Homework4SolS11

# Homework4SolS11 - HW 4 solutions a Scatter plot and acf...

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HW 4 solutions a) Scatter plot and acf plot: > rate=ts(ISOL_RATE[1:288],start=1987,frequency=12) > log.return=diff(log(rate)) > plot(log.return,xlab="time",ylab="log returns",main="scatter plot of log returns") scatter plot of log returns time log returns 1990 1995 2000 2005 2010 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 > acf(log.return,lag=48,main="ACF plot of log returns") The scatter plot shows that the log return data are symmetrically distributed with zero. But from the ACF plot we observe many spikes indicating correlatedness, and the spikes are seasonal, so there might be seasonality in the log return data.

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Histogram with normal curve > h=hist(log.return,prob=T,breaks=30,col="red") > x=seq(min(log.return),max(log.return),length=287) > curve(dnorm(x,mean=mean(log.return),sd=sd(log.return)),add=TRUE,col="blue",lwd="3") Histogram of log.return log.return Density -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0 1 2 3 4 From the histogram and the normal curve, we observe some heavy tailness on both sides, which is a usual phenomenon for financial time series data. b) Fit GARCH(1,1) model: > garch1=garch(log.return,order=c(1,1)) > summary(garch1) Call: garch(x = log.return, order = c(1, 1)) Model: GARCH(1,1) Residuals: Min 1Q Median 3Q Max -2.9010 -0.6459 0.1242 0.7279 2.6367 Coefficient(s): Estimate Std. Error t value Pr(>|t|) a0 1.278e-02 2.234e-02 0.572 0.567 a1 4.166e-02 7.799e-02 0.534 0.593 b1 1.829e-12 1.673e+00 1.09e-12 1.000
Diagnostic Tests: Jarque Bera Test data: Residuals X-squared = 4.3246, df = 2, p-value = 0.1151 Box-Ljung test data:

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Homework4SolS11 - HW 4 solutions a Scatter plot and acf...

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