192,134 research outputs found
Penalized likelihood estimation and iterative kalman smoothing for non-gaussian dynamic regression models
Dynamic regression or state space models provide a flexible framework for analyzing non-Gaussian time series and longitudinal data, covering for example models for discrete longitudinal observations. As for non-Gaussian random coefficient models, a direct Bayesian approach leads to numerical integration problems, often intractable for more complicated data sets. Recent Markov chain Monte Carlo methods avoid this by repeated sampling from approximative posterior distributions, but there are still open questions about sampling schemes and convergence. In this article we consider simpler methods of inference based on posterior modes or, equivalently, maximum penalized likelihood estimation. From the latter point of view, the approach can also be interpreted as a nonparametric method for smoothing time-varying coefficients. Efficient smoothing algorithms are obtained by iteration of common linear Kalman filtering and smoothing, in the same way as estimation in generalized linear models with fixed effects can be performed by iteratively weighted least squares estimation. The algorithm can be combined with an EM-type method or cross-validation to estimate unknown hyper- or smoothing parameters. The approach is illustrated by applications to a binary time series and a multicategorical longitudinal data set
Bayesian Computation in Dynamic Latent Factor Models
Bayesian computation for filtering and forecasting analysis is developed for
a broad class of dynamic models. The ability to scale-up such analyses in
non-Gaussian, nonlinear multivariate time series models is advanced through the
introduction of a novel copula construction in sequential filtering of coupled
sets of dynamic generalized linear models. The new copula approach is
integrated into recently introduced multiscale models in which univariate time
series are coupled via nonlinear forms involving dynamic latent factors
representing cross-series relationships. The resulting methodology offers
dramatic speed-up in online Bayesian computations for sequential filtering and
forecasting in this broad, flexible class of multivariate models. Two examples
in nonlinear models for very heterogeneous time series of non-negative counts
demonstrate massive computational efficiencies relative to existing
simulation-based methods, while defining similar filtering and forecasting
outcomes.Comment: 21 pages, 7 figure
Residential real estate price forecasting in Portugal
This paper employs three panel data and seven machine learning methods, including linear and nonlinear models, to perform accurate predictions of house prices for fifty-one parishes in six municipalities of Portugal. To construct the predictive models, nine time series economic factors and two non-time series features are applied as explanatory variables. Finally, the neigh boring parish's lagged house prices per square meter data is added as a predictor to increase the forecasting accuracies. The utilized models are Artificial Neural Network, eXtream Gradient Boosting, Linear regression, Lasso and Ridge regression, Bayesian regression, Polynomial regression, Pooled OLS, Panel OLS, and First Difference OLS
Some recent developments in Markov Chain Monte Carlo for cointegrated time series
We consider multivariate time series that exhibit reduced rank cointegration, which means a lower dimensional linear projection of the process becomes stationary. We will review recent suitable Markov Chain Monte Carlo approaches for Bayesian inference such as the Gibbs sampler of [41] and the Geodesic Hamiltonian Monte Carlo method of [3]. Then we will propose extensions that can allow the ideas in both methods to be applied for cointegrated time series with non-Gaussian noise. We illustrate the efficiency and accuracy of these extensions using appropriate numerical experiments
Bayesian nonparametric graphical models for time-varying parameters VAR
Over the last decade, big data have poured into econometrics, demanding new
statistical methods for analysing high-dimensional data and complex non-linear
relationships. A common approach for addressing dimensionality issues relies on
the use of static graphical structures for extracting the most significant
dependence interrelationships between the variables of interest. Recently,
Bayesian nonparametric techniques have become popular for modelling complex
phenomena in a flexible and efficient manner, but only few attempts have been
made in econometrics. In this paper, we provide an innovative Bayesian
nonparametric (BNP) time-varying graphical framework for making inference in
high-dimensional time series. We include a Bayesian nonparametric dependent
prior specification on the matrix of coefficients and the covariance matrix by
mean of a Time-Series DPP as in Nieto-Barajas et al. (2012). Following Billio
et al. (2019), our hierarchical prior overcomes over-parametrization and
over-fitting issues by clustering the vector autoregressive (VAR) coefficients
into groups and by shrinking the coefficients of each group toward a common
location. Our BNP timevarying VAR model is based on a spike-and-slab
construction coupled with dependent Dirichlet Process prior (DPP) and allows
to: (i) infer time-varying Granger causality networks from time series; (ii)
flexibly model and cluster non-zero time-varying coefficients; (iii)
accommodate for potential non-linearities. In order to assess the performance
of the model, we study the merits of our approach by considering a well-known
macroeconomic dataset. Moreover, we check the robustness of the method by
comparing two alternative specifications, with Dirac and diffuse spike prior
distributions
Aspects of recursive Bayesian estimation
This thesis is concerned with the theoretical and practical aspects of some problems in Bayesian time series analysis and recursive estimation. In particular, we examine procedures for accommodating outliers in dynamic linear models which involve the use of heavy-tailed error distributions as alternatives to normality.
Initially we discuss the basic principles of the Bayesian approach to robust estimation in general, and develop those ideas in the context of linear time series models. Following this, the main body of the thesis attacks the problem of intractibility of analysis under outlier accommodating assumptions. For both the dynamic linear model and the classical autoregressive-moving average schemes we develop methods for parameter estimation, forecasting and smoothing with non-normal data. This involves the theoretical examination of non-linear recursive filtering
algorithms as robust alternatives to the Kalman filter and numerical examples of the use of these procedures on simulated data. The asymptotic behaviour of some special recursions is also detailed in connection with the theory of stochastic approximation.
Finally, we report on an application of Bayesian time series analysis in the monitoring of medical time series, the particular problem involving kidney transplant patients
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