When solving the log likelihood expression for autoregressive models, I cam across the variance covariance matrix Tau
given under slide 9 Parameter estimation of time series tutorial. Now, in order to use
fminsearch
to maximize the likelihood function expression, I need to express the likelihood function where the variance covariance matrix arises. Can somebody please show with an example how I can implement (determinant of Gamma)^-1/2
? Any other example apart from autoregressive model will also do.
How about
sqrt(det(Gamma))
for the sqrt-determinant andinv(Gamma)
for inverse?But if you do not want to implement it yourself you can look at yulewalkerarestimator
UPD: For estimation of autocovariance matrix use xcov
also, this topic is a bit more explained here