Let xt follow a structural time series model of the form: X{ = U + &...

 

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Let xt follow a structural time series model of the form: X{ = U + & με = αμ–1 + 1 + 0 nt = ßnt-1+ut (5a) (5b) (5c) where the three shocks ut, Vt, and &t are each WN(0, 1) and are also mutually uncorre- lated at all time horizons. (a) What type of ARMA(p, q) model do the relations in (5) imply for x? Use time series algebra to prove your answer. Let xt follow a structural time series model of the form: X{ = U + & με = αμ–1 + 1 + 0 nt = ßnt-1+ut (5a) (5b) (5c) where the three shocks ut, Vt, and &t are each WN(0, 1) and are also mutually uncorre- lated at all time horizons. (a) What type of ARMA(p, q) model do the relations in (5) imply for x? Use time series algebra to prove your answer.

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