chapt4y - NY Times 23 Sept 2008 time series of the day Stat...

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Unformatted text preview: NY Times 23 Sept 2008 - time series of the day Stat 153 - 23 Sept 2008 D. R. Brillinger Chapter 4 - Fitting t.s. models in the time domain sample autocovariance coefficient. Under stationarity, ... ) / 1 ( ) , ( N O c c Cov m k = ∞ → → N as k c E k ) ( ) ( γ ,... 2 , 1 , , / ) )( ( 1 =-- = +- = ∑ k N x x x x c k t k N t t k Estimated autocorrelation coefficient / c c r k k = large and . . ,..., If 1 N d i i x x N N r E k / 1 ) (- ≈ N r Var k / 1 ) ( ≈ asymptotically normal interpretation N / 2 : around CI 95% e approximat ± Uses of acf mixing (asymptotically independent)? MA(q)? Seasonal component? ergodic ∑ = ∞ → → N t t N X f E N X f 1 as y probabilit in )) ( ( / ) ( Estimating the mean ∑ = = N t t N X X 1 / unbiased , ) ( μ = X E ∑- =- + = 1 1 2 / )] ( ) 1 ( 2 1 [ ) ( N r N r N r X Var ρ σ Can be bigger or less than σ 2 /N N AR / ) 1 1 ( approx ) 1 ( For 2 α α σ- + Fitting an autoregressive, AR(p) Easy. Remember regression and least squares n i x Y i...
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chapt4y - NY Times 23 Sept 2008 time series of the day Stat...

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