Robert Lund and Xueheng Shi

Changepoints are discontinuity times (abrupt changes) in a time-ordered sequence of data. In climate settings, changepoints often occur when measuring stations are relocated or gauges are changed. Moving a climate station even 100 yards, for example, can shift temperatures by several degrees, especially if the solar exposure of the new location differs. In the United States, first-order climate stations average roughly six relocations or gauge changes per century. In many instances, these change times are not known to users analyzing the records. Changepoint times can also be triggered by natural causes when weather patterns shift.

A single changepoint for a random sequence {X_t}^N_t = 1 of length N is an unknown time τ∈[{2,3,…,N} (time 1 is not allowed to be a changepoint) where X_t for t ≤ τ has a particular marginal distribution, and this distribution changes after t > τ. There are many ways in which the marginal distribution can change. Perhaps the simplest way allows series means to shift at the changepoint time, but keeps the same distribution type before and after the changepoint. While the mean shift case is the focus here, researchers have also studied shifts in process variabilities (volatilities) in finance and in autocovariances in speech recognition.

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