Weighted KDE Mode

🙏🏻 The ‘ultimate’ typical value estimator, for the highest computational cost @ time complexity O(n^2). I am not afraid to say: this is the last resort BFG9000 you can ‘ever’ get to make dem market demons kneel before y’all

Quickguide
pls read it, you won’t find it anywhere else in open access

When to use:
If current market activity is so crazy || things on your charts are really so bad (contaminated data && (data has very heavy tails || very pronounced peak)), the only option left is to use the peak (mode) of Kernel Density Estimate, instead of median not even mentioning mean. So when WMA won’t help, when WPNR won’t help, you need this thing.

Setting it up:

• Interval: choose what u need, you can use usual moving windows, but I also added yearly and session anchors alike in old VWAP (always prefer 24h instead of Session if your plan allows). Other options like cumulative window are also there.
  
  
• Parameters: this script ain't no joke, it needs time to make calculations, so I added a setting to calculate only for the last N bars (when “starting at bar N” is put on 0). If it’s not zero it acts as a starting point after which the calculations happen (useful for backtesting). Other parameters keep em as they are, keep student5 kernel, turn off appropriate weights if u apply it to other than chart data, on other studies etc.
  

But instead of listening to me just experiment with parameters and see what they change, would take 5 mins max

Been always saying that VWAP is ish, not time-aware etc, volume info is incorporated in a lil bit wrong way… So I decided not just to fix VWAP (you can do it yourself in 5 mins), but instead to drop there the Ultimate xD typical value estimator that is ever possible to do. Time aware, volume / inferred volume aware, resistant to all kinds of BS. This is your shieldwall.


How it works:
You can easily do a weighted kernel density estimation, in our case including temporal and intensity information while accumulating densities. Here are some details worth mentioning about the thing:

Kernels are raw (not unit variance), that’s easier to work with later.

h_constants for each kernel were calculated ^^ given that ^^ with python mpmath module with high decimal precision.

In bandwidth calculation instead of using empirical standard deviation as a scaler, I use...

ta.range(src, len) / math.sqrt(12)

...that takes data range and converts it to standard deviation, assuming data is uniformly distributed. That’s exactly what we need: a scaler that is coherent with the KDE, that has nothing to do with stdevs, as the kernels except for gaussian ones (that we don’t even need to use). More importantly, if u take multiple windows and see over time which distro they approach on the long term, that would be the uniform one (not the normal one as many think). Sometimes windows are multimodal, sometimes Laplace like etc, so in general all together they are uniform ish.

The one and only kernel you really need is Student t with v = 5, for the use case I highlighted in the first part of the post for TV users. It’s as far as u can get until ish becomes crazy like undefined variance etc. It has the highest kurtosis = 9 of all distros, perfect for the real use case I mentioned. Otherwise, you don’t even need KDE 4 real, but still I included other senseful kernels for comparison or in case I am trippin there.

Btw, don’t believe in all that hype about Epanechnikov kernel which in essence is made from beta distribution with alpha = beta = 2, idk why folk call it with that weird name, it’s beta2 kernel. Yes on papers it really minimises AMISE (that’s how I calculated h constants for all dem kernels in the script), but for really crazy data (proper use case for us), it ain't provides even ‘closely’ compared with student5 kernel. Not much else to add.


Shout out to RicardoSantos for inspiration, I saw your KDE script a long time ago brotha, finna got my hands on it.


∞