Statistics 4540/6571
Assignment #5: March 24, 2004
Due in class: April 5, 2004

• All problem and page numbers are from the textbook Time Series Analysis and its Applications.

1. This problem refers to the series jj.dat you used on Assignment #4.
   1. Create a time series plot of the first differences of the data. What do you notice?

   2. Fit an ARIMA $(1,1,0) \times (1,0,0)_4$ to the log-transformed data, and use this model to forecast the earnings per share for the 4 quarters of 1981. Make sure you report your forecasts on the data's original scale.

2. Read pages 215-216 of the text, along with the pages given out in class from Bloomfield's book, and write a 1 or 2 paragraph summary on the concepts of aliasing and the folding, or Nyquist frequency. You may draw a plot (by hand) if it helps your explanation.

3. Problem #3.9(a).

4. Problem #3.12.

5. Refer to the time series varve.ts on Assignment #1.
   1. Plot the series, sample ACF, raw periodogram and a smoothed periodogram of the series. The choice of values in the spans option of spec.pgram is up to you-as long as they're not too big or small.

   2. Describe the important features of the ACF and (smoothed) periodogram. Is some information available in only one of the plots?

   3. Find 95% confidence intervals for the two most important frequencies.

6. Grad Students Only. Read the material on pages 240, 246 and 247 on a tapered series.

   Then, solve problem #3.18.