TS Module 9: Non-stationary time series advanced HW

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NEAS	NEAS posted 12 Years Ago #12723 #
Supreme Being Group: Administrators Posts: 4.5K, Visits: 1.6K	TS Module 9: Non-stationary time series advanced HW (The attached PDF file has better formatting.) 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 Y_t = Y_t-1 + á + å_t, where á is a constant and å_t has a constant variance ó²_t. 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 X_t shares of the stock on each birthday, where X_t 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 Z_t shares of the stock on each birthday, where Z_t is a random walk = X_t + X_t-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. Attachments TS Module 9 nonstationary autoregresive process HW revised.pdf (2.5K views, 33.00 KB) 0
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mfhaus15	mfhaus15 posted 11 Years Ago #14186 #
Forum Newbie Group: Forum Members Posts: 1, Visits: 23	I was wondering how you know that if the total investment is the sum of annual stock purchases, you must take second differences to make the time series stationary. [NEAS: If total investment is the sum of annual stock purchases, then the first difference of total investment is the annual stock purchase. If stock purchases have a constant trend, then the first difference of stock purchases is stationary.] Edited 10 Years Ago by NEAS 0
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