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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 Spring '13
 ChristopherDougherty
 Econometrics, Regression Analysis, β2 Xi, Exam Practice Question, Past Exam Practice

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