64th ISI World Statistics Congress - Ottawa, Canada

64th ISI World Statistics Congress - Ottawa, Canada

Analyzing High-dimensional Time Series

Category: International Society for Business and Industrial Statistics (ISBIS)


This session has three talks.
Talk 1 by Katherine B. Ensor is on Multivariate Non-Stationary Time Series Model for End-of-Day Trading Volume, and is joint work with Lada Kyj, Vanguard and Michael Jackson, New Territory Advisors (a venture enterprise). Trading volume is an important metric of liquidity and hence, a component for managers of large investment portfolios as they seek to bring the best value to their customers and members. We develop a hierarchical non-stationary time-series process to capture and forecast end-of-day trading dynamics across a cohort of equities. Our model hierarchy will include factors for time-of-day, trading day perturbations such as holidays, and seasonal structure. We present sector-specific dynamics and will compare this approach to a seasonal nonlinear autoregressive neural network forecast to the end-of-day trading volume.

Talk 2 by Scott H. Holan is on Bayesian Circular Lattice Filters for Computationally Efficient Estimation of Multivariate Time-Varying Autoregressive Models, and is joint work with Yuelei Sui, Amazon Inc. and Wen-His Yang, U. Queensland. While the time-varying autoregressive (TV-VAR) model is a well-established model for multivariate nonstationary time series, in most cases, the large number of parameters results in a high computational burden, ultimately limiting its usage. This talk proposes a computationally efficient multivariate Bayesian Circular Lattice Filter to extend the usage of the TV-VAR model to a broader class of high-dimensional problems. The fully Bayesian framework allows both the autoregressive (AR) coefficients and innovation covariance to vary over time. The estimation method is based on the Bayesian lattice filter (BLF), which is extremely computationally efficient and stable in univariate cases. The effectiveness of the approach is illustrated via a comprehensive simulation study. A real data illustration of the methodology through quarterly gross domestic product (GDP) data and Northern California wind data is provided.

Talk 3 is on Bayesian Modeling of Multivariate Integer-valued Autoregressive Processes by Refik Soyer, which is joint work with Di Zhang (GWU) and Hedibert Lopes (Arizona State University). Integer autoregressive (INAR) processes play a vital role in modeling count series. This talk discusses a dynamic multivariate INAR(1) model by integrating a random environment following a state-space evolution into the univariate INAR(1) model. The random environment provides an efficient and scalable multivariate generalization of the univariate model with dynamic multivariate negative binomial predictive distributions. It also allows the dynamic multivariate INAR(1) model to account for time-varying contemporary dependency structures, and employs MCMC and Particle Learning algorithms. On a real dataset, the dynamic multivariate INAR(1) model substantially outperforms competing models in terms of one-step-ahead out-of-sample forecasts.

The discussion will be given by Nalini Ravishanker who will tie together the ideas presented by the three speakers and discuss the role of R-INLA for speeding-up the computations in the high-dimensional (big data) setup, with brief Illustrations from different application domains.