{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online