A Bayesian Approach to Switching Linear Gaussian State-Space Models for Unsupervised Time-Series Segmentation

2008 ◽  
Author(s):  
Silvia Chiappa
Keyword(s):  
Time Series ◽  
State Space ◽  
Bayesian Approach ◽  
State Space Models ◽  
Gaussian State ◽  
Time Series Segmentation

scholarly journals A closed-form filter for binary time series

2021 ◽  
Vol 31 (4) ◽  
Author(s):  
Augusto Fasano ◽  
Giovanni Rebaudo ◽  
Daniele Durante ◽  
Sonia Petrone
Keyword(s):  
Time Series ◽  
Monte Carlo ◽  
Closed Form ◽  
State Space ◽  
Binary Data ◽  
Sequential Monte Carlo ◽  
State Space Models ◽  
Cumulative Distribution ◽  
Gaussian State ◽  
Binary Time Series

AbstractNon-Gaussian state-space models arise in several applications, and within this framework the binary time series setting provides a relevant example. However, unlike for Gaussian state-space models — where filtering, predictive and smoothing distributions are available in closed form — binary state-space models require approximations or sequential Monte Carlo strategies for inference and prediction. This is due to the apparent absence of conjugacy between the Gaussian states and the likelihood induced by the observation equation for the binary data. In this article we prove that the filtering, predictive and smoothing distributions in dynamic probit models with Gaussian state variables are, in fact, available and belong to a class of unified skew-normals (sun) whose parameters can be updated recursively in time via analytical expressions. Also the key functionals of these distributions are, in principle, available, but their calculation requires the evaluation of multivariate Gaussian cumulative distribution functions. Leveraging sun properties, we address this issue via novel Monte Carlo methods based on independent samples from the smoothing distribution, that can easily be adapted to the filtering and predictive case, thus improving state-of-the-art approximate and sequential Monte Carlo inference in small-to-moderate dimensional studies. Novel sequential Monte Carlo procedures that exploit the sun properties are also developed to deal with online inference in high dimensions. Performance gains over competitors are outlined in a financial application.

Bayesian Inference for Time Series State Space Models

2011 ◽  
pp. 59-124 ◽  
Author(s):  
Paolo Giordani ◽  
Michael Pitt ◽  
Robert Kohn
Keyword(s):  
Time Series ◽  
Particle Filter ◽  
State Space ◽  
Empirical Work ◽  
State Space Models ◽  
Gaussian State ◽  
Advantages And Disadvantages ◽  
Nonlinear State Space Models ◽  
Non Gaussian ◽  
Main Ideas

This article provides a description of time series methods that emphasize modern macroeconomics and finance. It discusses a variety of posterior simulation algorithms and illustrates their use in a range of models. This article introduces the state space framework and explains the main ideas behind filtering, smoothing, and likelihood computation. It also mentions the particle filter as a general approach for estimating state space models and gives a brief discussion of its methods. The particle filter is a very useful tool in the Bayesian analysis of the kinds of complicated nonlinear state space models that are increasingly being used in macroeconomics. It also deals with conditionally Gaussian state space models and non-Gaussian state space models. A discussion of the advantages and disadvantages of each algorithm is provided in this article. This aims to help with the use of these methods in empirical work.

scholarly journals DETECTION LIMITS FOR LINEAR NON-GAUSSIAN STATE-SPACE MODELS

2006 ◽  
Vol 39 (13) ◽  
pp. 282-287 ◽  
Author(s):  
Gustaf Hendeby ◽  
Fredrik Gustafsson
Keyword(s):  
State Space ◽  
Detection Limits ◽  
State Space Models ◽  
Gaussian State ◽  
Non Gaussian

scholarly journals Predicting crypto-currencies using sparse non-Gaussian state space models

2018 ◽  
Vol 37 (6) ◽  
pp. 627-640 ◽  
Author(s):  
Christian Hotz-Behofsits ◽  
Florian Huber ◽  
Thomas Otto Zörner
Keyword(s):  
State Space ◽  
State Space Models ◽  
Gaussian State ◽  
Non Gaussian
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