Fearnhead, Paul; Wyncoll, David; Tawn, Jonathan A sequential smoothing algorithm with linear computational cost. (English) Zbl 1406.62093 Biometrika 97, No. 2, 447-464 (2010). Summary: We propose a new particle smoother that has a computational complexity of \(O(N)\), where \(N\) is the number of particles. This compares favourably with the \(O(N^{2})\) computational cost of most smoothers. The new method also overcomes some degeneracy problems in existing algorithms. Through simulation studies we show that substantial gains in efficiency are obtained for practical amounts of computational cost. It is shown both through these simulation studies, and by the analysis of an athletics dataset, that our new method also substantially outperforms the simple filter-smoother, the only other smoother with computational cost that is \(O(N)\). Cited in 25 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62F15 Bayesian inference 62L10 Sequential statistical analysis 62M20 Inference from stochastic processes and prediction 60G70 Extreme value theory; extremal stochastic processes Keywords:extreme value theory; forward-backward algorithm; particle filtering; particle smoothing; two-filter formula PDFBibTeX XMLCite \textit{P. Fearnhead} et al., Biometrika 97, No. 2, 447--464 (2010; Zbl 1406.62093) Full Text: DOI Link