Two Reduced-Bias Autocorrelation Estimators: r F1 and r F2

Abstract

Among the problems associated with the application of time-series analysis to typical psychological data are difficulties in parameter estimation. For example, estimates of autocorrelation coefficients are known to be biased in the small-sample case. Previous work by the present authors has shown that, in the case of conventional autocorrelation estimators of ρ₁ the degree of bias is more severe than is predicted by formulas that are based on large-sample theory. Two new autocorrelation estimators, rF₁ and rF₂, were proposed; a Monte Carlo experiment was carried out to evaluate the properties of these statistics. The results demonstrate that both estimators provide major reduction of bias. The average absolute bias of rF₂ is somewhat smaller than that of rF₁ at all sample sizes, but both are far less biased than is the conventional estimator found in most time-series software. The reduction in bias comes at the price of an increase in error variance. A comparison of the properties of these estimators with those of other estimators suggested in 1991 shows advantages and disadvantages for each. It is recommended that the choice among autocorrelation estimators be based upon the nature of the application. The new estimator rF₂ is especially appropriate when pooling estimates from several samples.