Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series B, Pt. 3 , pp. 356--368

TESTS OF A RANDOM WALK MODEL AGAINST A CLASS OF REGRESSION MODELS AND THEIR POWERS

By

M. W. LESLIE CHANDRAKANTHA, *Claflin College*

J. S. MEHTA, *Temple University*

and

P. A. V. B. SWAMY, *Federal Reserve Board*

SUMMARY. This paper considers ratios of sample second moments about zero (or the respective sample means) of the differences of variables which are one and $k$ periods apart, with $k > 1$, and shows how the tests based on these ratios give strong evidence against random walk models or regression models with unknown functional forms.

*AMS (1980) subject classification.* 60J15, 62J02, 62J05, 62G10, 62F04, 62G35.

*Key words and phrases.* Random walks, regressions, ratios of variances, powers of tests.