is how is the initial/prior SAR (SARt-1) calculated at first with new data or at a transition point (changing from a rising to failing SAR).

Any advice or books with the full mathematical definition would be much appreciated. Many thanks.

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So after looking through and doing some reverse engineering of some implementations I think I have found the answer.

public static ParabolicSAR GenerateFirstSAR (ParabolicSAR sar,double[] high, double[] low) {
    if (high[0] < high[1]) {
        ...
        sar.sars.add(Math.min(low[0], low[1]));
        ...
    } else {
        ...
        sar.sars.add(Math.max(high[0], high[1]));
        ...
    }
    return sar;
}

In this high is an array of all the high points but you really only need 2 and then low is the low points. Same rule applies.

So this broken down means that for a rising condition the primary SAR is the minium value from the first 2 low points.

Math.min(low[0], low[1])

And visa versa for a failing condition.

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