Consider the monthly log returns of CRSP equal-weighted index from Jan- uary 1962 to December...

2.13. Consider the monthly log returns of CRSP equal-weighted index from Jan- uary 1962 to December 1999 for 456 observations. You may obtain the data from CRSP directly or from the filem-ew6299.txton the Web.

(a) Build an AR model for the series and check the fitted model.

(b) Build an MA model for the series and check the fitted model.

(c) Compute 1- and 2-step-ahead forecasts of the AR and MA models built in the previous two questions.

(d) Compare the fitted AR and MA models.

2.14. This problem is concerned with the dynamic relationship between the spot and futures prices of the S&P 500 index. The data filesp5may.dathas three columns: log(futures price), log(spot price), and cost-of-carry (×100). The data were obtained from the Chicago Mercantile Exchange for the S&P 500 stock index in May 1993 and its June futures contract. The time interval is 1 minute (intraday). Several authors used the data to study index futures arbitrage. Here we focus on the first two columns. Letftandstbe the log prices of futures and spot, respectively. Consideryt=ft-ft-1and xt=st-st-1. Build a regression model with time series errors between{yt} and{xt}, withytbeing the dependent variable.

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2.15. The quarterly gross domestic product implicit price deflator is often used as a measure of inflation. The fileq-gdpdef.txtcontains the data for the United States from the first quarter of 1947 to the last quarter of 2008. Data format is year, month, day, and deflator. The data are seasonally adjusted and equal to 100 for year 2000. Build an ARIMA model for the series and check the validity of the fitted model. Use the fitted model to predict the inflation for each quarter of 2009. The data are obtained from the Federal Reserve Bank of St Louis.