Homework Assignments

All assigned problems are from Shumway and Stoffer; problem numbers are as in the 3^rd edition, with 2^nd edition numbers in parentheses, where these are different. Each Problem will be linked to its solution after the assignment is due.

Number	Due	Assignment
1	Thursday, August 25	Obtain a set of time series data for some simple exercises. If you work with time series data, you could use data you already have. Otherwise, look for data related to an area in which you're interested. You could explore the Federal Reserve's FRED database, or a finance-related site like Yahoo!, or a climate-related site like CRU. Graph your data against time. Does the mean appear constant? Does the variance appear constant? If either the mean or variance does not appear to be constant, find a way to make it more nearly constant (fit and subtract a trend, or convert to differences, or transform to logarithms, etc.) When you have eliminated variations in the mean and variance as far as possible, summarize the data by calculating the mean and standard deviation, graphing a histogram (or, better, a qq-plot), making a boxplot, etc.
2	Thursday, September 1	Problems 1.2, 1.4, 1.5, 1.7, 1.9, 1.10, and 1.13
3	Thursday, September 8	Problems 1.20 (1.19), 1.21 (1.20), 1.22 (1.21), 1.26 (1.25)[1], and 1.27 (1.26)
4	Thursday, September 15	Problems 2.1, 2.6, 2.8, and 2.9 (2.11) (R script)
5	Thursday, September 22	Problems 3.2, 3.4 (3.3), 3.6 (3.5), and 3.7 (3.6)[2]
6	Thursday, September 29	Problems 3.8 (3.7), 3.9 (3.8), 3.10 (3.9), and 3.11-a (3.10-a)
7	Tuesday, October 11	Problems 3.18(a) (3.17(a)), 3.21 (3.20), 3.28 (3.27), 3.30 (3.28), 3.32 (3.30), and 3.38 (3.36)
8	Thursday, October 20	Problems 4.1, 4.3, 4.4, 4.6
9	Thursday, October 27	Problems 4.8, 4.9[3], 4.12, 4.13, 4.16
10	Thursday, November 10	Problems 4.17, 4.18, 4.19, 4.20, 4.23, 4.34 In addition, for the time series that you worked on in Assignment 1, construct various estimates of the spectral density function. Note that the spectral density function exists only for a stationary series, so you should focus on a version of the series that appears stationary. Try the simple averaging version (f-bar) for at least two values of m. Also try weighted averages (f-hat), using both triangular weights and smoother, bell-shaped, weights, also least two versions of each. Notice how the graphical nature of the estimate changes as you change the shape of the weights. Turn in a brief summary of what you did and what you observed, with graphs of one or two choices, not a complete set of graphs.
11	Thursday, November 17	Problems 5.2 (5.3), 5.6 (5.4) (R script), 5.7 (5.5) (R script)

[1] Problem 1.25(b) has a typo (in both editions): μ should be μ_t, as in part (a).

[2] The solution to Problem 3.6 (a) contains an error. See the correct solution.

[3] Problem 4.9 asks for confidence intervals for the dominant frequencies; it should read confidence intervals for the spectral density at the dominant frequencies.

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