Recursive mean adjustment in time-series inferences

When time-series data are positively autocorrelated, mean adjustment using the overall sample mean causes biases for sample autocorrelations and parameter estimates, which decreases the coverage probabilities of confidence intervals. A new method for mean adjustment is proposed, in which a datum at a time is adjusted for the mean through the partial sample mean, the average of data up to the time point. The method is simple and reduces the biases of the parameter estimators and the sample autocorrelations when data are positively autocorrelated. The empirical coverage probabilities of the confidence intervals of the autoregressive coefficient become quite close to the nominal level.