Question: 1. ARMA(1,1). Consider the ARMA(1,1) model xt = xt1 t t1, where 1 < < 1, 1 < < 1, and t N(0,2), independently across

1. ARMA(1,1). Consider the ARMA(1,1) model xt = xt1 t t1, where 1 < < 1, 1 < < 1, and t N(0,2), independently across time. (a) Show that xt can be represented as an infinite-order auto-regression: x t = ! a j w t j , j=0 wherewt iidN(0,1),anda0 =,a1 =( ),andaj 1 =aj forj>1. (b) What is the variance of x? (c) What is the covariance of xt and xt1? (d) What is the autocorrelation function of xt? (e) What configuration of parameter values generates positive autocorrelations

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