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?


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 $k$.

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