multistep ahead forecasts BGARCH
Posted: Fri Sep 10, 2010 2:30 am
Hi there,
I have estimated a BGARCH-BEKK model for series y1 and y2, have saved the GARCH1,GARCH2,COV1_2, and RESID1, RESID2. I want to compute the the conditional covariance forecast. I know how to do one-step ahead forecasts for condional covariance (eg: cov(y1_t, y2_t |give information up to time t-1)
The covariance i want to find however is this:
Cov(y1_t , y2_t-3 |given information upto time t-4)
How do i estimate the conditional covariance between y1 at time t, and y2 at time t-3?
Do I use the resid1 at time t, and the resid2 at time t-3, and plug them into the cov1_2 equation below?
Substituted Coefficients:
=====================
GARCH1 = 0.0354610255464+0.0712346925422*RESID1(-1)^2+0.811747511913*GARCH1(-1)
GARCH2 = 0.048152492071+0.124405077198*RESID2(-1)^2+0.742586402952*GARCH2(-1)
COV1_2 = 0.0389799691133 + 0.0941379701548*RESID1(-1)*RESID2(-1) + 0.776397234009*COV1_2(-1)
I have estimated a BGARCH-BEKK model for series y1 and y2, have saved the GARCH1,GARCH2,COV1_2, and RESID1, RESID2. I want to compute the the conditional covariance forecast. I know how to do one-step ahead forecasts for condional covariance (eg: cov(y1_t, y2_t |give information up to time t-1)
The covariance i want to find however is this:
Cov(y1_t , y2_t-3 |given information upto time t-4)
How do i estimate the conditional covariance between y1 at time t, and y2 at time t-3?
Do I use the resid1 at time t, and the resid2 at time t-3, and plug them into the cov1_2 equation below?
Substituted Coefficients:
=====================
GARCH1 = 0.0354610255464+0.0712346925422*RESID1(-1)^2+0.811747511913*GARCH1(-1)
GARCH2 = 0.048152492071+0.124405077198*RESID2(-1)^2+0.742586402952*GARCH2(-1)
COV1_2 = 0.0389799691133 + 0.0941379701548*RESID1(-1)*RESID2(-1) + 0.776397234009*COV1_2(-1)