exercises for Thu Jan 27

1. We've started the course! On Thu Jan 20 I gave a broad introduction to the various time series themes we'll be working with, via key concepts and indication of models and methods; lots of detail will come in the coming few weeks.

2. We'll be needing the first three weeks of the course to go through be basics of Ch 1, with various footnotes and excursions.   

3. We'll be using the R package "astsa", so please jump into it, get familiar with its basic setup, read the vignette, have a look at a few datasets. In particular, check the dataset "jj" (Figure 1.1 in the book), try a few simple models, to see what goes on. In particular, try simple linear regression, and check residuals; identify in which ways that approach will not be good enough.

4. Prove formula (1.35) in the book, in detail, and apply it to the case where the correlation function is rho(h) = rho^h, with rho inside (-1,1).

5. Simulate a time series x_1, ..., x_n, with say n = 500, taking x_1 = eps_1 and x_i = rho x_{i-1} + eps_i for i = 2, 3, 4, ..., with the eps_i being iid N(0,1). Investigate the variance and correlation structure, and see how acf(xdata) behaves.

6. Do the book's exercises 1.4, 1.6, 1.20.