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Lecture35-2010 - time series x t = α 01 α 11 z t ν 1 t w...

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Non-Stationary Time Series and Cointegration: Lecture XXXV Charles B. Moss December 6, 2010 I. Non-Stationary Time Series A. Defining a non-stationary time series Δ z t = μ + t z t = t i =1 Δ z t i (1) B. Infinite variance V ( z t ) = t i =1 E 2 t = lim t →∞ V ( V t ) = (2) C. Dickey-Fuller regression y t = ( φ 1) y t 1 + t (3) D. Spurious regression z t = t i =0 Δ z t i = t i =0 ( μ z + 1 t ) y t = t i =0 Δ y t i = t i =0 ( μ y + 2 t ) (4) 1
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AEB 6571 Econometric Methods I Professor Charles B. Moss Lecture XXXV Fall 2010 These two series ( z t and y t ) independent in the tradiational sense (by construction). However, they will generate a significant rela- tionship using ordinary least squares. z t = α 0 + α 1 y t + ν t (5) II. Cointegration A. Next, we define a structural relationship between two non-stationary
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Unformatted text preview: time series x t = α 01 + α 11 z t + ν 1 t w t = α 02 + α 12 z t + ν 2 t z t = t X i =0 Δ z t − i = t X i =0 ( μ z + ± 1 t ) (6) B. This common factor yields a structural relationship z t = w t − α 02 α 12 − ν 2 t (7) In fact we could assume that α 02 → 0 and α 12 → 1. C. At the least x t = ± α 01 − α 02 α 12 ² + α 11 α 12 w t + [ ν 1 t − α 12 ν 2 t ] x t = β + β 1 w t + ν ∗ t (8) The critical point is that the variance in Equation 8 is bounded (or the error is stationary). 2...
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