The usual formatting rules:
Homework 5
STAT 5511 (Spring 2020) Charles R. Doss
• Your homework (HW) should be formatted to be easily readable by the grader.
• You may use knitr or Sweave in general to produce the code portions of the HW. However, the output from knitr/Sweave that you include should be only what is necessary to answer the question, rather than just any automatic output that R produces. (You may thus need to avoid using default R functions if they output too much unnecessary material.)
– For example: for output from regression, the main things we would want to see are the estimates for each coefficient (with appropriate labels of course) together with the computed OLS/linear regression standard errors and p-values.
• Code snippets that directly answer the questions can be included in your main homework document; ideally these should be preceded by comments or text at least explaining what question they are answering. Extra code can be placed in an appendix.
• All plots produced in R should have appropriate labels on the axes as well as titles. Any plot should have explanation of what is being plotted given clearly in the accompanying text.
• Plots and figures should be appropriately sized, meaning they should not be too large, so that the page length is not too long. (The arguments fig.height and fig.width to knitr chunks can achieve this.)
1. Shumway and Stoffer (4th ed.), question 3.9
2. Shumway and Stoffer (4th ed.), question 3.11,
For the next two questions, download the file HW5dat.rsav from Canvas and load(‘‘HW5dat.rsav’’). It has two time series objects, dat1 and dat2, which you will analyze in the next two questions.
The analysis for each dataset should begin on a new page and should have as label the name of the dataset (dat1 or dat2). Your job is to fit the best ARIMA(p,d,q) model to each dataset that you
can. Your output should be in the following format. (Points will be deducted if it is not.)
• On the first page of output for each problem, you should first have a summary (labeled “Sum- mary”) that provides the model chosen, parameter estimates, standard errors, and p-values in that model. Specify explicitly if you exclude a constant term. For example, “I chose an ARIMA(1, 2, 3) model including a constant/intercept term. The parameter estimates were …”.
• After the summary, should be an explanation (labeled “Explanation”). Provide a clear expla- nation 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 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 explanation. (The output may be plots or output from various commands.) All of it should be clearly formatted, and labeled or described.
Finally, please refer to the original/raw (untransformed) time series as Xt in your descriptions and as xx in your code.
3. Analyze dat1.
4. Analyze dat2.