Implement "auto-correlate" experiment

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Statistical experiments with financial data

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Implement "auto-correlate" experiment #85

Closed sergey-a-berezin closed 1 year ago

sergey-a-berezin commented 1 year ago

This experiment is a general study of auto-correlation of log-profit series. Effectively, it computes one thing:

normalizes all the input series, so they can be meaningfully joined together;
computes auto-correlation for the entire joint sequence for a range of time shifts in [1..n]. There is obviously no need to compute it for 0 (correlation will be 1), and also no need to distinguish positive and negative shift, since they are symmetric.
plots a graph of correlations vs. shift.

sergey-a-berezin commented 1 year ago

Since sequences X[i] will be normalized to mean = 0 and sigma = 1, auto-correlation simply accumulates sum(X[i] * X[i+shift]), and the final correlation is that divided by the total number of samples.

sergey-a-berezin commented 1 year ago

Add a writeup for the experiment. Apparently, there is some hint on a slight negative correlation at "shift=1", but it's within the noise. This is something to test later and estimating if it can be exploited.

However, checking for auto-correlation within individual stocks and split by time intervals (4 intervals by 6 years), the pattern seems to be random. It's quite possible that with very large numbers correlation becomes negative (the price tends to move back), but it requires very large numbers to average out.