Midterm (takehome) exam
UMN STAT 5511 (Fall 2021)
Charles R. Doss
Exam Instructions
Assigned: Saturday, Nov 20, 2021 12:01 am (i.e., Friday at midnight). Update: it was made available
around 10:00am Saturday morning.
Due: Uploaded to Canvas on Wednesday, Nov 24, 2020, before 11:59pm (Central Time). Upload your
exam as a single pdf file. Give yourself time to upload it so you do not miss the deadline.
This is a takehome exam. You may not work (give or receive help) with any one else on this exam; that
includes other students, as well as friends, family, colleagues, faculty, or anyone else. If you have ques-
tions you should contact the professor. You may reference all of your course materials (as well as outside
textbooks or the internet). (However: for full credit you will generally need to give an answer that refers
to what you learned specifically in class. If you use ideas or material from outside class, you will need to
explain what you are doing, and they may not yield full credit.)
Note: statistics students have been caught cheating by working on takehome exams together. Any students
caught cheating in such a manner will fail the course and have a mark put on their academic record, as a
minimum punishment. Being caught cheating can lead to expulsion from the university.
Questions
On this takehome exam, you will analyze three data sets. Find mid2-data.rsav on the course webpage.
Load it into R by running load("path/mid2-data.rsav") where “path/mid2-data.rsav” is replaced
by the full path on your hard drive to the file mid2-data.rsav (the syntax for which is operating system
dependent). The file contains three data objects: dat1, dat2, and dat3. Each dataset corresponds to a
separate exam question. (Thus, this exam has three questions.) You should find the best ARIMA(p, d, q)
fit(s) for each dataset (or a transformation thereof) that you can. Your output should be in the following
format. (Points will be deducted if it is not.)
• The analysis for each question/dataset should begin on a new page and should have as label the name
of the dataset (“dat1”, “dat2”, or “dat3”).
• On the first page you should state on which page each question begins. [Note: One simple way to auto-
mate this in LaTex is to use \section{} to start each dataset and then include a \tableofcontents.
You could also use \label{} and \pagref{} commands.]
• On the first page of output for each problem, you should first have a summary (labeled “Summary”)
that provides the model chosen, whether any transformation was used, parameter estimates, standard
errors, and p-values in that model. Specify explicitly if you exclude a constant term. For example,
“For the series Yt = X
1/2
t , I chose an ARIMA(1, 2, 3) model, including the intercept term. The
parameter estimates were ...”. If you believe the data cannot distinguish between two (or more)
models you should describe both (all) of them in this manner here. (But if the grader(s) disagree then
you may lose points.)
• After the summary, should be an explanation (labeled “Explanation”). Provide a clear explanation of
why you selected the model you selected. Refer to the output of your analysis, which will be below.
The model selection and diagnostic techniques we have discussed in class can be discussed here. You
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do not need to (and should not) provide an exhaustive list of all possible models, but should rather
provide explanation for which models were reasonable contenders (and why), and which model (or
models) were the best out of those contenders (and why).
• After the explanation is the “Output” you refer to in your summary. (The output may be plots or
output from various commands.) All of it should be clearly labeled or described. You do not need
to provide exhaustive output from every command you have run, but you should include enough to
justify all the arguments you make in your summary.
Finally, please refer to the original/raw (untransformed) time series as Xt in your descriptions and as xx
in your code. Refer to any transformed series as Yt in your descriptions and yy in your code.
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