Maximum Likelihood Estimation of the AR(1) Model

[@paugim1]

Thank you for the video! Very useful & perfectly explained

[@lcsl5605]

Hello Rasmus. Thank you very much for this video. It's very well explained.
Do you have this same explanation for the AR(P)?

[@rasmuspedersen3195]

The same derivations apply to AR(p) models. See for instance Hamilton's 1994 textbook "Time Series Analysis"

[@kanyisasepoko1158]

How about the same estimation of the AR (2)?

[@rasmuspedersen3195]

Quite the same. Now you should consider the conditional distribution of y_{t} given both y_{t-1} and y_{t-2} in order to find the likelihood contribution. The MLE for the two autoregressive coefficients now corresponds to the least squares estimator obtained by regressing y_{t} on both y_{t-1} and y_{t-2}. /Rasmus

[@amiralao9279]

@@rasmuspedersen3195 thank you so much !

[@최현호-s3c]

Amazing

[@komalshekhawat7171]

Here the mle estimator 's sum goes from t= 1 to T but there is y_{t-1} , So it should be from t=2 to T. please help

[@rasmuspedersen3195]

You may think of this as conditioning on the fixed value y_{0}.

[@kennychen4483]

Thanks for the video sir!!!!!!

[@farhahanggana5199]

Do you have some source for this one? Like paper or journal or book?

[@rasmuspedersen3195]

I am quite sure that it is covered in Hamilton's 1994 textbook "Time Series Analysis".

[@annahoran2384]

Hello sir, do you know about how to do mle in markov switching autoregressive?

[@rasmuspedersen3195]

It is considered in Hamilton's 1994 textbook "Time Series Analysis".
It is implemented in PcGive for OxMetrics, and I bet that there exist packages for R, Python, etc. as well.

[@thequantartist]

Hi, what is the software you're using to annotate?

[@rasmuspedersen3195]

Hi Victor,
I use PDF Annotator.
Best,
Rasmus

[@komalshekhawat7171]

Here the mle estimator 's sum goes from t= 1 to T but there is y_{t-1} , So it should be from t=2 to T. please help