2
$\begingroup$

I am fitting the following ARX(1,1)-GARCHX(1,1,1):

\begin{align*} y_t&=c+a_1y_{t-1}+\gamma_1x_t+\varepsilon_t\\ h_t&=\delta+\omega_1h_{t-1}+\theta_1\varepsilon_{t-1}^2+\pi_1x_{1,t} \end{align*}

Delta is negative, suggesting the conditional variance can theoretically be negative. Does anyone know how to get around this problem? My variables are already in logarithmic form, and I have tried standardising them to no avail. Any help would be much appreciated.

$\endgroup$
2
  • $\begingroup$ G_123, please use your account to make edits. @behrouzmaleki, your edit made sense but the OP apparently really meant it. $\endgroup$
    – Bob Jansen
    Nov 29, 2016 at 19:53
  • 2
    $\begingroup$ It is not because the intercept is negative that the model will necessarily broken. What matters usually is that unconditional variance remains positive, did you try to express that condition as I did here for the simple GARCH: see this related question: quant.stackexchange.com/questions/26357/…. Btw, are you sure of the cotemporaneous effect of $x$ on $y$ in your model equations? $\endgroup$
    – Quantuple
    Nov 30, 2016 at 10:36

0

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Browse other questions tagged or ask your own question.