Slides35-2010

# Slides35-2010 - Next, we defne a structural relationship...

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Non-Stationary Time Series and Cointegration: Lecture XXXV Charles B. Moss December 6, 2010 Charles B. Moss () Non-Stationary Time Series and Cointegration December 6, 2010 1 / 6

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1 Non-Stationary Time Series 2 Cointegration Charles B. Moss () Non-Stationary Time Series and Cointegration December 6, 2010 2 / 6
Non-Stationary Time Series Defning a non-stationary time series Δ z t = μ + ± t z t = t X i =1 Δ z t i (1) Infnite variance V ( z t )= t X i =1 E ± ± 2 t ² = t σ lim t →∞ V ( V t )= (2) Charles B. Moss () Non-Stationary Time Series and Cointegration December 6, 2010 3 / 6

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Dickey-Fuller regression y t =( φ 1) y t 1 + ± t (3) 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) These two series ( z t and y t ) independent in the tradiational sense (by construction). However, they will generate a signifcant relationship using ordinary least squares. z t = α 0 + α 1 y t + ν t (5) Charles B. Moss () Non-Stationary Time Series and Cointegration December 6, 2010 4 / 6
Cointegration

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Unformatted text preview: Next, we defne a structural relationship between two non-stationary 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) 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. Charles B. Moss () Non-Stationary Time Series and Cointegration December 6, 2010 5 / 6 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). Charles B. Moss () Non-Stationary Time Series and Cointegration December 6, 2010 6 / 6...
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## Slides35-2010 - Next, we defne a structural relationship...

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