Yt 1 2 xt t where x and y are independent random walk

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Unformatted text preview: tationary. 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 . 7 / 52 Introduction Stationary Processes Nonstationary Processes SpuriousStationarity Differencefor Nonstationarity Cointegration Trend Regressions Testing Stationarity Difference Stationarity Suppose we have the following model: Xt = Xt −1 + εt The first difference of X is: ∆Xt = Xt − Xt −1 = εt This is stationary. So differencing removes the nonstationarity. Hence such processes are called difference stationary. 8 / 52 Introduction Stationary Processes Nonstationary Processes SpuriousStationarity Differencefor Nonstationarity Cointegration Trend Regressions Testing Stationarity Difference Stationarity Suppose we have the following model: Xt = Xt −1 + εt The first difference of X is: ∆Xt = Xt − Xt −1 = εt This is stationary. So differencing removes the nonstationarity. Hence such processes are called difference stationary. 9 / 52 Introduction Stationary Processes Nonstationary Processes SpuriousStationarity Differencefor Nonstationarity Cointegration Trend Regressions Testing Stationarity Difference Stationarity Suppose we have the following model: Xt = Xt −1 + εt The first difference of X is: ∆Xt = Xt − Xt −1 = εt This is stationary. So differencing removes the nonstationarity. Hence such processes are called difference stationary. 10 / 52 Introduction Stationary Processes Nonstationary Processes SpuriousStationarity Differencefor Nonstationarity Cointegration Trend Regressions Testing Stationarity Difference Stationarity If Xt is nonstationary and ∆Xt is stationary, then we have a process that is I (1). But if Xt and ∆Xt are nonstationary and ∆2 Xt is stationary,then we have a process that is I (2) and so on. We call these numbers the orders of integration. 11 / 52 Introduction Stationary Processes Nonstationary Processes SpuriousStationarity Differencefor Nonstationarity Cointegration Trend Regressions Testing Stationarity Difference Stationarity If Xt is nonstationary and ∆Xt is stationary, then we have a process that is I (1). But if Xt and Xt are nonstationary and ∆2 Xt is stationary,then we have a process that is I (2) and so on. We call these numbers the orders of integration. 12 / 52 Introduction Stationary Processes Nonstationary Processes SpuriousStationarity Differencefor Nonstationarity Cointegration Trend Regressions Testing Stationarity Difference Stationarity If Xt is nonstationary and ∆Xt is stationary, then we have a process that is I (1). But if Xt and ∆Xt are nonstationary and ∆2 Xt is stationary,then we have a process that is I (2) and so on. We call these numbers the orders of integration. 13 / 52 Introduction Stationary Processes Nonstationary Processes Spurious Regressions Testing for Nonstationarity Cointegration Spurious Regressions Why do we care about nonstationarity? Because it can mess up OLS! Refer to the famous simulations by Granger and Newbold. Yt = β1 + β2 Xt + εt where X and Y are independent random walk pr...
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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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