On the Small Sample Distribution of the R/S Statistic

JEL Classification C15

Michael Harrison and Glenn Treacy

Department of Economics, Trinity College, Dublin 2, Ireland.


This paper gives an account of the R/S statistic and its known properties. It assesses the adequacy of the asymptotic distribution of R/S in the case of samples of small and moderate size, and suggests an improved approximation based on the beta distribution. The results indicate that the proposed beta approximation is superior to the asymptotic distribution for practical purposes. Hence a new table of critical values is presented as an alternative to that of Lo (1991).