Random variation often looks like a trend. The response in this exercise has n = 120 observations, as if 12 years of monthly data. The values of the response were simulated using random numbers so that Yt = Yt -1 + et with Y1 = e1 and et N(0,s2)
This type of random process is known as a random walk; the next value is the prior value plus random variation.
(a) Graph Yt versus t and ft a simple linear trend model. Without checking conditions for the SRM, does the slope appear to be statistically significant?
(b) According to the ft of the linear trend model, give a 95% confidence interval for E(Yt - Yt -1)? Does that interval agree with the structure of a random walk?
(c) How can one check that the linear trend model is not appropriate for these data?
(d) Do the prices of Exxon-Mobil (Exercise 33) appear as though they were produced by a random walk?