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Lecture Introductory econometrics for finance – Chapter 8: Modelling long-run relationship in finance

In this chapter, students will be able to understand: Highlight the problems that may occur if non-stationary data are used in their levels form, test for unit roots, examine whether systems of variables are cointegrated, estimate error correction and vector error correction models, explain the intuition behind Johansen’s test for cointegration,. | Chapter 8 Modelling long-run relationship in finance ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 1 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’ c Chris Brooks 2013 2 Value of R 2 for 1000 Sets of Regressions of a Non-stationary Variable on another Independent Non-stationary Variable 200 frequency 160 120 80 40 0 0.00 0.25 0.50 0.75 2 ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 3 Value of t-ratio on Slope Coefficient for 1000 Sets of Regressions of a Non-stationary Variable on another Independent Non-stationary Variable 120 100 frequency 80 60 40 20 0 –750 –500 –250 ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 0 t-ratio 250 500 750 4 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 = µ + yt−1 + ut (1) and the deterministic trend process: yt = α + βt + ut (2) where ut is iid in both cases. ‘Introductory Econometrics for Finance’ c Chris Brooks .