According to the random walk hypothesis for stock prices, a stock
price yn follows a random walk model yn = yn−1 +vn, vn ∼ N(0,σ2).
(1) Assume that yn = 17,000 and σ
2 = 40,000 on a certain day.
Obtain the k-days ahead prediction of the stock price and its prediction error variance for k = 1,...,5.
(2) Obtain the probability that the stock price exceeds 17,000 yen
after four days have passed.
(3) Do actual stock prices satisfy the random walk hypothesis? If not,
consider a modification of the model.
(4) Estimate the trend of actual stock price data. (Nikkei 225
Japanese stock price data is available in the R package TSSS.)