Maximum Likelihood Estimation - the Ornstein-Uhlenbeck Process(part 2)

In part one, we looked at the method of maximum likelihood estimation in the context of the normal distribution. Keeping with the theme of this channel, we also showed how to calculate these parameters numerically if one cannot derive an analytical solution. In the video, we look at using maximum likelihood estimation for extracting the parameters where our random variable follows an Ornstein-Uhlenbeck process. We will look at some simulated data and extract the parameters numerically. Since these videos will eventually lead to parameter analysis for mean-reverting pairs trades, we will also compare our answers with the results given analytically in the book, Optimal Mean Reverting Trading mentioned in the description of part one.
Github: github.com/kpm...
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[@kalebnunn2100]

you are the best!!!! I learn more from ur videos than just about any other on the internet.

[@FrancescoDelaidelli]

Hello Kevin, would it be possible to have the notebook with the code? I am having issue with some part of the code . Thanks!

[@jaredvv86]

Just found your videos. They are great thanks for posting. Please keep them coming.

[@worldcooking]

Nice work. Cat`t wait for the next pair trading video. Thanks a lot.

[@prashlovessamosa]

Thanks

[@RachelDance]

Dude, I could hug you right now, that part where you sort out the zero values coming from the distribution just made my WEEK! Im curious though, does there exist anywhere the (probably quite tedious, but nevertheless) derivation of those optimal parameters? Found them in a paper as well but im sure its 'left as an exercise for the reader'...! I got mine by least squares method and solving the OU analytically, and they seem to be numerically the same to maybe, 4.d.p which is great, but I cant map the two together. I cant derive these ones from scratch, and i'm interested to know how its done :) thanks from the UK!

[@kpmooney]

I've never seen the derivation written out. As you say, it looks quite tedious, and personally, I'm to making mistakes when working through pages of algebra and caucus by hand.

[@MrJanjai]

I'm currently trying to apply this to a detrended time series. Problem is: I'm getting a negativ theta s.t. I cant log Xxy - theta * Xx - theta * Xy + N * theta**2. Any ideas what I'm doing wrong? Great video, thx!

[@hichamm.a.c.i9058]

thank you for this video, please what's the name of the book ?

[@kpmooney]

Optimal Mean Reversion Trading by Tim Leung and Xin Li.

[@lll8188]

It was very helpful! But in analytic caculate, one parenthesis is missing from the denominator of theta*, and the - sign of the mu* is missing. I'm telling you just in case. Thank you very much!

[@kpmooney]

Thank you. I fixed it on the github page.

[@noadino]

This is great , can you help me to find maximum liklihood for a function with pso algorithm pleeeease

[@kpmooney]

Yeah, but it will be a while before I have time for it.

[@volarb9613]

You beautiful man

[@FrancescoDelaidelli]

Hello Kevin, would it be possible to have the notebook with the code? I am having issue with some part of the code . Thanks!