Parametric and Non-parametric Hypothesis Tests. Theory (& some code)
A few days back, we shared some notes on statistical theory and concepts that drive statistical modelling and estimation.
Today, we want to use the statistical distributions discussed and construct hypothesis tests to draw meaningful conclusions about unknown parameter distributions we hope to estimate. We also discuss hypothesis tests with non-parametric assumptions, which will be of critical importance when analyzing data with high levels of noise, such as in astrophysics and finance.
We want to draw particular focus to the non-parametric tests, as well as the Monte Carlo and bootstrapping methods we talked about in the previous post. Finally, we have covered enough ground to discuss some applied statistical methods and directly apply them to the analysis of quant trading systems. This is the reward of having developed enough theory, and now we can more rigorously discuss practically useful algorithms. I encourage all readers to give the mentioned sections one more read, so that the next post on analysis of trading systems make sense to you immediately.
Preview of the Topics Discussed:
Notes PDF:
I am not happy about my delivery in the analysis of variance methods, which is why I wrote (to be reviewed). I am not immediately using this topic for any future discussions, so I have not rewritten it, but I do intend to improve it in future sections because I am not satisfied with it.
My intention is for the next post on trading systems to be semi-paywalled, such that the simpler algorithms are made available to all, and the more complex and powerful solutions are for paid subscribers. Additionally, I am looking to incorporate the trading strategy hypothesis testing suites to the existing back-testing framework that we have, which is the Russian Doll Testing framework discussed in post here. This is our optimized vector backtesting engine for single strategy and multi-strategy portfolios meant for our paid readers:
This will give our readers access to powerful backtesting Python engines that are not only computationally efficient but also contain the firepower in terms of statistical analysis to validate their own quantitative ideas.
The current plan is as follows:
the next post will be a release of the roadmap and links to all of our resources
we will then release the notes in probabilistic analysis of trading systems, semi-paywalled
we will then release the combined notes for paid readers on the topics discussed so far, starting from least squares methods all the way to probabilistic analysis of trading systems. Currently, these notes should be around 150 pages long.
in January of next year, we aim to release the hypothesis testing suite involving the Python code discussed in the notes on probabilistic analysis of trading systems. (for paid readers)
Following that, we will continue with the usual stuff on alpha ideas, development of theory and application of theory. We will continue to tango between developing core, fundamental theory and touching on more advanced, state of the art methods. This is because the advanced methods are almost always a variant of the fundamental ideas, and one cannot be discussed with the other.
Preview of next post content:
Happy trading!
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