chapt3x

chapt3x - 3 mo treasury yield borrowing costs Dow...

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Unformatted text preview: 3 mo treasury yield borrowing costs Dow industrials NY Times 18 Sept 2008 front page Stat 153 - 16 Sept 2008 D. R. Brillinger Chapter 3 mean function )] ( [ ) ( t X E t = μ variance function )] ( [ ) ( 2 t X Var t = σ autocovariance ) ( ), ( ( ) , ( 2 1 2 1 t X t X Cov t t = γ Strictly stationary Normal/gaussian - all joint distributions jointly normal Wide sense stationary vs. second-order μ μ = ) ( t 2 2 ) ( σ σ = t )] ( ), ( [ ) ( τ τ γ + = t X t X Cov lag : ), ( / ) ( ) ( τ γ τ γ τ ρ = Properties of autocovariance ) ( ) ( τ γ τ γ- = 1 | ) ( | ≤ τ γ Useful models Purely random Building block , , 1 ) ( ≠ = = = k k k ρ ,... 2 / , 1 / , , ) , ( ) ( 2- +- + = = = = = + k k Z Z Cov k Z k t t σ γ Random walk not stationary , 1 = + =- X Z X X t t t μ t X E t = ) ( 2 ) ( Z t t X Var σ = random purely Z X X X t t t t , 1 =- = ∇- ∑ = = t i i t Z X 1 * ) ( ) ( ) ( Y bE X aE bY aX E + = + ) ( ) , ( 2 ) ( ) ( 2 2 Y Var b Y X abCov X Var a bY aX Var + + = + ) , ( ) , ( ) , ( ) , ( ) , ( V Y bdCov U Y bcCov V X adCov U X acCov dV cU bY aX Cov + + + = + + Moving average...
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chapt3x - 3 mo treasury yield borrowing costs Dow...

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