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

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Non-Stationary Time Series and Cointegration: Lecture XXXV Charles B. Moss December 6, 2010 I. Non-Stationary Time Series A. Defning a non-stationary time series Δ z t = μ + ± t z t = t X i =1 Δ z t i (1) B. Infnite variance V ( z t )= t X i =1 E ± ± 2 t ² = 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 X i =0 Δ z t i = t X i =0 ( μ z + ± 1 t ) y t = t X i =0 Δ y t i = t X 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 signi±cant rela- tionship using ordinary least squares. z t = α 0 + α 1 y t + ν t (5) II. Cointegration A. Next, we de±ne a structural relationship between two non-stationary
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Unformatted text preview: time series x t = 01 + 11 z t + 1 t w t = 02 + 12 z t + 2 t z t = t X i =0 z t i = t X i =0 ( z + 1 t ) (6) B. This common factor yields a structural relationship z t = w t 02 12 2 t (7) In fact we could assume that 02 0 and 12 1. C. At the least x t = 01 02 12 + 11 12 w t + [ 1 t 12 2 t ] x t = + 1 w t + t (8) The critical point is that the variance in Equation 8 is bounded (or the error is stationary). 2...
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This note was uploaded on 07/15/2011 for the course AEB 6180 taught by Professor Staff during the Spring '10 term at University of Florida.

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

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