Consider the process {X} satisfying the recursion X = 0.5X_1+0.5X2+6 where {} is a sequence of...

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Consider the process {X} satisfying the recursion X = 0.5X_1+0.5X2+6 where {} is a sequence of independent random variables with mean zero and unit variance. Show that {X} is an ARIMA (p,d,q) process, by checking that Adxt is a covariance stationary and invertible ARMA processes, for some d = 0, 1, 2,.... Specify p, d and q. [50%] Consider a covariance stationary GARCH(1,1) process for an excess return series {rt}, where Tt+1 =0++12+1 04+1 == w + ar + Bo 1-1 where {+} is a sequence of independent standard normal random variables, w > 0 and a > 0, > 0, a + <1. Show that the process {rt} is uncorrelated but not independent. [50%] Consider the process {X} satisfying the recursion X = 0.5X_1+0.5X2+6 where {} is a sequence of independent random variables with mean zero and unit variance. Show that {X} is an ARIMA (p,d,q) process, by checking that Adxt is a covariance stationary and invertible ARMA processes, for some d = 0, 1, 2,.... Specify p, d and q. [50%] Consider a covariance stationary GARCH(1,1) process for an excess return series {rt}, where Tt+1 =0++12+1 04+1 == w + ar + Bo 1-1 where {+} is a sequence of independent standard normal random variables, w > 0 and a > 0, > 0, a + <1. Show that the process {rt} is uncorrelated but not independent. [50%]