文档介绍：Chapter 7
Modelling long-run relationship in finance
© Chris Brooks 2002 陈磊 2004
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1 Stationarity and Unit Root Testing
The stationarity or otherwise of a series can strongly influence its behaviour and properties - . 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 R2 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.
do we need to test for Non-Stationarity?
© Chris Brooks 2002 陈磊 2004
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Value of R2 for 1000 Sets of Regressions of a Non-stationary Variable on another Independent Non-stationary Variable
© Chris Brooks 2002 陈磊 2004
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Value of t-ratio on Slope Coefficient for 1000 Sets of Regressions of a Non-stationary Variable on another Independent Non-stationary Variable
© Chris Brooks 2002 陈磊 2004
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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.
© Chris Brooks 2002 陈磊 2004
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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 > 1.
Typically, the explosive case is ignored and we use = 1 to characterise the non-stationarity because
> 1 does not describe many data series in economics and finance.
> 1 has an intuitively unappealing property: shocks to the system are not on