Important model for time series data Let X1, X2, be a sequence of independent random variables all having the same distribution with E(X i ) and Var(X i ) 2 0 For n 1 define the new random variable Y n X n 1 X n 1 2 X n 2 Find the correlation between Y n and Y n j when a) j 3, b) j 1, c) j 2

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Question: Important model for time series data. Let X1, X2, . . . be a sequence of independent random variables all having the same distribution with

Important model for time series data. Let X1, X2, . . . be a sequence of independent random variables all having the same distribution with E(X_i) = and Var(X_i) = ² > 0. For n 1 define the new random variable Y_n = X_n + ₁X_n+1 + ₂X_n+2. Find the correlation between Y_n and Y_n+jwhen a) j 3, b) j = 1, c) j = 2.

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