* * GARCHMVSIMULATE.RPF * Example of simulation of a multivariate (DVECH) GARCH process * compute nobs=500 compute n=2 * all nobs * * u is the simulated GARCH process * dec vect[series] u(n) * * H is the series of variance matrices, UU is the series of lagged outer * products of the residuals. * dec series[symm] h uu dec symm vc(n,n) va(n,n) vb(n,n) compute vc=||.05|.01,.05|| compute va=||.05|.05,.05|| compute vb=||.90|.85,.90|| * * Compute the stationary covariance matrix. (Because this is a DVECH, * this can be done element by element). * dec symm h0(n,n) ewise h0(i,j)=vc(i,j)/(1-va(i,j)-vb(i,j)) * dec frml[symm] hf hu dec symm hx dec vect ux * frml hf = vc+va.*uu{1}+vb.*h{1} frml hu = hx=hf,ux=%ranmvnormal(%decomp(hx)),uu=%outerxx(ux),%pt(u,t,ux),hx * * Initialize the UU and H series for the pre-sample values * gset uu = h0 gset h = h0 * * Generate starting in entry 2. * gset h 2 500 = hu(t) * * Graph the series and variance series * graph(footer="First simulated series") # u(1) graph(footer="Second simulated series") # u(2) set h11 = h(t)(1,1) graph(footer="Simulated variance for first series") # h11