Standard Deviations with different Average

[cbadr]

Hello,


I have developed custom Standard Deviation based on different average like the:

1. Geometrical average

2. Harmonic average

3. Quadratic average


As shown in the attached pic, i would like to understand why, for the same Period:

1. The Regular Stdev is almost equal to the Harmonic StdDev
2. The Geom Stdev is almost equal to the Quadratic StdDev


It's more like a maths problem but i would be interested to have a feedback...


Thanks

[koganam]

Hello,


I have developed custom Standard Deviation based on different average like the:

1. Geometrical average

2. Harmonic average

3. Quadratic average


As shown in the attached pic, i would like to understand why, for the same Period:

1. The Regular Stdev is almost equal to the Harmonic StdDev
2. The Geom Stdev is almost equal to the Quadratic StdDev


It's more like a maths problem but i would be interested to have a feedback...


Thanks

That would be impossible to tell with certainty without seeing the code. Offhand, it would most likely be because your code refactors to identical code between the matching methods.

[cbadr]

Thanks for the answer.
Here the code i used for the Geometrical Average:
But after investigations on google, i realized i couldn't used the same Std calculation once the Mean is calculated.
I'll have to update the formula accordingly.
Any thoughts on this?

protected override void OnBarUpdate()
        {
            if (CurrentBar < 1)
            {
                Value.Set(0);
                sumSeries.Set(Input[0]);
            }
            else
            {
                sumSeries.Set(Input[0] * sumSeries[1] * (CurrentBar >= Period ? 1/Input[Period]: 1));
                double avg = Math.Pow(sumSeries[0],1/Math.Min(CurrentBar + 1, Period));
                double sum = 0;
                for (int barsBack = Math.Min(CurrentBar, Period - 1); barsBack >= 0; barsBack--)
                    sum += (Input[barsBack] - avg) * (Input[barsBack] - avg);

                Value.Set(Math.Sqrt(sum / Math.Min(CurrentBar + 1, Period)));
            }
        }

[koganam]

Thanks for the answer.
Here the code i used for the Geometrical Average:
But after investigations on google, i realized i couldn't used the same Std calculation once the Mean is calculated.
I'll have to update the formula accordingly.
Any thoughts on this?

protected override void OnBarUpdate()
        {
            if (CurrentBar < 1)
            {
                Value.Set(0);
                sumSeries.Set(Input[0]);
            }
            else
            {
                sumSeries.Set(Input[0] * sumSeries[1] * (CurrentBar >= Period ? 1/Input[Period]: 1));
                double avg = Math.Pow(sumSeries[0],1/Math.Min(CurrentBar + 1, Period));
                double sum = 0;
                for (int barsBack = Math.Min(CurrentBar, Period - 1); barsBack >= 0; barsBack--)
                    sum += (Input[barsBack] - avg) * (Input[barsBack] - avg);

                Value.Set(Math.Sqrt(sum / Math.Min(CurrentBar + 1, Period)));
            }
        }

Whereas you are using a rather inefficient algorithm, I nonetheless do not quite understand what you are asking. You appear to be calculating a mean, then looping backwards and summing the squares of the deviations from the mean. That is the basic definition of how to determine the variance and hence StdDev. So what is the issue?

[cbadr]

The issue is about understanding the result of the StdDev from a Geometric VS Harmonic VS Squared Mean.


From wikipedia i found that the formula to get the Geometric Std is mention there:

https://en.wikipedia.org/wiki/Geometric_standard_deviation

Thats a first thing i have to update on the script.


Then really i am wondering if the Std formala is the same for the other Mean?

[koganam]

The issue is about understanding the result of the StdDev from a Geometric VS Harmonic VS Squared Mean.


From wikipedia i found that the formula to get the Geometric Std is mention there:

https://en.wikipedia.org/wiki/Geometric_standard_deviation

Thats a first thing i have to update on the script.


Then really i am wondering if the Std formala is the same for the other Mean?

For an unbiased estimator, the standard deviation is always the Root Mean Square Deviation, the square root of the variance, regardless of what mean you are using, albeit the mean used is almost always the arithmetic mean, rather than any other.

Why do you think that a geometric mean may be more appropriate for what you are trying to do, if I may ask.