R : Copyright 2001, The R Development Core Team Version 1.3.1 (2001-08-31) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type `license()' or `licence()' for distribution details. R is a collaborative project with many contributors. Type `contributors()' for more information. Type `demo()' for some demos, `help()' for on-line help, or `help.start()' for a HTML browser interface to help. Type `q()' to quit R. > library(tseries) > data(EuStockMarkets) > ftse <- diff(log(EuStockMarkets))[,"FTSE"] > ftse.garch <- garch(ftse, order=c(1,1)) ***** ESTIMATION WITH ANALYTICAL GRADIENT ***** I INITIAL X(I) D(I) 1 0.569929E-04 0.100E+01 2 0.500000E-01 0.100E+01 3 0.500000E-01 0.100E+01 IT NF F RELDF PRELDF RELDX STPPAR D*STEP NPRELDF 0 1 -0.806E+04 1 8 -0.806E+04 0.99E-05 0.26E-04 0.1E-04 0.2E+12 0.1E-05 0.27E+07 2 9 -0.806E+04 0.63E-06 0.64E-06 0.1E-04 0.2E+01 0.1E-05 0.10E+01 3 18 -0.807E+04 0.49E-03 0.84E-03 0.3E+00 0.2E+01 0.5E-01 0.10E+01 4 21 -0.808E+04 0.12E-02 0.10E-02 0.6E+00 0.2E+01 0.2E+00 0.11E+00 5 22 -0.809E+04 0.13E-02 0.25E-02 0.4E+00 0.2E+01 0.4E+00 0.92E+01 6 34 -0.809E+04 0.10E-02 0.23E-02 0.2E-05 0.4E+01 0.2E-05 0.42E-02 7 35 -0.809E+04 0.22E-04 0.18E-04 0.2E-05 0.2E+01 0.2E-05 0.89E-03 8 36 -0.809E+04 0.18E-05 0.19E-05 0.2E-05 0.2E+01 0.2E-05 0.12E-02 9 45 -0.810E+04 0.25E-03 0.27E-03 0.3E-01 0.7E+00 0.4E-01 0.12E-02 10 47 -0.810E+04 0.47E-03 0.47E-03 0.2E-01 0.1E+01 0.4E-01 0.44E-02 11 49 -0.811E+04 0.10E-02 0.11E-02 0.4E-01 0.1E+01 0.8E-01 0.16E-01 12 51 -0.811E+04 0.19E-03 0.28E-03 0.8E-02 0.2E+01 0.2E-01 0.42E-02 13 54 -0.812E+04 0.80E-03 0.83E-03 0.2E-01 0.8E+00 0.5E-01 0.44E-02 14 55 -0.812E+04 0.63E-03 0.93E-03 0.2E-01 0.1E+01 0.5E-01 0.30E-02 15 57 -0.813E+04 0.47E-03 0.68E-03 0.8E-02 0.1E+01 0.2E-01 0.91E-03 16 58 -0.813E+04 0.35E-04 0.44E-04 0.7E-02 0.6E+00 0.2E-01 0.55E-04 17 59 -0.813E+04 0.18E-06 0.19E-04 0.4E-02 0.0E+00 0.9E-02 0.19E-04 18 61 -0.813E+04 0.64E-05 0.17E-04 0.5E-03 0.1E+01 0.1E-02 0.25E-04 19 62 -0.813E+04 0.59E-05 0.70E-05 0.5E-03 0.2E+01 0.1E-02 0.15E-04 20 64 -0.813E+04 0.17E-05 0.21E-05 0.1E-02 0.4E+00 0.2E-02 0.23E-05 21 65 -0.813E+04 0.64E-07 0.62E-07 0.4E-04 0.0E+00 0.9E-04 0.62E-07 22 66 -0.813E+04 0.12E-08 0.97E-09 0.3E-04 0.0E+00 0.7E-04 0.97E-09 23 67 -0.813E+04 0.87E-11 0.11E-11 0.1E-05 0.0E+00 0.3E-05 0.11E-11 24 68 -0.813E+04 0.74E-13 0.89E-16 0.8E-08 0.0E+00 0.2E-07 0.89E-16 25 69 -0.813E+04 0.39E-14 0.42E-18 0.4E-09 0.0E+00 0.8E-09 0.42E-18 26 70 -0.813E+04 0.00E+00 0.43E-23 0.1E-11 0.0E+00 0.3E-11 0.43E-23 ***** X- AND RELATIVE FUNCTION CONVERGENCE ***** FUNCTION -0.812580E+04 RELDX 0.125E-11 FUNC. EVALS 70 GRAD. EVALS 26 PRELDF 0.433E-23 NPRELDF 0.433E-23 I FINAL X(I) D(I) G(I) 1 0.872214E-06 0.100E+01 0.195E-02 2 0.453209E-01 0.100E+01 0.114E-06 3 0.941866E+00 0.100E+01 0.113E-06 > summary(ftse.garch) Call: garch(x = ftse, order = c(1, 1)) Model: GARCH(1,1) Residuals: Min 1Q Median 3Q Max -4.57065 -0.57878 0.01228 0.69132 6.67351 Coefficient(s): Estimate Std. Error t value Pr(>|t|) a0 8.722e-07 3.083e-07 2.829 0.00467 ** a1 4.532e-02 6.791e-03 6.674 2.49e-11 *** b1 9.419e-01 1.018e-02 92.478 < 2e-16 *** --- Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1 Diagnostic Tests: Jarque Bera Test data: Residuals X-squared = 215.3627, df = 2, p-value = < 2.2e-16 Box-Ljung test data: Squared.Residuals X-squared = 0.1001, df = 1, p-value = 0.7517 >