Abstract
ABSTRACTState space models are well-known for their versatility in modeling dynamic systems that arise in various scientific disciplines. Although parametric state space models are well studied, nonparametric approaches are much less explored in comparison. In this article we propose a novel Bayesian nonparametric approach to state space modeling, assuming that both the observational and evolutionary functions are unknown and are varying with time; crucially, we assume that the unknown evolutionary equation describes dynamic evolution of some latent circular random variable. Based on appropriate kernel convolution of the standard Weiner process, we model the time-varying observational and evolutionary functions as suitable Gaussian processes that take both linear and circular variables as arguments. Additionally, for the time-varying evolutionary function, we wrap the Gaussian process thus constructed around the unit circle to form an appropriate circular Gaussian process. We show that our process thus cr...
Highlights
1.1 Flexibility of state space modelsThe versatility of state space models is clearly reflected from their utility in multifarious disciplines such as engineering, finance, medicine, ecology, statistics, etc
One reason for such widespread use of state space models is their inherent flexibility which allows modeling complex dynamic systems through the underlying latent states associated with an “evolutionary equation” and an “observational equation” that corresponds to the observed dynamic data
This has been possible because of our nonparametric ideas and because our model allows the unknown observational and the evolutionary function based on Gaussian processes to change with time
Summary
The versatility of state space models is clearly reflected from their utility in multifarious disciplines such as engineering, finance, medicine, ecology, statistics, etc. When both the linear and circular time series data are available, Holzmann et al (2006) consider hidden Markov models in a discrete mixture context to statistically analyse such data sets. Our aim in this article is to propose a novel nonparametric state space approach when the circular time series data are unobserved, even though they are known to affect the available linear time series data
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