The Random Walk of Stock Prices: Implications of Recent Nonpara- Metric Tests

This paper applies six recently developed nonparametric tests of serial independence to monthly US stock returns. Findings of previous studies based on the BDS test are supported since most of the new tests also reject the random walk hypothesis. Furthermore, power properties of the new tests are compared with those of the BDS test. The latter has much power against ARCH and GARCH alternatives whereas some of the more recent tests are superior against other alternatives. Finally, the power study of this paper shows, contrary to common belief, that ARCH and GARCH effects do not seem to explain rejection of the random walk. An early version of this paper was presented on a stock market workshop at Copenhagen Business School. Comments from Elroy Dimson and Richard Priestley are gratefully acknowledged. Gauss codes prepared for this paper are available upon request to the authors. †Economics Department, Purdue University. ‡Address: Department of Economics, Copenhagen Business School, Solbjerg Plads 3, C5, 2000 Frederiksberg, Denmark. Phone: +45 3815 2575. Fax: +45 3815 2576. E-mail: [email protected]. Abstract This paper applies six recently developed nonparametric tests of serial independence to monthly US stock returns. Findings of previous studies based on the BDS test are supported since most of the new tests also reject the random walk hypothesis. Furthermore, power properties of the new tests are compared with those of the BDS test. The latter has much power against ARCH and GARCH alternatives whereas some of the more recent tests are superior against other alternatives. Finally, the power study of this paper shows, contrary to common belief, that ARCH and GARCH effects do not seem to explain rejection of the random walk.This paper applies six recently developed nonparametric tests of serial independence to monthly US stock returns. Findings of previous studies based on the BDS test are supported since most of the new tests also reject the random walk hypothesis. Furthermore, power properties of the new tests are compared with those of the BDS test. The latter has much power against ARCH and GARCH alternatives whereas some of the more recent tests are superior against other alternatives. Finally, the power study of this paper shows, contrary to common belief, that ARCH and GARCH effects do not seem to explain rejection of the random walk.