Finite Impulse Response Digital Filter (Power Weighted Moving Average).

Here is comparison Power Weighted Moving Average (power = 1) and LWMA.

Hi Vladimir

Sorry didnt catch the post of trend0 earlier, wanna ask if any hypothesis or intuition on what does the indicator do? And why it is better than the original moving average? As you know, pure synthesize without hypothesis is dangerous mindset on overfitting. Cheers on the development though🚀.

Cheers
Louis

This backtest shows how digital filters behave differently with the same period, but with different power in different market modes.

Thanks for sharing, Vladimir  I'm curious, though: what exactly is a Finite Impulse Response Digital Filter? If indeed it is just a power weighted moving average, why don't we just call it that? IE: Under what circumstances would one refer to it as otherwise?  Are all ‘moving averages’ also ‘filters’ in some way? 

I feel there is more to learn here, but it's not clear, why there would be a need for what seems to be additional complexity / cognitive overhead. I've seen some articles on digital signal processing for quants, but brushed them aside.  Is there indeed some merit in that school of thought?

.ekz.,

-> Are all ‘moving averages’ also ‘filters’ in some way? 

Yes

In my previous post FIR_0 is SMA, FIR_10 is LWMA.

-> what exactly is a Finite Impulse Response Digital Filter?

You may find the full classification of digital filters in  Chapter 14 - Chapter 21 of

"The Scientist and Engineer's Guide to Digital Signal Processing".

Ahhh.. very interesting, Vladimir , and very helpful. I'll add this to my ever-expanding reading list. 

As usual, thanks for all the knowledge  :)

I made some corrections to the code,

    def calc_filter(self):
        prices = np.array([])
        for i in range(len(self.prices)):
            price = self.prices[i] 
            prices = np.append(prices, price)
        return self.power_weighted_moving_average(prices)

Now Power Weighted Moving Average (power = 0),  perfectly match History.mean().

Interesting, but what use cases would this have over just using SMA/EMA?

GEightyFour,

If you choose the power factor in the range from -1 to 2, 

then there are only two values that perfectly match the classic indicators.

Power Weighted Moving Average is equal to SMA if power = 0.

Power Weighted Moving Average is equal LWMA if power = 1.

Others can add a specific flavor to your algorithm because they behave differently.

Hi Vladimir,

We can simplify the calculation by replacing

self.Value = self.calc_filter()

with

self.Value = sum(self.prices * self.weights) / sum(self.weights)

See the attached backtest for reference.

Best,
Derek Melchin

Derek Melchin,

Thank you for concise code.