I have a time series $x_t$ of length $n$. I would like to model it using rolling window approach with window length (width) $w$:
- window $1$: $x_1,\dots,x_w$,
- window $2$: $x_2,\dots,x_{w+1}$,
- $\dots$,
- window $n-w+1$: $x_{n-w+1},\dots,x_n$.
In each window, I would like to estimate a GARCH model. I could just do it using brute force. However, this is quite expensive computationally.
I wonder if I could borrow information from neighbouring windows and make the estimation more computationally efficient. Is there an algorithm available that is doing that?
(E.g. if I was estimating a regression model, I could use the ideas suggested in the thread "Efficient online linear regression").
ugarchroll
in therugarch
package in R and it seems it just uses brute force. But I may be mistaken. $\endgroup$