Quantifying the effects of temporal autocorrelation on climatological regression models using geostatistical techniques

Abstract

When time-dependent data are used in regression models, temporal autocorrelation violates ordinary least squares assumptions and impedes their proper testing and interpretation. The problem of temporal autocorrelation is exacerbated by the uneven temporal spacing inherent in many data sets. Using simple linear regression models of stomatal conductance as examples, we compare the effectiveness of two methods for removing temporal autocorrelation from regression models (first-differencing and Cochrane–Orcutt) and we introduce the geostatistical technique of semivariograms as a method for quantifying temporal autocorrelation in uneven time series. The Cochrane–Orcutt method proved more effective than first-differencing at removing autocorrelation and produced regression models without changing the significance of the independent variables. Semivariograms were used to quantify the time dependence of the unevenly spaced stomatal conductance time series. This technique revealed the dominant autocorrelation at the minimum time lag (0.5 h) and the 24-h periodicity caused by the climatological variables used in the model. We conclude that geostatistical techniques provide a robust method for quantifying temporal structure and periodicity in unevenly spaced time series.