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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.

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G_123
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  • G_123, please use your account to make edits. @behrouzmaleki, your edit made sense but the OP apparently really meant it. – Bob Jansen Nov 29 '16 at 19:53
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    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: http://quant.stackexchange.com/questions/26357/why-is-the-garch-intercept-supposed-to-be-strictly-positive. Btw, are you sure of the cotemporaneous effect of $x$ on $y$ in your model equations? – Quantuple Nov 30 '16 at 10:36

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