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

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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