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Register a new userBayesian time-aligned factor analysis of paired multivariate time series
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Added by
Arkaprava Roy
Publication date
2019
fields
Mathematical Statistics
and research's language is
English
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Many modern data sets require inference methods that can estimate the shared and individual-specific components of variability in collections of matrices that change over time. Promising methods have been developed to analyze these types of data in static cases, but very few approaches are available for dynamic settings. To address this gap, we consider novel models and inference methods for pairs of matrices in which the columns correspond to multivariate observations at different time points. In order to characterize common and individual features, we propose a Bayesian dynamic factor modeling framework called Time Aligned Common and Individual Factor Analysis (TACIFA) that includes uncertainty in time alignment through an unknown warping function. We provide theoretical support for the proposed model, showing identifiability and posterior concentration. The structure enables efficient computation through a Hamiltonian Monte Carlo (HMC) algorithm. We show excellent performance in simulations, and illustrate the method through application to a social synchrony experiment.
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While there is an increasing amount of literature about Bayesian time series analysis, only a few Bayesian nonparametric approaches to multivariate time series exist. Most methods rely on Whittles Likelihood, involving the second order structure of a stationary time series by means of its spectral density matrix. This is often modeled in terms of the Cholesky decomposition to ensure positive definiteness. However, asymptotic properties such as posterior consistency or posterior contraction rates are not known. A different idea is to model the spectral density matrix by means of random measures. This is in line with existing approaches for the univariate case, where the normalized spectral density is modeled similar to a probability density, e.g. with a Dirichlet process mixture of Beta densities. 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. The proposed procedure is shown to perform well for both simulated and real data. Posterior consistency and contraction rates are also established.
The multivariate Bayesian structural time series (MBSTS) model citep{qiu2018multivariate,Jammalamadaka2019Predicting} as a generalized version of many structural time series models, deals with inference and prediction for multiple correlated time series, where one also has the choice of using a different candidate pool of contemporaneous predictors for each target series. The MBSTS model has wide applications and is ideal for feature selection, time series forecasting, nowcasting, inferring causal impact, and others. This paper demonstrates how to use the R package pkg{mbsts} for MBSTS modeling, establishing a bridge between user-friendly and developer-friendly functions in package and the corresponding methodology. A simulated dataset and object-oriented functions in the pkg{mbsts} package are explained in the way that enables users to flexibly add or deduct some components, as well as to simplify or complicate some settings.
This paper deals with inference and prediction for multiple correlated time series, where one has also the choice of using a candidate pool of contemporaneous predictors for each target series. Starting with a structural model for the time-series, Bayesian tools are used for model fitting, prediction, and feature selection, thus extending some recent work along these lines for the univariate case. The Bayesian paradigm in this multivariate setting helps the model avoid overfitting as well as capture correlations among the multiple time series with the various state components. The model provides needed flexibility to choose a different set of components and available predictors for each target series. The cyclical component in the model can handle large variations in the short term, which may be caused by external shocks. We run extensive simulations to investigate properties such as estimation accuracy and performance in forecasting. We then run an empirical study with one-step-ahead prediction on the max log return of a portfolio of stocks that involve four leading financial institutions. Both the simulation studies and the extensive empirical study confirm that this multivariate model outperforms three other benchmark models, viz. a model that treats each target series as independent, the autoregressive integrated moving average model with regression (ARIMAX), and the multivariate ARIMAX (MARIMAX) model.
Our goal is to estimate causal interactions in multivariate time series. Using vector autoregressive (VAR) models, these can be defined based on non-vanishing coefficients belonging to respective time-lagged instances. As in most cases a parsimonious causality structure is assumed, a promising approach to causal discovery consists in fitting VAR models with an additional sparsity-promoting regularization. Along this line we here propose that sparsity should be enforced for the subgroups of coefficients that belong to each pair of time series, as the absence of a causal relation requires the coefficients for all time-lags to become jointly zero. Such behavior can be achieved by means of l1-l2-norm regularized regression, for which an efficient active set solver has been proposed recently. Our method is shown to outperform standard methods in recovering simulated causality graphs. The results are on par with a second novel approach which uses multiple statistical testing.
In vaccine development, the temporal profiles of relative abundance of subtypes of immune cells (T-cells) is key to understanding vaccine efficacy. Complex and expensive experimental studies generate very sparse time series data on this immune response. Fitting multi-parameter dynamic models of the immune response dynamics-- central to evaluating mechanisms underlying vaccine efficacy-- is challenged by data sparsity. The research reported here addresses this challenge. For HIV/SIV vaccine studies in macaques, we: (a) introduce novel dynamic models of progression of cellular populations over time with relevant, time-delayed components reflecting the vaccine response; (b) define an effective Bayesian model fitting strategy that couples Markov chain Monte Carlo (MCMC) with Approximate Bayesian Computation (ABC)-- building on the complementary strengths of the two approaches, neither of which is effective alone; (c) explore questions of information content in the sparse time series for each of the model parameters, linking into experimental design and model simplification for future experiments; and (d) develop, apply and compare the analysis with samples from a recent HIV/SIV experiment, with novel insights and conclusions about the progressive response to the vaccine, and how this varies across subjects.
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