On the Alignment and Merging of Multiple Time Series Fragments
K. Mukherjee, Robert H. Shumway, Kenneth L. Verosub · 2003
Abstract: In the investigation of possible surrogates for long-term temperature records, it is often the case that there are only fragmen-tary time series segments available with unknown beginning and ending dates. Often, there will be some time-calibrated segments available for matching purposes. Examples are tree ring thicknesses (Fritts, 1991), or glacial varve chronologies (Shumway and Verosub, 1993), which are often used as surrogates for paleoclimatic temperature. We consider here a speci¯c local least squares criterion for aligning multiple time series fragments and show the consistency and asymptotic normality of the time-lag estimator. We apply the criterion to the problem of align-ing 50 glacial varve fragments, collected over a period of 3000 years. A state-space model with additive ¯xed e®ects and a random walk signal is used to construct a 3000-year surrogate for global temperature. The signal is compared to the current global temperature series and we note that the current trend is not that unusual when compared to speci¯c segments of the long-term signal.