2
$\begingroup$

I calculated log likelihoods for two times series models, a GARCH and a TGARCH. The GARCH model is nested within the TGARCH, and their respective log-likelihoods are:

\begin{aligned} \text{LL_GARCH} \ \ \ &= 2.92 \\ \text{LL_TGARCH} &= 2.96 \\ \end{aligned}

I calculated $-2\ln(2.92 / 2.96)$ to get a value of $.0272$, which is not significant on even 1 degree of freedom (chi-square distribution).

Am I conducting the likelihood ratio test correctly?

$\endgroup$
1
$\begingroup$

I think you are doing it correctly. You take $-2$ times the logarithm of the ratio of (1) the likelihood of the reduced model to (2) the likelihood of the full model, $-2\ln(L_{reduced}/L_{full})$. In your case, GARCH is a reduced model and TGARCH is the full model.

You should compare the test statistic to a $\chi^2(k)$ distribution where $k$ is the number of coefficients that are set to zero in the TGARCH model to obtain a GARCH model. Depending on the precise specification of TGARCH and GARCH in your application (lag order etc.), $k$ can be 1 or greater. But if you fail to reject the null hypothesis for $\chi^2(1)$ (i..e the test statistic is smaller than the critical value), you will also fail for $\chi^2(k)$ where $k>1$ since the critical values get larger with $k$.

| cite | improve this answer | |
$\endgroup$

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.