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Unformatted text preview: / 62 Introduction Stationary Processes Nonstationary Processes Spurious Regressions Testing for Nonstationarity Cointegration F EC220 Review Lectures
Lecture 6
Bonsoo Koo May 11, 2010 Bonsoo Koo EC220 Review Lectures Introduction Stationary Processes Nonstationary Processes Spurious Regressions Testing for Nonstationarity Cointegration F
Today Today: Nonstationarity Stationary Processes
Nonstationary Processes
Spurious Regressions
Testing for Nonstationarity
Fitting models with Nonstationary Time Series 1 / 52 Introduction Stationary Processes Nonstationary Processes Spurious Regressions Testing for Nonstationarity Cointegration Stationary Processes
Xt is stationary if
E (Xt ) is independent of t .
V (Xt ) is independent of t .
Cov (Xt , Xt +s ) does not depend on t.
Consider:
Xt = β Xt −1 + εt
where β  < 1. Then
Corr (Xt , Xt +s ) = β s
This by deﬁnition is stationary. 2 / 52 Introduction Stationary Processes Nonstationary Processes SpuriousStationarity Differencefor Nonstationarity Cointegration
Trend Regressions Testing Stationarity Nonstationary Processes There are 2 types of nonstationary processes
Trend Stationary
Difference Stationary 3 / 52 Introduction Stationary Processes Nonstationary Processes SpuriousStationarity Differencefor Nonstationarity Cointegration
Trend Regressions Testing Stationarity Trend Stationarity
Trend stationary processes look something like:
Xt = β1 + β2 t + εt
So we have a deterministic time trend. The term trend
stationarity means that the process is stationary around the
trend. Such processes can be handled easily by removing the
time trend.
˜
Xt
ˆ
Xt ˆ
= Xt − Xt
= b1 + b2 t 4 / 52 Introduction Stationary Processes Nonstationary Processes SpuriousStationarity Differencefor Nonstationarity Cointegration
Trend Regressions Testing Stationarity Trend Stationarity
Trend stationary processes look something like:
Xt = β1 + β2 t + εt
So we have a deterministic time trend. The term trend
stationarity means that the process is stationary around the
trend. Such processes can be handled easily by removing the
time trend.
˜
Xt
ˆ
Xt ˆ
= Xt − Xt
= b1 + b2 t 5 / 52 Introduction Stationary Processes Nonstationary Processes SpuriousStationarity Differencefor Nonstationarity Cointegration
Trend Regressions Testing Stationarity Difference Stationarity In difference stationary processes, if nonstationarity is
stochastic rather than deterministic.
Xt = Xt −1 + εt
This is a random walk. E (Xt ) = X0 and Var (Xt ) = t σ 2 . So this
is nonstationary.
Adding a constant makes it a random walk with drift.
Xt = β + Xt −1 + εt
E (Xt ) = t β + X0 and Var (Xt ) = t σ 2 . 6 / 52 Introduction Stationary Processes Nonstationary Processes SpuriousStationarity Differencefor Nonstationarity Cointegration
Trend Regressions Testing Stationarity Difference Stationarity In difference stationary processes, if nonstationarity is
stochastic rather than deterministic.
Xt = Xt −1 + εt
This is a random walk. E (Xt ) = X0 and Var (Xt ) = t σ 2 . So this
is nons...
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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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