Analysis of Short Time Series: Correcting for Autocorrelation

Abstract

Short time series are common in environmental and ecological studies. For sample sizes of 10 to 50, I examined the performance of methods for adjusting confidence intervals of the mean and parameters of a linear regression for autocorrelation. Similar analyses are common in econometric studies, and serious concerns have been raised about the adequacy of the common adjustment approaches, especially for estimating the slope of a linear regression when the explanatory variable has a time trend. Use of a bias—corrected estimate of the autocorrelation, either in an adjusted t test or in two—stage approach, outperformed other methods, including maximum likelihood and bootstrap estimators, in terms of confidence interval coverage. The bias correction was, however, sometimes awkward to apply. It was generally better to test for autocorrelation at the 0.5 level and use ordinary least squares if the test was not significant, although this pretesting mainly helped for weak autocorrelation and small sample sizes. For the best methods, the coverage was sometimes still substantially less than the stated 95% when autocorrelation was strong, even for sample sizes as large as 50. This was true for estimates of the mean, the regression intercept, and, when the explanatory variable had a time trend, the slope. Simulation results and an example show that different adjustment methods can produce substantially different estimates and confidence intervals. Cautious interpretation of confidence intervals and hypothesis tests is recommended.