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10. Which is the lag-2 autocorrelation of the time series (x)? a. 1.00000000 b. 0.37687036 c. 0.25391195 d. 0.01252511 11. Which is the mean of the time series (x)? a 0.0077 b. 0.01180982 C. 0.02330508 d. 0.01252033 12. Which is the variance of the time series (x)? 2 0.00009427 b. 0.0001072596 C. 0.0001140595 d 0.0001087317 O tom

Please read the following R scripts for the analysis of S&P 500 returns and answer questions from 15 to 20. > sp=scan( "sp500.txt") Read 792 items >pacfisp3) >ml=garchFit(-arma(3,0)+garch(1.1), data=sp5,trace=F) > summary(ml) Title: GARCH Modelling Call: garchFit(formula = -arma(3,0)+garch(1, 1), data = sp5, trace = F) Mean and Variance Equation: data ~ arma(3,0) + garch(1,1) (data = sp5] Conditional Distribution: norm Error Analysis: Estimate 7.708e-03 ar 3.197e 02 ar2 3.026e-02 ar 3 -1.065e-02 omega 7975e-05 alphal 1.242e-01 betal 8530-01 Std. Error 1.607e-03 3.837e-02 3.841e-02 3.756e-02 2.810-05 2.247e-02 t value 4.798 0.833 -0.788 0.284 2.838 5.529 Pr>t) 1.6le-06 *** 0.40473 0.43076 0.77677 0.00454 ** 29

>ml=gar > summary(ml) Title: GARCH Modelling Call: garchFit(formla = -arma(3.0)+garch(1, 1), data = sp5, trace = F) Mean and Variance Equation: data - arma/3.0) + garch(1, 1) (data = sp5] Conditional Distribution: nomm Error Analysis: Estimate 7.708-03 arl 3.197e-02 ar2 3.026e-02 ar3 -1.065e-02 omega 7.975e-05 alphal 1.242e-01 Std. Error 1.607e-03 3.837e-02 3.841e-02 3.756e-02 2.810-05 2.247e-02 2.183e-02 t value 4.798 0.833 0.788 -0.284 2.838 5.529 39.075 Pr(>\t) 1.61e-06*** 0.40473 0.43076 0.77677 0.00454 ** 3.22e-08 *** <2e-16 *** betal 8.530-01 Log Likelihood 1272.179 normalized: 1.606287 7 這裡输入文字來搜尋

15. For the estimated model (ml in the R scripts), we could write the model as r4 = % + 678-1++2+&+1-3 +Qx, 44 = 0;£t, of = ap + a a-1 + B2 0-1. Which of the following is false for the estimated coefficients? a. 40 = 0.007708 ay = 0.1242 C. Bu = 0.853 b. d = 0.03197 e = -0.03026 16. For the estimated model (ml in the scripts) as written in question 15, which of the parameter estimates is'are insignificant different from zero at 5% significance level? a. c. a d. auß e both a and d 8