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State‐space model for proxy‐based millennial reconstruction
Authors:Terry C K Lee  Min Tsao  Francis W Zwiers
Institution:1. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, Canada;2. Climate Research Division, Environment Canada, Toronto, ON, Canada
Abstract:It is important to study historical temperature time series prior to the industrial revolution so that one can view the current global warming trend from a long‐term historical perspective. Because there are no instrumental records of such historical temperature data, climatologists have been interested in reconstructing historical temperatures using various proxy time series. In this paper, the authors examine a state‐space model approach for historical temperature reconstruction which not only makes use of the proxy data but also information on external forcings. A challenge in the implementation of this approach is the estimation of the parameters in the state‐space model. The authors developed two maximum likelihood methods for parameter estimation and studied the efficiency and asymptotic properties of the associated estimators through a combination of theoretical and numerical investigations. The Canadian Journal of Statistics 38: 488–505; 2010 © 2010 Crown in the right of Canada
Keywords:State‐space model  Kalman filter  temperature reconstruction  MSC 2000: Primary 62M10  secondary 62M20
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