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class13-642-08 - Econ 642 Monday May 12 class 13 Econ 642...

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Econ 642, Monday May 12, class 13 Econ 642, Monday May 12, class 13 Robert de Jong 1 1 Department of Economics Ohio State University Robert de Jong Econ 642, Monday May 12, class 13
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Econ 642, Monday May 12, class 13 AR(1) process x t = ρ 1 x t - 1 + e t : for stability, | ρ 1 | < 1 is needed Var ( x t ) = Var ( ρ 1 x t - 1 + e t ) = ρ 2 1 Var ( y t - 1 ) + σ 2 so Var ( y t ) = σ 2 / ( 1 - ρ 2 1 ) Robert de Jong Econ 642, Monday May 12, class 13
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Econ 642, Monday May 12, class 13 Highly persistent series in regression analysis y t = y t - 1 + e t random walk Var ( y t ) = Var ( e t ) + Vare t - 1 ) + ... + Var ( e 1 ) = σ 2 t Variance explodes Figure 11.1: picture of a random walk Robert de Jong Econ 642, Monday May 12, class 13
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Econ 642, Monday May 12, class 13 Random walk, I(1), or unit root process y t = y t - 1 + e t Random walk with drift: y t = α 0 + y t - 1 + e t First difference Δ y t is stationary In the presence of unit roots, usual t-values and tests may not be correct! Robert de Jong Econ 642, Monday May 12, class 13
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Econ 642, Monday May 12, class 13 Deciding whether a series is I(1) Statistical tests: Chapter 18 Informal test: looking at the first order autocorrelation
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