Time Series

(1) Consider the growth rates of the U.S. quarterly gross national product (GNP) from 1947.I to 2011.IV. The original data, from the Federal Reserve Bank of St Louis, are in the file q-gnp-4711.txt (year, month, day, gnp), and the GNP is in billions of dollars. The growth rate is the first differenced series of the log(GNP).(a) Plot the GNP growth rates. The reduction in volatility, starting in the 1980s, is referred to as the great moderation in the economic literature.(b) Build an AR(3) model for the growth rate series. (c) Does the model confirm the existence of business cycles? Explain.(d) Is the model you fitted a causal AR process? (2) Consider the data in the file Strikes.txt. (a) Difference the data twice at lag 1 and subtract the mean.(b) Fit an AR(2) model for the strikes data.(c) Is the model you fitted a causal AR process?(d) Find the values of the model autocorrelation function rho(k) for k >=0 for the fitted model.(e) Plot the sample and model autocorrelation functions. See attachement for data. This hwk is due on Sunday at 10 pm. 


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