K. Ensor, STAT 421 1 Spring 2004 Garch-m The process or return is dependent on the volatility , c are constants C is the “risk premium parameter”; c>0.

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Presentation transcript:

K. Ensor, STAT Spring 2004 Garch-m The process or return is dependent on the volatility , c are constants C is the “risk premium parameter”; c>0 indicates the return is positively related to its volatility.

K. Ensor, STAT Spring 2004

K. Ensor, STAT Spring 2004 Estimated Coefficients: Value Std.Error t value Pr(>|t|) C e-003 ARCH-IN-MEAN e-002 A e-004 ARCH(1) e-009 GARCH(1) e Output from Splus m-garch fit garch(x~1+var.in.mean,~garch(1,1)) Differs from Tsay’s fit slightly.

K. Ensor, STAT Spring 2004 S&P500 Index Square root Of volatility

K. Ensor, STAT Spring 2004 Summary Graphs

K. Ensor, STAT Spring 2004 Hong Kong stock market index return (bottom graph) and estimated volatility.

K. Ensor, STAT Spring 2004 Estimated Coefficients: Value Std.Error t value Pr(>|t|) AR(1) A ARCH(1) GARCH(1) garchfit<-garch(HK~- 1+arma(1,0),~garch(1,1),cond.dist="t",dist.est=T)

K. Ensor, STAT Spring 2004 HK - Garch fit +/- 2SD

K. Ensor, STAT Spring 2004

K. Ensor, STAT Spring Estimated Coefficients: Value Std.Error t value Pr(>|t|) AR(1) e-002 A e-003 ARCH(1) e-007 GARCH(1) e garchfit<-garch(HK~- 1+arma(1,0),~garch(1,1),cond.dist="gaussian",dist.est=T)

K. Ensor, STAT Spring 2004

K. Ensor, STAT Spring 2004

K. Ensor, STAT Spring 2004

K. Ensor, STAT Spring 2004 Japanese stock market index and volatility based on Gaussian GARCH(1,1) model

K. Ensor, STAT Spring Estimated Coefficients: Value Std.Error t value Pr(>|t|) A e-003 ARCH(1) e-007 GARCH(1) e garchfit <-garch(JI~- 1,~garch(1,1),cond.dist="gaussian",dist.est= T)

K. Ensor, STAT Spring 2004 JI

K. Ensor, STAT Spring 2004 JI

K. Ensor, STAT Spring 2004 Let’s trying looking at the multivariate GARCH.

K. Ensor, STAT Spring 2004 Series 1: Hong Kong Stock Index Series 2: Japanese Stock Index

K. Ensor, STAT Spring 2004 Series 1: Hong Kong Stock Index Squared Series 2: Japanese Stock Index Squared

K. Ensor, STAT Spring Estimated Coefficients: Value Std.Error t value Pr(>|t|) AR(1; 1, 1) e-002 AR(1; 2, 2) e-001 A(1, 1) e-003 A(2, 2) e-001 ARCH(1; 1, 1) e-006 ARCH(1; 2, 2) e-005 GARCH(1; 1, 1) e+000 GARCH(1; 2, 2) e mgarchfit=mgarch(X~- 1+arma(1,0),~garch(1, 1)) Page 367 of text

K. Ensor, STAT Spring 2004

K. Ensor, STAT Spring 2004

K. Ensor, STAT Spring 2004