# The hypothesis now is h0 2 1 0 vs h1 2 1 0 the test

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Unformatted text preview: elation function given by ρ(s) = ˆ ¯ ¯ (Xt − X )(Xt +s − X ) ¯ (Xt − X )2 ¯ (Xt +s − X )2 If the |β | &lt; 1 then this quantity approximates the true autocorrelation function. 26 / 52 Introduction Stationary Processes Nonstationary Processes Spurious Regressions Testing for Nonstationarity Cointegration Autocorrelation function ADF Autocorrelation function 27 / 52 Introduction Stationary Processes Nonstationary Processes Spurious Regressions Testing for Nonstationarity Cointegration Autocorrelation function ADF Autocorrelation function 28 / 52 Introduction Stationary Processes Nonstationary Processes Spurious Regressions Testing for Nonstationarity Cointegration Autocorrelation function ADF Autocorrelation function The problems are It is hard to differentiate between processes where β2 = 1 which is nonstationary and β2 = 0.95 which is stationary. It is hard to interpret strange graphs which may result from random walk 29 / 52 Introduction Stationary Processes Nonstationary Processes Spurious Regressions Testing for Nonstationarity Cointegration Autocorrelation function ADF ADF Suppose we have the model: Xt = β2 Xt −1 + εt We would like to test the hypothesis: H0 : β2 = 1 vs H1 : β2 &lt; 1 Note that we are not interested in negative unit roots or β &gt; 1. To test this hypothesis, we use a trick - we can transform the equation: ∆Xt = (β2 − 1)Xt −1 + εt 30 / 52 Introduction Stationary Processes Nonstationary Processes Spurious Regressions Testing for Nonstationarity Cointegration Autocorrelation function ADF ADF Suppose we have the model: Xt = β2 Xt −1 + εt We would like to test the hypothesis: H0 : β2 = 1 vs H1 : β2 &lt; 1 Note that we are not interested in negative unit roots or β &gt; 1. To test this hypothesis, we use a trick - we can transform the equation: ∆Xt = (β2 − 1)Xt −1 + εt 31 / 52 Introduction Stationary Processes Nonstationary Processes Spurious Regressions Testing for Nonstationarity Cointegration Autocorrelation function ADF ADF Suppose we have the model: Xt = β2 Xt −1 + εt We would like to test the hypothesis: H0 : β2 = 1 vs H1 : β2 &lt; 1 Note that we are not interested in negative unit roots or β &gt; 1. To test this hypothesis, we use a trick - we can transform the equation: ∆Xt = (β2 − 1)Xt −1 + εt 32 / 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 &lt; 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. 33 / 52 Introduction Stationary Processes Nonstationary Processes Spurious Regressions Testing for Nonstationarity Cointegration Autocorrelation function ADF ADF ∆Xt = (β2...
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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).

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