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Unformatted text preview: STAT 420 Examples for 11/29/2007 Fall 2007 1. Calculate r 1 and r 2 for the time series 16 22 19 25 18 ( Note: In practice reliable autocorrelation estimates are only obtained from series consisting of approximately 50 observations or more. ) r k = ( ) ( ) ( ) & & = = + N N t t k t k t t y y y y y y 1 2 1 PACF Corr ( Y t , Y t + k  Y t + 1 , … , Y t + k – 1 ) Consider a regression type model Y t + k = φ k 1 Y t + k – 1 + φ k 2 Y t + k – 2 + … + φ k k Y t + e t + k ↓ Consider Cov ( … , Y t + k – j ), j = 1, 2, … , k . Divide by γ : & ρ 1 = φ k 1 ρ + φ k 2 ρ 1 + … + φ k k ρ k – 1 ρ 2 = φ k 1 ρ 1 + φ k 2 ρ + … + φ k k ρ k – 2 … ρ k = φ k 1 ρ k – 1 + φ k 2 ρ k – 2 + … + φ k k ρ PACF ( k ) = Corr ( Y t , Y t + k  Y t + 1 , … , Y t + k – 1 ) = φ k k . k = 1 : ρ 1 = φ 1 1 ρ = φ 1 1 φ 1 1 = ρ 1 k = 2 : ρ 1 = φ k 1 ρ + φ k 2 ρ 1 ρ 2 = φ k 1 ρ 1 + φ k 2 ρ φ 2 1 = 2 1 2 1 1 1 ρ ρ ρ ρ φ 2 2 = 2 1 2 1 2 1 ρ ρ ρ and so on… AR(1) MA(1) ρ k = φ k ρ 1 = 2 1 θ θ + ρ k = 0, k > 1 φ...
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This note was uploaded on 04/29/2010 for the course STAT stat 420 taught by Professor Stepanov during the Spring '07 term at University of Illinois at Urbana–Champaign.
 Spring '07
 STEPANOV
 Correlation

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