# Fitting a non linear AR + GARCH(1,1)-M model

I want to fit the following model to a time series:

$$y_{t}=\alpha_{0}+\alpha_{1}y_{t-1}+\alpha_{2}y_{t-1}^{2}+\lambda h_{t}+\varepsilon_{t}$$

$$h_{t}=\beta_{0}+\beta_{1}\varepsilon_{t-1}^{2}+\beta_{2}h_{t-1}$$

How can I do this with R or with any other statistical software?

Thanks

-
Sorry ... I missed the "non" in "non-linear" and the square ... I will delete my answer, it is not an answer to your question. – Richard Mar 8 '13 at 14:54

$$y_{t}=\alpha_{0}+\alpha_{1}y_{t-1}+\varepsilon_{t}$$ $$h_{t}=\beta_{0}+\beta_{1}\varepsilon_{t-1}^{2}+\beta_{2}h_{t-1}$$ + the arch in mean effect ($\lambda h_{t}$ ): $$y_{t}=\alpha_{0}+\alpha_{1}y_{t-1} +\lambda h_{t}+\varepsilon_{t}$$ $$h_{t}=\beta_{0}+\beta_{1}\varepsilon_{t-1}^{2}+\beta_{2}h_{t-1}$$ + the explanatory variable in the mean process ($y_{t-1}^{2}$):
$$y_{t}=\alpha_{0}+\alpha_{1}y_{t-1}+\alpha_{2}y_{t-1}^{2}+\lambda h_{t}+\varepsilon_{t}$$ $$h_{t}=\beta_{0}+\beta_{1}\varepsilon_{t-1}^{2}+\beta_{2}h_{t-1}$$ All econometrical packages allowing to add 1)an arch in mean effect and 2) an explanatory variable can be used (the G@rch package (Ox) for example).