Fewer jumps, less memory: Homogenized temperature records and long memory

Abstract

Air temperature records are commonly subjected to inhomogeneities, e.g., sudden jumps caused by a relocation of the measurement station or by installing a new type of shelter. We study the effect of these inhomogeneities on the estimation of the Hurst exponent and show that they bias the estimates toward larger values. The Hurst exponent is a parameter to measure long-range dependence (LRD), which is a characteristic frequently used to describe the natural variability of temperature records. Analyzing a set of temperature time series before and after homogenization with respect to LRD, we find that the average Hurst exponent is clearly reduced for the homogenized series. To test whether (1) jumps cause this positive bias and (2) the homogenization does not artificially reduce the Hurst exponent estimates, we perform a simulation study. This test shows that inhomogeneities in the form of jumps bias the Hurst exponent estimation and that the homogenization procedure is able to remove this bias, leaving the Hurst exponent unchanged. This result holds for fractional autoregressive integrated moving average (FARIMA)-based as well as for detrended fluctuation analysis-based estimation. We conclude that the use of homogenized series is necessary to prevent misleading conclusions about the dependence structure and thus about subsequent analysis such as trend tests. Copyright 2008 by the American Geophysical Union.