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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 longrun 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 NonStationarity? • 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 “ tratios” 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 Nonstationary Variable on another Independent ‘Introductory Econometrics for Finance’ © Chris ‘Introductory Econometrics for Finance’ © Chris 44 Value of tratio on Slope Coefficient for 1000 Sets of Regressions of a Nonstationary Variable on another ‘Introductory Econometrics for Finance’ © Chris ‘Introductory Econometrics for Finance’ © Chris 55 Two types of NonStationarity • Various definitions of nonstationarity 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 nonstationarity: 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 NonStationarity • 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 nonstationarity 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 Nonstationarity: 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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 Spring '07
 ChrisBrooks
 Econometrics, Regression Analysis, Statistical hypothesis testing, Cointegration, Error correction model, Johansen test

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