Xt xt 1 t this is a random walk e xt x0 and var xt

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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).

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