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Assignment 1 (due on June 30, 23:59)

Tsay (2010), Analysis of Financial Time Series.

Exercise 2.2, page 104.

2.2. Suppose that the daily log return of a security follows the model rt =0.01+0.2rt−2 +at,

where {at } is a Gaussian white noise series with mean zero and variance 0.02. What are the mean and variance of the return series rt ? Compute the lag-1 and lag-2 autocorrelations of rt . Assume that r100 = −0.01, and r99 = 0.02. Compute the 1- and 2-step-ahead forecasts of the return series at the forecast origin t = 100. What are the associated standard deviations of the forecast errors?

Exercise 2.4, page 105.

2.4. Consider the monthly simple returns of the Decile 1, Decile 2, Decile 9, and Decile 10 of NYSE/AMEX/NASDAQ based on market capitalization. The data span is from January 1970 to December 2008, and the data are obtained from CRSP.

(a) For the return series of Decile 2 and Decile 10, test the null hypothesis that the first 12 lags of autocorrelations are zero at the 5% level. Draw your conclusion.

(b) Build an ARMA model for the return series of Decile 2. Perform model checking and write down the fitted model.

(c) Use the fitted ARMA model to produce 1- to 12-step-ahead forecasts of the series and the associated standard errors of forecasts.

Data for exercise 2.4: https://faculty.chicagobooth.edu/ruey-s-tsay/research/analysis-of-financial-time-series-3rd-edition

Monthly simple returns of Deciles 1, 2, 9, & 10: m-deciles08.txt