Autocorrelation and bias in short time series: An alternative estimator

The conventional first-order autocorrelation coefficient r(1) generates an empirical bias when it is applied to short time series. The properties of this estimator have been examined with a Monte Carlo simulation study using the MATLAB program (version 5.2). This study also analyzes the function of the empirical bias with the polynomic regression and derives a polynomic fitting model for different sample sizes. In this way, a new estimator that has been corrected by the absolute value of the fitting model (r(1)') is proposed. Having analyzed the statistical properties of the estimator r(1)', it is shown that the empirical bias generated by r(1)' is less in relationship to r(1) and r(1)+. The results of the study make it possible to verify that the mean squared error associated to the estimator r(1) is less than that of r(1). Thus, the coefficient r(1)' is recommended to estimate the lag-one autocorrelation coefficient in samples under 50 observations.