Cointegration: the Engle and Granger approach
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1 Cointegration: the Engle and Granger approach Matthieu Stigler October 29, 2008 Matthieu Stigler Cointegration: () the Engle and Granger approach October 29, / 14
2 1 Stationarity 2 ARMA models for stationary variables 3 Some extensions of the ARMA model 4 Non-stationarity 5 Seasonality 6 Non-linearities 7 Multivariate models 8 Structural VAR models 9 Cointegration the Engle and Granger approach 10 Cointegration 2: The Johansen Methodology 11 Multivariate Nonlinearities in VAR models 12 Multivariate Nonlinearities in VECM models Matthieu Stigler Matthieu.Stigler@gmail.com Cointegration: () the Engle and Granger approach October 29, / 14
3 1 Lectures 2 Cointegration 1: the Engle and Granger approach Definition Economic interpretation Vector error correction model (VECM) The Engel-Granger theorem Common trend representation Estimation and testing VECM approach Testing Small Monte-Carlo study with R 3 Granger causality 4 Impulse response function VECM case Matthieu Stigler Matthieu.Stigler@gmail.com Cointegration: () the Engle and Granger approach October 29, / 14
4 Matthieu Stigler Cointegration: () the Engle and Granger approach October 29, / 14
5 Outline 1 Lectures 2 Cointegration 1: the Engle and Granger approach Definition Economic interpretation Vector error correction model (VECM) The Engel-Granger theorem Common trend representation Estimation and testing VECM approach Testing Small Monte-Carlo study with R 3 Granger causality 4 Impulse response function VECM case Matthieu Stigler Matthieu.Stigler@gmail.com Cointegration: () the Engle and Granger approach October 29, / 14
6 Matthieu Stigler Cointegration: () the Engle and Granger approach October 29, / 14
7 Outline 1 Lectures 2 Cointegration 1: the Engle and Granger approach Definition Economic interpretation Vector error correction model (VECM) The Engel-Granger theorem Common trend representation Estimation and testing VECM approach Testing Small Monte-Carlo study with R 3 Granger causality 4 Impulse response function VECM case Matthieu Stigler Matthieu.Stigler@gmail.com Cointegration: () the Engle and Granger approach October 29, / 14
8 Matthieu Stigler Cointegration: () the Engle and Granger approach October 29, / 14
9 Outline 1 Lectures 2 Cointegration 1: the Engle and Granger approach Definition Economic interpretation Vector error correction model (VECM) The Engel-Granger theorem Common trend representation Estimation and testing VECM approach Testing Small Monte-Carlo study with R 3 Granger causality 4 Impulse response function VECM case Matthieu Stigler Matthieu.Stigler@gmail.com Cointegration: () the Engle and Granger approach October 29, / 14
10 Matthieu Stigler Cointegration: () the Engle and Granger approach October 29, / 14
11 Outline 1 Lectures 2 Cointegration 1: the Engle and Granger approach Definition Economic interpretation Vector error correction model (VECM) The Engel-Granger theorem Common trend representation Estimation and testing VECM approach Testing Small Monte-Carlo study with R 3 Granger causality 4 Impulse response function VECM case Matthieu Stigler Matthieu.Stigler@gmail.com Cointegration: () the Engle and Granger approach October 29, / 14
12 Matthieu Stigler Cointegration: () the Engle and Granger approach October 29, / 14
13 Outline 1 Lectures 2 Cointegration 1: the Engle and Granger approach Definition Economic interpretation Vector error correction model (VECM) The Engel-Granger theorem Common trend representation Estimation and testing VECM approach Testing Small Monte-Carlo study with R 3 Granger causality 4 Impulse response function VECM case Matthieu Stigler Matthieu.Stigler@gmail.com Cointegration: () the Engle and Granger approach October 29, / 14
14 Outline 1 Lectures 2 Cointegration 1: the Engle and Granger approach Definition Economic interpretation Vector error correction model (VECM) The Engel-Granger theorem Common trend representation Estimation and testing VECM approach Testing Small Monte-Carlo study with R 3 Granger causality 4 Impulse response function VECM case Matthieu Stigler Matthieu.Stigler@gmail.com Cointegration: () the Engle and Granger approach October 29, / 14
15 Matthieu Stigler Cointegration: () the Engle and Granger approach October 29, / 14
16 What about log? Does the representation stays linear? Outline 1 Lectures 2 Cointegration 1: the Engle and Granger approach Definition Economic interpretation Vector error correction model (VECM) The Engel-Granger theorem Common trend representation Estimation and testing VECM approach Testing Small Monte-Carlo study with R 3 Granger causality Matthieu Stigler Matthieu.Stigler@gmail.com Cointegration: () the Engle and Granger approach October 29, / 14
17 Matthieu Stigler Cointegration: () the Engle and Granger approach October 29, / 14
18 Inference on the coint vector Cointegration { relationshiph: y t = α + βz t + ε 1t z t = ε 2t Cointegration: ε 1t and ε 2t is stationnary. But ε 1t and ε 2t can be: serially correlated correlated with each other Usual inference (t-test) is valid only under the assumption: Residuals are white noise 1 variable1 is exogene Matthieu Stigler Matthieu.Stigler@gmail.com Cointegration: () the Engle and Granger approach October 29, / 14
19 Matthieu Stigler Cointegration: () the Engle and Granger approach October 29, / 14
20 Usual restrictions on VAR model become: α β = 0 and short run coeff = 0 See Lutkepohl 262 Matthieu Stigler Matthieu.Stigler@gmail.com Cointegration: () the Engle and Granger approach October 29, / 14
21 Outline 1 Lectures 2 Cointegration 1: the Engle and Granger approach Definition Economic interpretation Vector error correction model (VECM) The Engel-Granger theorem Common trend representation Estimation and testing VECM approach Testing Small Monte-Carlo study with R 3 Granger causality 4 Impulse response function VECM case Matthieu Stigler Matthieu.Stigler@gmail.com Cointegration: () the Engle and Granger approach October 29, / 14
22 Say we have one cointegration relationship: β 1 Y 1t + β 2 Y 2t β K Y Kt = 0 or Y 1t = β 2 β 1 Y 2t... β K β K Y Kt = 0 What is the impact of Y 2 on Y 1? Is it β 2 β 1 like in standrad regresssion? No because Y 2 impacts also Y 3,..., Y K! So see impulse response function! Matthieu Stigler Matthieu.Stigler@gmail.com Cointegration: () the Engle and Granger approach October 29, / 14
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