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The file aa-rv-20m.txt contains the realized daily volatility series of Alcoa stock returns from January 2, 2003 to May 7, 2004; see the example in Section 11.1. The volatility series is constructed using 20-minute intradaily log returns.
(a) Fit an ARIMA (0, 1, 1) model to the log volatility series and write down the model.
(b) Estimate the local trend model in Eqs. (11.1) and (11.2) for the log volatility series. What are the estimates of σe and ση? Obtain time plots for the filtered and smoothed state variables with point wise 95% confidence interval.