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Filtered Historical Simulation FHS for VAR
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If I wish to run a FHS for VaR model, first I estimate the GARCH model on the historical returns $r_t$, then I obtain the historical innovation time series as $z_t=fracr_tsigma_t$, where $sigma_t$ is the volatility estimated by GARCH.
Setting then $sigma_0$ and $r_0$ as the volatility and log return of the last day of my historical sample, I estimate the GARCH daily variance on day 1 of risk horizon as
$sigma_1^2=gamma+alpha r_0^2+ betasigma_0^2$ and $r_1=z_1 sigma_0^2$,
where $z_1$ is simulated through statistical bootstrap from the previous historical innovation time series.. Then the simulated log return over a
risk horizon of h days is the sum $r_1 +..+r_h$: I do it thousand of times, resembling a distribution on which computing the VaR.
My question are:
- If the original historical return $r_t$ present autocorrelation, should I first model them through AR model and THEN run the GARCH model redoing the above mentioned steps?
- Is it improper to call the innovation residuals?
- If the innovations are not i.i.d, should I model them with AR in mean equation of GARCH?
statistics time-series regression-analysis risk-assessment vector-auto-regression
asked Aug 2 at 14:13
Francesco Lorenzo Flamini
83
add a comment |Â
up vote
0
down vote
favorite
If I wish to run a FHS for VaR model, first I estimate the GARCH model on the historical returns $r_t$, then I obtain the historical innovation time series as $z_t=fracr_tsigma_t$, where $sigma_t$ is the volatility estimated by GARCH.
Setting then $sigma_0$ and $r_0$ as the volatility and log return of the last day of my historical sample, I estimate the GARCH daily variance on day 1 of risk horizon as
$sigma_1^2=gamma+alpha r_0^2+ betasigma_0^2$ and $r_1=z_1 sigma_0^2$,
where $z_1$ is simulated through statistical bootstrap from the previous historical innovation time series.. Then the simulated log return over a
risk horizon of h days is the sum $r_1 +..+r_h$: I do it thousand of times, resembling a distribution on which computing the VaR.
My question are:
- If the original historical return $r_t$ present autocorrelation, should I first model them through AR model and THEN run the GARCH model redoing the above mentioned steps?
- Is it improper to call the innovation residuals?
- If the innovations are not i.i.d, should I model them with AR in mean equation of GARCH?
statistics time-series regression-analysis risk-assessment vector-auto-regression
asked Aug 2 at 14:13
Francesco Lorenzo Flamini
83
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
If I wish to run a FHS for VaR model, first I estimate the GARCH model on the historical returns $r_t$, then I obtain the historical innovation time series as $z_t=fracr_tsigma_t$, where $sigma_t$ is the volatility estimated by GARCH.
Setting then $sigma_0$ and $r_0$ as the volatility and log return of the last day of my historical sample, I estimate the GARCH daily variance on day 1 of risk horizon as
$sigma_1^2=gamma+alpha r_0^2+ betasigma_0^2$ and $r_1=z_1 sigma_0^2$,
where $z_1$ is simulated through statistical bootstrap from the previous historical innovation time series.. Then the simulated log return over a
risk horizon of h days is the sum $r_1 +..+r_h$: I do it thousand of times, resembling a distribution on which computing the VaR.
My question are:
- If the original historical return $r_t$ present autocorrelation, should I first model them through AR model and THEN run the GARCH model redoing the above mentioned steps?
- Is it improper to call the innovation residuals?
- If the innovations are not i.i.d, should I model them with AR in mean equation of GARCH?
statistics time-series regression-analysis risk-assessment vector-auto-regression
asked Aug 2 at 14:13
Francesco Lorenzo Flamini
83
If I wish to run a FHS for VaR model, first I estimate the GARCH model on the historical returns $r_t$, then I obtain the historical innovation time series as $z_t=fracr_tsigma_t$, where $sigma_t$ is the volatility estimated by GARCH.
Setting then $sigma_0$ and $r_0$ as the volatility and log return of the last day of my historical sample, I estimate the GARCH daily variance on day 1 of risk horizon as
$sigma_1^2=gamma+alpha r_0^2+ betasigma_0^2$ and $r_1=z_1 sigma_0^2$,
where $z_1$ is simulated through statistical bootstrap from the previous historical innovation time series.. Then the simulated log return over a
risk horizon of h days is the sum $r_1 +..+r_h$: I do it thousand of times, resembling a distribution on which computing the VaR.
My question are:
- If the original historical return $r_t$ present autocorrelation, should I first model them through AR model and THEN run the GARCH model redoing the above mentioned steps?
- Is it improper to call the innovation residuals?
- If the innovations are not i.i.d, should I model them with AR in mean equation of GARCH?
statistics time-series regression-analysis risk-assessment vector-auto-regression
asked Aug 2 at 14:13
Francesco Lorenzo Flamini
83
asked Aug 2 at 14:13
Francesco Lorenzo Flamini
83
asked Aug 2 at 14:13
Francesco Lorenzo Flamini
83
asked Aug 2 at 14:13
Francesco Lorenzo Flamini
83
83
add a comment |Â
add a comment |Â
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