5
$\begingroup$

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

$\endgroup$
  • $\begingroup$ Sorry ... I missed the "non" in "non-linear" and the square ... I will delete my answer, it is not an answer to your question. $\endgroup$ – Richard Mar 8 '13 at 14:54
1
$\begingroup$

I would fit an AR(1)-GARCH(1,1) with arch in mean effect and with the square of the serie at lag 1 as explanatory variable in the mean process :

The AR(1)-GARCH(1,1) component for :

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

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.