Autoregressive density modeling with the Gaussian process mixture transition distribution

Matthew Heiner and Athanasios Kottas

Journal of Time Series Analysis, 2022, vol. 43, issue 2, 157-177

Abstract: We develop a mixture model for transition density approximation, together with soft model selection, in the presence of noisy and heterogeneous nonlinear dynamics. Our model builds on the Gaussian mixture transition distribution (MTD) model for continuous state spaces, extending component means with nonlinear functions that are modeled using Gaussian process (GP) priors. The resulting model flexibly captures nonlinear and heterogeneous lag dependence when several mixture components are active, identifies low‐order nonlinear dependence while inferring relevant lags when few components are active, and averages over multiple and competing single‐lag models to quantify/propagate uncertainty. Sparsity‐inducing priors on the mixture weights aid in selecting a subset of active lags. The hierarchical model specification follows conventions for both GP regression and MTD models, admitting a convenient Gibbs sampling scheme for posterior inference. We demonstrate properties of the proposed model with two simulated and two real time series, emphasizing approximation of lag‐dependent transition densities and model selection. In most cases, the model decisively recovers important features. The proposed model provides a simple, yet flexible framework that preserves useful and distinguishing characteristics of the MTD model class.

Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/jtsa.12603

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:jtsera:v:43:y:2022:i:2:p:157-177

Ordering information: This journal article can be ordered from
http://www.blackwell ... bs.asp?ref=0143-9782

Access Statistics for this article

Journal of Time Series Analysis is currently edited by M.B. Priestley

More articles in Journal of Time Series Analysis from Wiley Blackwell
Bibliographic data for series maintained by Wiley Content Delivery ().