T7 - STA4005B Time Series (2007-2008) Tutorial 7 (11/3,...

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Unformatted text preview: STA4005B Time Series (2007-2008) Tutorial 7 (11/3, 12/3) (Time & Venue: T9, BMS LT; W5, MMW 704) The partial autocorrelation function of AR(p) Initially, we may not know which order of autoregressive process (p) to fit to an observed time series. The partial autocorrelation is a device to determine the value of p . Consider AR( k ): t k t kk t k t k t k t a Z Z Z Z Z + + + + + = − − − − φ φ φ φ L 3 3 2 2 1 1 The Yule walker equations are k j kk j k j k j k j − − − − + + + + = ρ φ ρ φ ρ φ ρ φ ρ L 3 3 2 2 1 1 for K , 3 , 2 , 1 = j Thus ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ = ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ − − − k kk k k k k k ρ ρ ρ φ φ φ ρ ρ ρ ρ ρ ρ ρ M M M M L L L M O M M M L L 2 1 2 1 1 2 1 1 1 2 1 1 1 1 1 = 11 φ = 22 φ = 33 φ = kk φ 1 Model Specification: 1) Degree of differencing - d Differencing the time series until the time series fluctuates around a well-defined mean and its sample...
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T7 - STA4005B Time Series (2007-2008) Tutorial 7 (11/3,...

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