# TGARCH MODEL COEFFICIENT INTERPRETATION [closed]

Please how do i interpret the tgarch coefficient of 'RESID(-1)^2*(RESID(-1)<0)' that is negative but significant. All other coefficients in the equation are positive and significant. 'RESID(-1)^2' + 'RESID(-1)^2*(RESID(-1)<0)' will give a positive number.

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The conditional variance is equation is $$\sigma_t^2=\omega+(\alpha_1+\gamma_1\mathbb{1}\{\varepsilon_{t-1}<0\})\varepsilon_{t-1}^2+\beta_1\sigma_{t-1}^2$$ where $$\mathbb{1}(\cdot)$$ is the indicator function. (There may be higher-order lag terms which I will skip for simplicity.) If $$\varepsilon_{t-1}<0$$, then $$\sigma_t^2=\omega+(\alpha_1+\gamma_1)\varepsilon_{t-1}^2+\beta_1\sigma_{t-1}^2$$; otherwise $$\sigma_t^2=\omega+\alpha_1\varepsilon_{t-1}^2+\beta_1\sigma_{t-1}^2$$. The idea is that a negative error (shock, innovation) will have a different effect on the future conditional variance than a positive one will. According to the equation above, a negative $$\gamma_1$$ would mean a negative past error $$\varepsilon_{t-1}<0$$ will lead to smaller $$\sigma_t^2$$ than a positive past error $$\varepsilon_{t-1}>0$$ would, and the difference is $$\gamma_1\varepsilon_{t-1}^2$$. An empirical stylized fact in finance is that this should be reversed. So either your case is atypical or the model is formulated with $$\mathbb{1}\{\varepsilon_{t-1}>0\}$$ in place of $$\mathbb{1}\{\varepsilon_{t-1}<0\}$$.