Chris Brooks_ Cointegration

Chris Brooks_ Cointegration - Click to edit Master subtitle...

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Unformatted text preview: Click to edit Master subtitle style Introductory Econometrics for Finance Chris Introductory Econometrics for Finance Chris 11 Chapter 7 Modelling long-run relationship in finance Introductory Econometrics for Finance Chris Introductory Econometrics for Finance Chris 22 Stationarity and Unit Root Testing Why do we need to test for Non-Stationarity? The stationarity or otherwise of a series can strongly influence its behaviour and properties - e.g. persistence of shocks will be infinite for nonstationary series Spurious regressions. If two variables are trending over time, a regression of one on the other could have a high R 2 even if the two are totally unrelated If the variables in the regression model are not stationary, then it can be proved that the standard assumptions for asymptotic analysis will not be valid. In other words, the usual t-ratios will not follow a t- distribution, so we cannot validly undertake hypothesis tests about the regression parameters. Introductory Econometrics for Finance Chris Introductory Econometrics for Finance Chris 33 Value of R 2 for 1000 Sets of Regressions of a Non-stationary Variable on another Independent Introductory Econometrics for Finance Chris Introductory Econometrics for Finance Chris 44 Value of t-ratio on Slope Coefficient for 1000 Sets of Regressions of a Non-stationary Variable on another Introductory Econometrics for Finance Chris Introductory Econometrics for Finance Chris 55 Two types of Non-Stationarity Various definitions of non-stationarity exist In this chapter, we are really referring to the weak form or covariance stationarity There are two models which have been frequently used to characterise non-stationarity: the random walk model with drift: yt = + yt- 1 + ut (1) and the deterministic trend process: yt = = + t + ut (2) where ut is iid in both cases. Introductory Econometrics for Finance Chris Introductory Econometrics for Finance Chris 66 Stochastic Non-Stationarity Note that the model (1) could be generalised to the case where yt is an explosive process: yt = = + yt- 1 + ut where M > 1. Typically, the explosive case is ignored and we use M = 1 to characterise the non-stationarity because M > 1 does not describe many data series in economics and finance. M > 1 has an intuitively unappealing property: shocks to the system are not only persistent through time, they are propagated so that a given shock will have an increasingly large influence. Introductory Econometrics for Finance Chris Introductory Econometrics for Finance Chris 77 Stochastic Non-stationarity: The Impact of Shocks To see this, consider the general case of an AR(1) with no drift: yt = yt- 1 + ut (3) Let M take any value for now....
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Chris Brooks_ Cointegration - Click to edit Master subtitle...

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