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T6 - = t a E and 2 a t a Var σ =(a Show that is not second...

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STA4005B Time Series (2007-2008) Tutorial 6 (26/2, 27/2) (Time & Venue: T9, BMS LT; W5, MMW 704) Definition: A series { is said to follow an integrated autoregressive moving average model if the difference is a stationary ARMA process. If W } t Z th d t d t Z W = t is ARMA(p, q), we say that { } t Z is ARIMA(p, d, q). In general, the ARIMA(p, d, q) model can be expressed as t t d a B Z B B ) ( ) ( ) 1 ( θ φ = where the stationary AR operator and the invertible MA operator share no common factors. This is useful form for identifying models. p p B B B B φ φ φ φ = L 2 2 1 1 ) ( q q B B B B θ θ θ θ = L 2 2 1 1 ) ( Example 1 Given a process , identify the model as a specific ARIMA model. t t t t a Z Z Z + = 2 1 25 . 0 25 . 1 1

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