Abstract
We introduce statespace models where the functionals of the observational and the evolutionary equations are unknown, and treated as random functions evolving with time. Thus, our model is nonparametric and generalizes the traditional parametric statespace models. This random function approach also frees us from the restrictive assumption that the functional forms, although timedependent, are of fixed forms. The traditional approach of assuming known, parametric functional forms is questionable, particularly in statespace models, since the validation of the assumptions require data on both the observed time series and the latent states; however, data on the latter are not available in statespace models. We specify Gaussian processes as priors of the random functions and exploit the "lookup table approach" of \ctn{Bhattacharya07} to efficiently handle the dynamic structure of the model. We consider both univariate and multivariate situations, using the Markov chain Monte Carlo (MCMC) approach for studying the posterior distributions of interest. In the case of challenging multivariate situations we demonstrate that the newly developed Transformationbased MCMC (TMCMC) of \ctn{Dutta11} provides interesting and efficient alternatives to the usual proposal distributions. We illustrate our methods with a challenging multivariate simulated data set, where the true observational and the evolutionary equations are highly nonlinear, and treated as unknown. The results we obtain are quite encouraging. Moreover, using our Gaussian process approach we analysed a real data set, which has also been analysed by \ctn{Shumway82} and \ctn{Carlin92} using the linearity assumption. Our analyses show that towards the end of the time series, the linearity assumption of the previous authors breaks down.
Original language  English 

Pages (fromto)  35  48 
Number of pages  14 
Journal  Statistical Methodology 
Volume  21 
Early online date  4 Mar 2014 
DOIs  
Publication status  Published  1 Nov 2014 
Bibliographical note
This version contains much greater clarification of the lookup table idea and a theorem regarding this is also proven and included in the supplement. Will appear in Statistical MethodologyKeywords
 stat.ME
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Sandipan Roy
 Department of Mathematical Sciences  Senior Lecturer
 Centre for Mathematics and Algorithms for Data (MAD)
 EPSRC Centre for Doctoral Training in Statistical Applied Mathematics (SAMBa)
Person: Research & Teaching