I want to estimate the parameters of $a_t = a_{t-1}+\theta+\epsilon_t$ using MLE. Assume errors $\epsilon_t$ are serially correlated, then how would I choose the likelihood function?

  • $\begingroup$ Do you know anything about how they are serially correlated? $\endgroup$ – cc7768 Feb 3 '16 at 17:40
  • $\begingroup$ No, but let's assume a first order serial correlation $\epsilon_t = \rho\epsilon_{t-1}+e_t$ $\endgroup$ – london Feb 3 '16 at 17:49
  • $\begingroup$ What paramters are you estimating? Presumably the coefficeint on the lagged value.. $\endgroup$ – ChinG Feb 3 '16 at 22:57
  • $\begingroup$ yes, it is the parameter on $da_t$ $\endgroup$ – london Feb 5 '16 at 18:11

This is model is known an GARCH(general autoregressive conditional heteroskedasticity) where the AR component of the observable series $\{a_t\}$ is equal to unity.

The likelihood is determined by your model assumptions on the innovation terms $\varepsilon_t$ and $e_t$.

If you are looking for a canned function to estimate an GARCH see https://www.kevinsheppard.com/MFE_Toolbox. If you are looking for some more theory on how to form the likelihood see http://www.math.elte.hu/probability/markus/AlkmatTS1/ARCH_GARCH_Eload.html.

  • $\begingroup$ This is not an ARCH model. $\endgroup$ – luchonacho Apr 25 '17 at 19:41
  • $\begingroup$ Updated to reflect that it is really GARCH. My mistake. $\endgroup$ – hipHopMetropolisHastings Apr 25 '17 at 21:54

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.