Sunday, Aug 4: 4:00 PM - 5:50 PM
1850
Topic-Contributed Paper Session
Oregon Convention Center
Room: CC-F151
This session is focused on introducing several novel statistical methods for time series data. Specifically, the content of this session will be five presentations selected to highlight new models that (i) employ spectral methods to efficiently analyze high dimensional time series, (ii) incorporate modern learning methods including neural networks and trees, and (iii) build on shrinkage prior based regularization methods. This session will appeal to statistical methodologists with a range of backgrounds, both within and outside of the time series community. The session will also appeal to more applied statisticians who are interested in learning about new time series models that may address challenges they encounter when analyzing data in practice.
Applied
No
Main Sponsor
Business and Economic Statistics Section
Co Sponsors
Section on Statistical Computing
Section on Statistical Learning and Data Science
Presentations
Recent advances have generalized neural networks to learn operators, also referred to as neural operators. Neural operators map between possibly infinite dimensional function spaces and can be formulated as a composition of linear integral operators and nonlinear activation functions. This talks studies the distribution of such networks with random Gaussian weights and biases in which the hidden layer widths are proportional to a large constant. The used tools are based on a functional version of the Malliavin-Stein method.
Various approaches have been proposed to nonparametric estimation of the spectral density based on smoothing the periodogram. Most methods use a single smoothing parameter across all Fourier frequencies which may result in a biased estimate. Our approach to smoothing the periodogram is to place a dynamic shrinkage prior such that varying degrees of smoothing may be applied to different intervals of the Fourier frequencies resulting in an improved estimate of the spectrum.
Nonparametric cointegrating regression models have been extensively used in financial markets, stock prices, heavy traffic, climate data sets, and energy markets. Models with parametric regression functions can be more appealing in practice compared to non-parametric forms, but do result in potential functional misspecification. Thus, there exists a vast literature on developing a model specification test for parametric forms of regression functions. In this talk, I introduce two test statistics which are applicable for the endogenous regressors driven by long memory input shocks in the regression model. The limit distributions of the test statistics under these two scenarios are complicated and cannot be effectively used in practice. To overcome this difficulty, I use the subsampling method and compute the test statistics on smaller blocks of the data to construct their empirical distributions. With Monte Carlo simulation studies and an empirical example of relating gross domestic product to total output of carbon dioxide in multiple countries, I illustrate the properties of test statistics.
This talk introduces a flexible and adaptive nonparametric method for estimating the association between multiple covariates and power spectra of multiple time series. The proposed approach uses a Bayesian sum of trees model to capture complex dependencies and interactions between covariates and the power spectrum, which are often observed in studies of biomedical time series. Local power spectra corresponding to terminal nodes within trees are estimated using Bayesian penalized linear splines. The trees are random and fit using a Bayesian backfitting Markov chain Monte Carlo algorithm that sequentially considers tree modifications via reversible-jump techniques. For high-dimensional covariates, a sparsity-inducing Dirichlet hyperprior is considered, which provides sparse estimation of covariate effects and efficient variable selection. Empirical performance is evaluated via simulations to demonstrate the method's ability to accurately recover complex relationships and interactions. The methodology is used to study gait maturation in young children by evaluating age-related changes in power spectra of stride interval time series in the presence of other covariates.
Model development for sequential non-Gaussian data such as counts characterized by small counts and non-stationarities is essential for broader applicability and appropriate inference in the scientific community. Specifically, we introduce global-local shrinkage priors into a Bayesian dynamic generalized linear model to adaptively estimate both changepoints and a smooth trend for non-Gaussian time series. We utilize a parsimonious state-space approach to identify a dynamic signal with local parameters to track smoothness of the local mean at each time-step. This setup provides a flexible framework to detect unspecified changepoints in complex series, such as those with large interruptions in local trends. We detail the extension of our approach to time-varying parameter estimation within dynamic Negative Binomial regression analysis to identify structural breaks. Finally, we illustrate our algorithm with empirical examples in social sciences.