Consider the monthly yields of Moody’s Aaa & Baa seasoned bonds from January 1919 to November, 2011.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Question A (5 points)

Suppose that rt follows the model rt = rt−1 + at −0.9at−1, and we have r1001 = 1.2 and r1000 (1) = 1.0, where rt(1) denotes the 1 step ahead prediction of rt+1 at the forecast origin t. Compute r1001(1).

Question B (10 points)

Consider the daily log returns rt, in percentages, of the NASDAQ index for a certain period of time with 1841 observations. Answer the following questions, using the attached R output.

1. Let µ be the expected value of rt. Test H0 : µ = 0 versus Ha : µ ≠ 0. Obtain the test statistic and draw your conclusion.

2. Is the distribution of rt skew? Why?

3. Does the distribution of rt have heavy tails? Why?

4. Let ρ1 be the lag-1 ACF of rt. Test H0: ρ1 = 0 versus Ha : ρ ≠ 0. The sample lag-1 ACF is −0.086. Obtain the test statistic and draw your conclusion.

5. An MA(1) model is fitted. Write down the fitted model, including σ2 of the residuals.

Question C (20 points)

Consider the monthly yields of Moody’s Aaa & Baa seasoned bonds from January 1919 to November, 2011. The data are obtained from FRED of Federal Reserve Bank of St. Louis and in the file m-Aaa-1911.txt and m-Baa-1911.txt. What is the relationship between the two series? To answer this question, take the log transformation of the data to build a time series model for the Aaa yields using Baa yields as an explanatory variable. Write down the fitted model, including model checking. (hint: follow the procedure of the case study of 1- and 3- year Treasury rates that we discussed in the class)

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