Long Memory or Structural Breaks in Temperature and Proxy Time Series

Since the end of the last ice age the earth’s climate has enjoyed a period of relative stability. As the earth is now in a period of rising global temperatures a number of authors have considered the stochastic properties of time series of both atmospheric and oceanic temperatures from instrumental and proxy records on time scales of a few decades to several millenia in an effort to estimate the natural variability of the earth’s climate. These series almost universally exhibit the property of statistical long memory. Long memory time series were brought to prominence by H.E. Hurst in 1951 in his study of river flows. Since then the physical cause or causes of the so-called Hurst phenomena have remained elusive. Two sets of competing models have been proposed. The fractiona