Nonlinear Time Series Analysis of Economic and Financial Data

Volume 1 of the series Dynamic Modeling and Econometrics in Economics and Finance pp 111-128

Unit-Root Tests and Excess Returns

  • Marie-Josée GodboutAffiliated withBank of Canada
  • , Simon van NordenAffiliated withÉcole des Hautes Études Commercial

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When introducing students to the modem theory of financial markets, it is common to characterize the behavior of the log of asset prices as martingales, and their excess returns as being serially uncorrelated or even unpredictable. This is consistent with Fama’s (1970) characterization of weak, semi-strong, and strong market efficiency. To be sure, there is an extensive literature documenting the deviations of asset prices from this characterization. Despite this, most would accept the proposition that asset prices contain a unit root in their time-series representation and that excess returns do not. Put another way, the stylized fact is that asset prices are integrated of order one (I(1)) and excess returns are integrated of order zero (I(0)). However, a small number of prominent recent papers have presented evidence that appears to reject this characterization in a surprising way. They show that, according to some tests, some excess returns appear to contain a unit root.