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T11 - 5 2 1 1 = = a Z 1 2 = a σ t t a B Z B 3 1 1 2 1 −...

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STA4005B Time Series (2007-2008) Tutorial 11 (8/4, 9/4) (Time & Venue: T9, BMS LT; W5, MMW 704) Updating the ARIMA Forecasts If new information arrives, we need to re-calculate the forecasting L + + + + = + + + + 2 3 1 2 1 ) 1 ( ˆ t l t l t l t a a a l Z ψ ψ ψ µ L + + + + = + + 2 2 1 1 ) ( ˆ t l t l t l t a a a l Z ψ ψ ψ µ Then L + + + + = + + + + 1 2 1 1 1 ) ( ˆ t l t l t l t a a a l Z ψ ψ ψ µ ) ( 1 2 1 1 L + + + + = + + + t l t l t l a a a ψ ψ µ ψ Thus ) 1 ( ˆ )] ( ˆ [ ) ( ˆ 1 1 + + = + + l Z l Z Z l Z t t t l t ψ Example 3 Suppose and t t t t a Z Z Z + + = 2 1 5 . 0 1 . 1 5 11 , 9 2 1 = = Z Z and 10 3 = Z . Find and . ) 1 ( ˆ 3 Z ) 2 ( ˆ 3 Z If what is ? , 12 4 = Z ) 1 ( ˆ 4 Z 1
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