STATS 4A03/6A03: Time Series – Winter 2016 Assignment #1

| August 31, 2017

Question
STATS 4A03/6A03: Time Series – Winter 2016
Assignment #1– Due date: 3:30 PM on Monday January 18, 2016
NOTES:
(i) Solution papers to assignments should be dropped by the due date in the designated lockers
located in the ground level of Hamilton Hall, next to room HH/105.
(ii) Please make sure your solutions are readable, in sequential order and each part properly
labeled. Leave two blank lines or three between parts. Please write your NAME and
STUDENT NUMBER on every page. And staple your papers.
(iii) IMPORTANT: All plots and tables should be included in the question/part they belong
to, DO NOT APPEND THEM at the end of your paper.
(iv) Include any R code used. The code should be included in the problem/part where it is
used, next to the plot or table, DO NOT APPEND THEM at the end of your
paper.
(v) To be fair to all, no late assignments will be accepted.
NOTE: For each question, the apportioned marks will be earned on the basis
of the process employed to get the solution and the solution itself.
Problem 1. Consider the data on Average Monthly Temperature in Dubuque, Iowa, stored
in file “tempdub” in the TSA library.
(a) Reproduce the time plot in Exhibit 1.7 on page 6 in the book. Comment on the main
features you notice in the plot.
(b) Do a lag 1 plot of the temperatures. Comment on any features you notice regarding
potential association between yt and yt?1.
(c) Repeat (b) for lag 2.
Problem 2. Consider the time series yt
, t = 1, 2, …, n defined by
y?1 = 0, y0 = 0; yt = 0.9yt?2 + et
, t = 1, 2, …, n;
where e1, e2, …, en are independent and identically distributed as N(0, ?2 = 0.3).
(a) Write R code to generate the values y1, y2, …, yn for a given series size n.
(b) Run the program for n = 50. Report the y-values generated.
(c) Do a time plot of the series. Comment on any features you see.
1
(d) Do lag 1 and lag 2 scatterplots of the series. Compute the corresponding correlations.
Comment in any associations noted.
Problem 3. Consider the Monthly Log Stock Returns for American Express posted at:
http://faculty.chicagobooth.edu/ruey.tsay/teaching/fts/m-axp7399.dat
Note that the file has extension .dat. Import the data to R.
(a) Identify (i) the number of months covered by the time series, (ii) the 3 smallest log returns
and the months where they were observed, and (iii) the 3 largest log returns and the
months where they were observed.
(b) Produce a time plot for the log returns. Comment on any features revealed by the plot.
(c) Do a lag 1 plot of the log returns. Does the plot reveal any type of association? Comment.
Compute the lag 1 autocorrelation.
Problem 4. Book, page 19, #2.1.
Problem 5. Book, page 19, #2.2.
Problem 6. Let {et} be a mean 0 white noise process (i.e. et has mean 0 and some variance
?
2
, and et and es are independent, for all t and all s). Consider the time series Yt = et + ?et?1,
where ? is a constant.
(a) Find the autocovariance and autocorrelation functions for the time series.
(b) Evaluate the autocorrelation function for ? = 3 and ? = 1/3. Compare the two values.

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