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Changepoint Detection in Climate Time Series with Long-Term Trends

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  • 1 Department of Mathematical Sciences, Clemson University, Clemson, South Carolina
  • | 2 Department of Statistics, The University of Missouri, Columbia, Missouri
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Abstract

Climate time series often have artificial shifts induced by instrumentation changes, station relocations, observer changes, etc. Climate time series also often exhibit long-term trends. Much of the recent literature has focused on identifying the structural breakpoint time(s) of climate time series—the so-called changepoint problem. Unfortunately, application of rudimentary mean-shift changepoint tests to scenarios with trends often leads to the erroneous conclusion that a mean shift occurred near the series' center. This paper examines this problem in detail, constructing some simple homogeneity tests for series with trends. The asymptotic distribution of the proposed statistic is derived; en route, an attempt is made to unify the asymptotic properties of the changepoint methods used in today's climate literature. The tests presented here are linked to the ubiquitous t test. Application is made to two temperature records: 1) the continental United States record and 2) a local record from Jacksonville, Illinois.

Corresponding author address: Robert Lund, Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975. E-mail: lund@clemson.edu

Abstract

Climate time series often have artificial shifts induced by instrumentation changes, station relocations, observer changes, etc. Climate time series also often exhibit long-term trends. Much of the recent literature has focused on identifying the structural breakpoint time(s) of climate time series—the so-called changepoint problem. Unfortunately, application of rudimentary mean-shift changepoint tests to scenarios with trends often leads to the erroneous conclusion that a mean shift occurred near the series' center. This paper examines this problem in detail, constructing some simple homogeneity tests for series with trends. The asymptotic distribution of the proposed statistic is derived; en route, an attempt is made to unify the asymptotic properties of the changepoint methods used in today's climate literature. The tests presented here are linked to the ubiquitous t test. Application is made to two temperature records: 1) the continental United States record and 2) a local record from Jacksonville, Illinois.

Corresponding author address: Robert Lund, Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-0975. E-mail: lund@clemson.edu
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