How to calculate LogLikelihood between real data and predicted data?

Hey everyone!

I have used an AR-model to predict a time series and now I would like to calculate the LogLikelihood between my predicted datapoints and real datapoints to determine what set-up of my AR is the best by using the Akaika and Bayesian Information Criteria. On the internet I found the following idea:

 LogL=sum(log(pdf(pd,x)))

I cannot use this command though because matlab tells me it needs to know what kind of probability density function the pdf command should use. How can I solve this problem?

I tried this:

 LogL=sum(log(pdf('norm',pd,x,0,1)))

to try out what happens if I use a normal density function but my result is simply NaN...

Answer 1

[Roger Wohlwend]

When you estimate the model (using Matlab's arima class), you get the log-likelihood as the third output variable of the function estimate. I guess, that is the kind of log-likehood you want, because there is no such thing as a log-likelihood between real and predicted data. For the Akaika and BAyesian Information Criterion use the function aicbic (if you possess the Econometrics toolbox).

[JING QIAO]

May I ask how can I use aicbic in matlab for user defined functions? I tried to fit a set of data using different combinations of functions (sine, polynomial), I wanted to use aic/bic to test which one is a better function to model the data. From https://jp.mathworks.com/help/econ/aicbic.html, I need to provide the log-likelihood of the models. How can we calculate the log-likelihood?

Refer to https://jp.mathworks.com/help/ident/ref/idgrey.aic.html#buy65_c-model, it seems that the models are the ones defined by the matlab, such as

• idtf
• idgrey
• idpoly
• ..

Is there a way to use aic/bic for the models defined by the user (e.g,, y1= ax+bx^2+c, y2=ax+dx^3+sin(x))? Many thanks in advance!