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Unformatted text preview: − 1)Xt −1 + εt
We run this regression with OLS and we look at the coefﬁcient
of (β2 − 1). The hypothesis now is:
H0 : β2 − 1 = 0 vs H1 : β2 − 1 < 0
The test statistic is the Augmented Dickey Fuller statistic. The
problem with this statistic is that is has low power. It is hard to
differentiate between processes where β2 = 1 which is
nonstationary and β2 = 0.95 which is stationary.
One can allow for a time trend and drift term as well. 34 / 52 Introduction Stationary Processes Nonstationary Processes Spurious Regressions Testing for Nonstationarity Cointegration
Autocorrelation function ADF ADF ∆Xt = (β2 − 1)Xt −1 + εt
We run this regression with OLS and we look at the coefﬁcient
of (β2 − 1). The hypothesis now is:
H0 : β2 − 1 = 0 vs H1 : β2 − 1 < 0
The test statistic is the Augmented Dickey Fuller statistic. The
problem with this statistic is that is has low power. It is hard to
differentiate between processes where β2 = 1 which is
nonstationary and β2 = 0.95 which is stationary.
One can allow for a time trend and drift term as well. 35 / 52 Introduction Stationary Processes Nonstationary Processes Spurious Regressions Testing for Nonstationarity Cointegration F Cointegration Consider the following true model:
Yt = β1 + β2 Xt + εt
Suppose that Y and X are both I(1). Can we do OLS? Yes! But
if we don’t know that this is the true model, how do we know
whether the coefﬁcients are valid or not? We can do a test of
cointegration 36 / 52 Introduction Stationary Processes Nonstationary Processes Spurious Regressions Testing for Nonstationarity Cointegration F Cointegration Consider the following true model:
Yt = β1 + β2 Xt + εt
Suppose that Y and X are both I(1). Can we do OLS? Yes! But
if we don’t know that this is the true model, how do we know
whether the coefﬁcients are valid or not? We can do a test of
cointegration 37 / 52 Introduction Stationary Processes Nonstationary Processes Spurious Regressions Testing for Nonstationarity Cointegration F Cointegration Consider the following true model:
Yt = β1 + β2 Xt + εt
Suppose that Y and X are both I(1). Can we do OLS? Yes! But
if we don’t know that this is the true model, how do we know
whether the coefﬁcients are valid or not? We can do a test of
cointegration 38 / 52 Introduction Stationary Processes Nonstationary Processes Spurious Regressions Testing for Nonstationarity Cointegration F Cointegration Consider the following true model:
Yt = β1 + β2 Xt + εt
Suppose that Y and X are both I(1). Can we do OLS? Yes! But
if we don’t know that this is the true model, how do we know
whether the coefﬁcients are valid or not? We can do a test of
cointegration 39 / 52 Introduction Stationary Processes Nonstationary Processes Spurious Regressions Testing for Nonstationarity Cointegration F Cointegration Yt = β1 + β2 Xt + εt
Two variables are cointegrated if they move together. If this is
true, then the error term in the regression should be stationary.
That is the idea behind the test for cointegration.
run the regression with OLS
gr...
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This document was uploaded on 03/12/2014 for the course ECON 202 at University of London University of London International Programmes (Distance Learning).
 Spring '13
 ChristopherDougherty
 Econometrics

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