GARCHGARCH(1,1) Example Using S&P 500 Index Data on 10/1/02 to 9/28/07

S&P500LogSquaredMaximumS.D. 95%DateIndexReturnLog ReturnGARCH(1,1)LikelihoodGARCH ParametersConfidence Bands[A][B = LN(A/Lag(A))[C = B^2][D = + *Lag(D)+*Lag(C)][E = (-0.5*LN(2*)-0.5*LN(D)-0.5*(C/D))[F = 2 x SQRT(D)][G = -2 x SQRT(D)]

10/01/02847.91 =0.0000011872NOTES:10/02/02827.91-2.39%0.0570%0.0000750.038098 =0.05831118961.73%-1.73%10/03/02818.95-1.09%0.0118%0.0001043.097280 =0.92431796282.04%-2.04%1. Use Solver to set the value of $H$1210/04/02800.58-2.27%0.0515%0.0001041.194163persistence=0.98262915242.04%-2.04%2 By changing $H$7:$H$910/07/02785.28-1.93%0.0372%0.0001272.1040252.26%-2.26%3. The constraint is that $H$10