A1453
Title: Spatial clustering of big time series by Gibbs sampling and empirical BIC with an application to Australian rainfall
Authors: Yiyang Chen - University of Melbourne (Australia)
Guoqi Qian - The University of Melbourne (Australia) [presenting]
Abstract: Spatially distributed time series data arise ubiquitously in environmental monitoring, economics, and biomedical systems, where data from each spatial location evolves dynamically over time. Identifying spatial grouping structures among such series is fundamental which enables understanding of underlying patterns, regional similarities, and common temporal dynamics. However, spatially clustering time series remains a challenging problem due to the strong temporal dependence and high spatial dimensionality involved. A two-stage framework is developed to tackle this challenge. In the first stage, temporal dynamics are explicitly modelled under a seasonally adjusted autoregression (SAAR) framework. In the second stage, partitioning spatial locations is converted into partitioning the collection of the estimated parameter vectors in SAAR models corresponding to all spatial locations. Then partitioning the estimated parameter vectors is equivalent to generating random samples from a computationally intractable probability distribution defined on the sample space of the estimated parameter vectors and derived by empirical BIC. Generating such random samples can be implemented by a computationally feasible Gibbs sampling algorithm. It is shown that Gibbs sampling can find the optimal spatial partition with probability one. In the end, the developed method is evaluated through extensive simulation studies and further applied to a fused 22-year monthly Australian rainfall dataset.
