Let Y, be a stationary time series with autocovariance function Yr (s)a. Show that the new series X, = a + bt +Y, where a and b are fixed non-zero constants, is notstationary.b. Express the autocovariance function of AX, = X, - X-1 in terms of 7r (S) and show that this newseries is stationary.c. Show that if Y, is a moving average process of order 1, then the series AXt is not invertible and hasvariance larger than that of Y.

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MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Let Y, be a stationary time series with autocovariance function Yr (s). a. Show that the new series X, = a + bt +Y, where a and b are fixed non-zero constants, is not stationary. b. Express the autocovariance function of AX, = X,-X-1 in terms of 7r (5) and show that this new series is stationary.