Financial data often resemble a random walk (Exercise 35), but the variation of financial prices typically increases with the price. To allow the variation to change, a geometric random walk has the form (with Yt 7 0)Yt = Yt -1 + et with Y1 = e1 and et ~ N(0, Y2t σ2)
(a) If a time series of prices follows a geometric random walk, then what is the form of the associated returns (Yt - Yt -1) / Yt -1?
(b) If prices follow a geometric random walk, then what is the best predictor for the next price Yn +1 given you know ŷ = 50.
(c) How does the predictor in (c) differ from the predictor that you would use if the prices were from a simple random walk?
(d) Do the prices of Exxon-Mobil (Exercise 33) appear as though they were produced by a geometric random walk?