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Journal of Statistical Theory and Practice

, Volume 11, Issue 4, pp 693–718 | Cite as

Nonparametric dynamic state space modeling of observed circular time series with circular latent states: A Bayesian perspective

  • Satyaki Mazumder
  • Sourabh Bhattacharya
Article

Abstract

Circular time series have received relatively little attention in statistics, and modeling complex circular time series using the state space approach is nonexistent in the literature. In this article we introduce a flexible Bayesian nonparametric approach to state-space modeling of observed circular time series where even the latent states are circular random variables. Crucially, we assume that the forms of the observational and evolutionary functions, both of which are circular in nature, are unknown and time-varying. We model these unknown circular functions by appropriate wrapped Gaussian processes having desirable properties. We develop an effective Markov-chain Monte Carlo strategy for implementing our Bayesian model by judiciously combining Gibbs sampling and Metropolis–Hastings methods. Validation of our ideas with a simulation study and two real bivariate circular time-series data sets, where we assume one of the variables to be unobserved, revealed very encouraging performance of our model and methods. We finally analyze a data set consisting of directions of whale migration, considering the unobserved ocean current direction asthe latent circular process of interest. The results thatweobtain are encouraging, and the posterior predictive distribution of the observed process correctly predicts the observed whale movement.

Keywords

Circular time series latent circular process look-up table Markov-chain Monte Carlo state-space model wrapped Gaussian process 

AMS Subject Classification

62M10 65C05 

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Supplementary material

42519_2017_1305922_MOESM1_ESM.pdf (224 kb)
Supplement to “Nonparametric Dynamic State Space Modeling of Observed Circular Time Series with Circular Latent States: A Bayesian Perspective”

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Copyright information

© Grace Scientific Publishing, 20 Middlefield Ct, Greensboro, NC 27455 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsIndian Institute of Science Education and Research KolkataKolkataIndia
  2. 2.Interdisciplinary Statistical Research UnitIndian Statistical InstituteKolkataIndia

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