T6 - ) ( = t a E and . 2 ) ( a t a Var σ = (a) Show that {...

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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 ( θφ = 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 φφ = L 2 2 1 1 ) ( q q B B B B θ θθ = 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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Example 2 Consider an infinite MA process ) ( 2 1 L + + + = t t t t a a C a Z , where C is a fixed constant,
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Unformatted text preview: ) ( = t a E and . 2 ) ( a t a Var σ = (a) Show that { is not second order stationary (weakly stationary). } t Z (b) Let . Show that { is a stationary MA(1) model. 1 − − = t t t Z Z W } t W (c) Find the autocorrelation function of { } t W 2 Example 3 Let 2 1 2 1 25 . 45 . 4 . − − − − + + + + = t t t t t t a a a Z Z Z , where ) ( = t a E and . 2 ) ( a t a Var σ = a) Write the model in terms of B and identify the model as a specific ARIMA model. b) Simplify the model and identify it as a specific ARIMA model. c) Determine if the model is stationary and / or invertible. 3...
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This note was uploaded on 11/02/2011 for the course STAT 4005 taught by Professor Wu,kaho during the Spring '08 term at CUHK.

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T6 - ) ( = t a E and . 2 ) ( a t a Var σ = (a) Show that {...

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