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Bayesian Nonparametric Analysis of Multivariate Time Series: A Matrix Gamma Process Approach [article]

Alexander Meier, Claudia Kirch, Renate Meyer
2018 arXiv   pre-print
While there is an increasing amount of literature about Bayesian time series analysis, only a few Bayesian nonparametric approaches to multivariate time series exist.  ...  In this work, we present a related approach for multivariate time series, with matrix-valued mixture weights induced by a Hermitian positive definite Gamma process.  ...  Therefore, with the aim of proving posterior consistency of a nonparametric Bayesian approach to multivariate time series, we extend the Bernstein-Dirichlet process prior of Choudhuri et al. (2004a)  ... 
arXiv:1811.10292v1 fatcat:tsy5754qhrfivebw27dpgogefm

Nonparametric Bayesian Modeling of Multimodal Time Series [chapter]

Xuefeng Zhou, Hongmin Wu, Juan Rojas, Zhihao Xu, Shuai Li
2020 Nonparametric Bayesian Learning for Collaborative Robot Multimodal Introspection  
In this chapter, we take a Bayesian nonparametric approach in defining a prior on the hidden Markov model that allows for flexibility in addressing the problem of modeling the complex dynamics during robot  ...  Zhou et al., Nonparametric Bayesian Learning for Collaborative Robot Multimodal Introspection, https://doi.  ...  Nonparametric Bayesian Modeling of Multimodal Time Series Nonparametric Bayesian Modeling of Multimodal Time Series Nonparametric Bayesian Modeling of Multimodal Time Series Nonparametric  ... 
doi:10.1007/978-981-15-6263-1_2 fatcat:ekhgg7l6bramjgqh3ioa4ywm3u

Locally Adaptive Bayesian Multivariate Time Series

Daniele Durante, Bruno Scarpa, David B. Dunson
2013 Neural Information Processing Systems  
We propose a continuous multivariate stochastic process for time series having locally varying smoothness in both the mean and covariance matrix.  ...  In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process.  ...  The application to the problem of capturing temporal and geoeconomic structure between financial markets shows the utility of our approach in the analysis of multivariate financial time series.  ... 
dblp:conf/nips/DuranteSD13 fatcat:ivdkwah4a5b4jbbmx2cioncmuy

A Bayesian Nonparametric Approach for Time Series Clustering

Luis E. Nieto-Barajas, Alberto Contreras-Cristán
2014 Bayesian Analysis  
Within the Bayesian approach, the most commonly used model for time series analysis has been the normal dynamic linear model (Harrison and Stevens, 1976) .  ...  We illustrate our approach with a dataset of time series of shares prices in the Mexican stock exchange.  ...  Acknowledgements The first author acknowledges support to grant I130991-F from the National Council for Science and Technology of Mexico (CONACYT).  ... 
doi:10.1214/13-ba852 fatcat:yyqypo6uizhsnlk3xwep4t7pym

Mixed Membership Models for Time Series [article]

Emily B. Fox, Michael I. Jordan
2013 arXiv   pre-print
process can be viewed as a mixed membership characterization of the observed time series.  ...  In this article we discuss some of the consequences of the mixed membership perspective on time series analysis.  ...  Section 4 contains a brief survey of related Bayesian and Bayesian nonparametric time series models. 2. Background.  ... 
arXiv:1309.3533v1 fatcat:2ghqdzyksze45kv2uakr7fxnnm

Locally adaptive factor processes for multivariate time series [article]

Daniele Durante, Bruno Scarpa, David B. Dunson
2013 arXiv   pre-print
In modeling multivariate time series, it is important to allow time-varying smoothness in the mean and covariance process.  ...  We propose a locally adaptive factor process for characterizing multivariate mean-covariance changes in continuous time, allowing locally varying smoothness in both the mean and covariance matrix.  ...  /09 from the University of Padua, Italy.  ... 
arXiv:1210.2022v2 fatcat:vto3dnb7dbbixi6b6f34ohvtn4

A Bayesian Nonparametric Markovian Model for Nonstationary Time Series [article]

Maria DeYoreo, Athanasios Kottas
2016 arXiv   pre-print
The model for the transition density arises from the conditional distribution implied by a Bayesian nonparametric mixture of bivariate normals.  ...  We present a modeling approach for univariate time series data, which makes no assumptions of stationarity, and can accommodate complex dynamics and capture nonstandard distributions.  ...  G. (2016), “A nonparametric model for stationary time series,” Journal of Time Series Analysis, 37, 126–142.  ... 
arXiv:1601.04331v3 fatcat:vukiyniggnhgzftvjje3s5o6he

Adaptive Bayesian Time–Frequency Analysis of Multivariate Time Series

Zeda Li, Robert T. Krafty
2018 Journal of the American Statistical Association  
This article introduces a nonparametric approach to multivariate time-varying power spectrum analysis.  ...  The procedure adaptively partitions a time series into an unknown number of approximately stationary segments, where some spectral components may remain unchanged across segments, allowing components to  ...  Many applications are concerned not with the analysis of a single multivariate time series, but of the analysis of replicated multivariate time series and in how their time-varying spectra are associated  ... 
doi:10.1080/01621459.2017.1415908 pmid:31156284 pmcid:PMC6541451 fatcat:kjv5k3ka4ngivaskzdjs7oenhm

Adaptive Bayesian Spectral Analysis of High-dimensional Nonstationary Time Series [article]

Zeda Li, Ori Rosen, Fabio Ferrarelli, Robert T. Krafty
2019 arXiv   pre-print
This article introduces a nonparametric approach to spectral analysis of a high-dimensional multivariate nonstationary time series.  ...  Formulated in a fully Bayesian framework, the time series is adaptively partitioned into approximately stationary segments, where both the number and location of partition points are assumed unknown.  ...  More recently, a variety of approaches to the spectral analysis of multivariate nonstationary time series have been proposed.  ... 
arXiv:1910.12126v1 fatcat:ymdbjmjtebh2rhzl4an3je6kaq

Adaptive Bayesian Power Spectrum Analysis of Multivariate Nonstationary Time Series [article]

Zeda Li, Robert T. Krafty
2017 arXiv   pre-print
This article introduces a nonparametric approach to multivariate time-varying power spectrum analysis.  ...  The procedure adaptively partitions a time series into an unknown number of approximately stationary segments, where some spectral components may remain unchanged across segments, allowing components to  ...  Many applications are concerned not with the analysis of a single multivariate time series, but of the analysis of replicated multivariate time series and in how their time-varying spectra are associated  ... 
arXiv:1706.05661v2 fatcat:mmcyux6wizeerilcx5tzc7y6qm

Robust conditional spectral analysis of replicated time series

Zeda Li
2023 Statistics and its Interface  
In this article, we propose a novel nonparametric approach to the spectral analysis of multiple time series and the associated covariates.  ...  Through a tensor-product spline model of Cholesky components of the conditional copula spectral density matrix, the approach provides flexible nonparametric estimates of the copula spectral density matrix  ...  This work was funded in part by PSC-CUNY Research Award 63069-0051 and a Eugene M. Lang Junior Faculty Research Fellowship.  ... 
doi:10.4310/21-sii698 fatcat:nbpailuwxveu3pkwtnp3jy2uga

Warped Dynamic Linear Models for Time Series of Counts [article]

Brian King, Daniel R. Kowal
2022 arXiv   pre-print
The proposed approach is applied to a multivariate time series of daily overdose counts and demonstrates both modeling and computational successes.  ...  This framework unifies and extends a variety of discrete time series models and is valid for natural counts, rounded values, and multivariate observations.  ...  Finally, we showcased how the warpDLM approach can perform online inference of multivariate count time series data.  ... 
arXiv:2110.14790v2 fatcat:263jpem2drhflpvgzbylz7nj4a

Joint Modeling of Multiple Related Time Series via the Beta Process [article]

Emily B. Fox, Erik B. Sudderth, Michael I. Jordan, Alan S. Willsky
2011 arXiv   pre-print
We propose a Bayesian nonparametric approach to the problem of jointly modeling multiple related time series. Our approach is based on the discovery of a set of latent, shared dynamical behaviors.  ...  Using a beta process prior, the size of the set and the sharing pattern are both inferred from data.  ...  A preliminary version of this work (without detailed development or analysis) was first presented at a conference (Fox et al., 2010b) .  ... 
arXiv:1111.4226v1 fatcat:zset44fyqnh27kgto2xjcxlr2u

Series Representations for Multivariate Time-Changed Lévy Models

Vladimir Panov
2015 Methodology and Computing in Applied Probability  
More precisely, we consider a two-dimensional Lévy process such that each component is a time-changed (subordinated) Brownian motion and the dependence between subordinators is described via some Lévy  ...  The main result of this paper is the series representation for our model, which can be efficiently used for simulation purposes.  ...  Acknowledgment The author is grateful to Igor Sirotkin, the student of the Higher School of Economics, for his help with the preparation of Section 8.  ... 
doi:10.1007/s11009-015-9461-8 fatcat:kushgi3l6vcylgahzzmojp26qu

Bayesian Time-Series Model for Short-Term Traffic Flow Forecasting

Bidisha Ghosh, Biswajit Basu, Margaret O'Mahony
2007 Journal of transportation engineering  
The Seasonal Autoregressive Integrated Moving Average (SARIMA) model is one of the popular univariate time-series models in the field of short-term traffic flow forecasting.  ...  Each of the estimated parameters from the Bayesian method has a probability density function conditional to the observed traffic volumes.  ...  a multivariate approach.  ... 
doi:10.1061/(asce)0733-947x(2007)133:3(180) fatcat:5wfxpcv4l5epngv5fqbr3xucwy
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