Compute the sample mean, standard deviation, skewness, excess kurtosis, minimum, and maximum of the log returns of each exchange rate.

1. Daily foreign exchange rates (spot rates) can be obtained from the Federal Reserve Bank of New York. The data are the noon buying rates in New York City certified by the Federal Reserve Bank of New York. Consider the exchange rates between the U.S. dollar and the British pound and Japanese yen from January 2, 2007 to November 30, 2011.

(i) Compute the daily log return of each exchange rate.

(ii) Compute the sample mean, standard deviation, skewness, excess kurtosis, minimum, and maximum of the log returns of each exchange rate.

(iii) Obtain a density plot of the daily log returns of Dollar-Yen exchange rate.

(iv) Test H0 : = 0 versus Ha : 6= 0, where denotes the mean of the daily log return of Dollar-Yen exchange rate. Use the 5% significance level to draw the conclusion. If not specifically specified, use 5% significance level to draw conclusions in the exercises.

2. Consider the US quarterly real gross national product from the first quarter of 1947 to the third quarter of 2011. The data are in the file q-GNPC96.txt, seasonally adjusted, and in billions of chained 2005 dollars. Let xt be the growth rate series of the real GDP.

(a) The ar command identifies an AR(4) model for xt via the AIC criterion. Fit the model. Is the model adequate? Why?

(b) The sample PACF of xt species an AR(3) model. Fit the model. Is it adequate? Why?

(c) What is the model for xt if one uses in-sample model comparison? Why?

(d) Divide the data into estimation and forecasting subsamples using the fourth quarter of 2000 as the initial forecast origin and apply the backtesting procedure with MSFE as the criterion. Select a model for xt. Justify the choice.

To answer questions in Problems 3, (a) use 5% significance level in tests, and (b) use 10 lags of serial correlations for return series.

3. Consider the daily stock returns of Procter & Gamble from September 1, 2001, to September 30, 2011. The simple returns are available from CRSP and in the le d-pg-0111.txt. Transform the simple returns to log returns.

(a) Is there any serial correlation in the log returns?

(b) Fit an MA model, where the maximum order is Q = 20, to the log returns to remove serial correlations. Write down the fitted model. Is the model adequate?

(c) Let rt be the residuals of the MA model and xt = 100*rt. Is there ARCH effect in xt?

(d) Fit an EGARCH model to xt. Perform model checking and write down the fitted model.

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