Consider the following MA(2) process: 24 = Ut + a¡Ut–1 + a2Ut-2, where ut is a zero-mean white noise process with variance oʻ. (a) Calculate the conditional and unconditional means of z4, that is, E 24+1 and E[Z4]. (b) Calculate the conditional and unconditional variances of z4, that is, Var:[z4+1] and Var[z4]. (c) Derive the autocorrelation function of this process for all lags as functions of the parameters a and a2.

Consider the following MA(2) process: 24 = Ut + a¡Ut–1 + a2Ut-2, where ut is a zero-mean white noise process with variance oʻ. (a) Calculate the conditional and unconditional means of z4, that is, E 24+1 and E[Z4]. (b) Calculate the conditional and unconditional variances of z4, that is, Var:[z4+1] and Var[z4]. (c) Derive the autocorrelation function of this process for all lags as functions of the parameters a and a2.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider the following MA(2) process: 24 = Ut + a¡Ut–1 + a2Ut-2, where ut is a zero-mean white noise process with variance oʻ.
(a) Calculate the conditional and unconditional means of z4, that is, E 24+1 and E[Z4].
(b) Calculate the conditional and unconditional variances of z4, that is, Var:[z4+1] and Var[z4].
(c) Derive the autocorrelation function of this process for all lags as functions of the parameters a and a2.

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