TS Module 9: Non-stationary time series advanced HW
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Homework assignment: random walk time series
A bank firm offers a set of investments as lifetime birthday gifts. Each investment buys shares of a stock that follow a random walk. For simplicity, assume the random walk is arithmetic: the share price can be positive or negative. The share price is Yt = Yt-1 +
á + åt, where á is a constant and åt has a constant variance ó2t.
Investment #1 buys 100 shares of the stock on each birthday. The value of Investment #1 at time t is the value of all the shares bought so far. What is the time series followed by the value of Investment 1?
Investment #2 buys Xt shares of the stock on each birthday, where Xt is a white noise process with mean of 100 and standard deviation of 10. The value of Investment #2 at time t is the value of all the shares bought so far. What is the time series followed by the value of Investment #2?
Investment #3 buys Zt shares of the stock on each birthday, where Zt is a random walk = Xt + Xt-1. The value of Investment #3 at time t is the value of all the shares bought so far. What is the time series followed by the value of Investment #3?
The type of time series means the number of differences to make it stationary, not the parameters or the ARIMA form. For each investment, give a brief explanation of whether one needs to take first, second, or third differences to make the time series stationary.