7-1 Chapter 7 Modelling long-run relationshil in finance c Chris Brooks2002陈磊2004
© Chris Brooks 2002 陈磊2004 7-1 Chapter 7 Modelling long-run relationship in finance
7-2 1 Stationarity and Unit Root Testing 1. 1Why 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 rz 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. c Chris Brooks2002陈磊2004
© Chris Brooks 2002 陈磊2004 7-2 1 Stationarity and Unit Root Testing • 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 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. 1.1Why do we need to test for Non-Stationarity?
Value of rl for 1000 Sets of Regressions of a Non- 7-3 stationary variable on another Independent non stationary Variable 200 160 120 80 0.25 0.50 0.75 c Chris Brooks2002陈磊2004
© Chris Brooks 2002 陈磊2004 7-3 Value of R2 for 1000 Sets of Regressions of a Nonstationary Variable on another Independent Nonstationary Variable
Value of t-ratio on Slope Coefficient for 1000 Sets 7-4 of regressions of a Non-stationary Variable on another Independent Non-stationary Variable 120 100 80 60 20 750-500-250 250500了50 c Chris Brooks2002陈磊2004
© Chris Brooks 2002 陈磊2004 7-4 Value of t-ratio on Slope Coefficient for 1000 Sets of Regressions of a Non-stationary Variable on another Independent Non-stationary Variable
7-5 1.2 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: y=+y1+ and the deterministic trend process y,=a+Bt+ut where u is iid in both cases c Chris Brooks2002陈磊2004
© Chris Brooks 2002 陈磊2004 7-5 1.2 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