Given a time series with Events (chart patterns), I want to assess whether events (chart patterns) occur systematic or randomly in a time series.
My idea is to
The key question is how to compare the results. The events (chart patterns) have a specific length and can be overlapping (as illustrated in the image).
I could easily just use the number of events in the original time series and compare them to the count/number of events in the simulated time series by simulating enough time series to construct a confidence interval.
But this would not account for clustering, overlapping and the size of events. Hence, it is not enough to just compare the count/number of events (patterns) but also if there is clustering (margin between events) or differences in the size of the patterns.
I could do the same test for different statistics. But I am wondering if there is a more elegant way.
The image is an example with orange lines being events of different size/length in time. They are overlapping but do not seem to be clustered. If they would be clustered they might only appear in the beginning and end of the time series.
My question is:
How to test if events (with different size, overlapping, and maybe clustered) occur systematic in a time series or randomly?
Are there any similar problems in other disciplines?
Well the first test that comes to mind is the old nonparametric runs test:
https://www.bing.com/search?q=runs+test&qs=n&form=QBRE&sp=-1&pq=runs+test&sc=8-9&sk=&cvid=B3F2FD5E0629437797C907853DCFB83B
From there you could look at tests of randomness:
https://www.bing.com/search?q=randomness+tests&qs=n&form=QBRE&sp=-1&pq=randomness+tests&sc=8-16&sk=&cvid=3995E436CE45464B9CE6B3455E93FCAB
Be sure to look at tests for random number generators like
: 1.3.5.13. Runs Test for Detecting Non-randomness
https://www.itl.nist.gov/div898/handbook/eda/section3/eda35d.htm
and:
A statistical test suite for random and pseudorandom ...
https://nvlpubs.nist.gov/nistpubs/Legacy/SP/nistspecialpublication800-22r1a.pdf
Jim Gentle has done much work in this area See:
https://www.bing.com/search?q=randomness+tests+James+Gentle&qs=n&form=QBRE&sp=-1&pq=randomness+tests+james+gentle&sc=0-29&sk=&cvid=2C6E42309E484AD8B731F231E55E414D
and finally some software:
https://www.bing.com/search?q=randomness+tests+software&qs=n&form=QBRE&sp=-1&pq=randomness+tests+software&sc=1-25&sk=&cvid=ED08930DE21147F9A56F6FCF5F15E57D
Hopefully something useful to you lives somewhere in this mess.
Best wishes, David Booth
At a first sight and without being an expert here, your approach seems sensible to me. The clustering problem might be solved by defining "meta patterns" (e.g. a particular "meta pattern" is present iff patterns A, B, C... all occur, possibly in that timely order and/or not more than a given time span apart). You cen then analyze the occurrence of these "meta patterns" just as you do for the (simple) patterns.
I suggest using ACF and PACF plots or Runs test which its null hypothesis is independence.
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