Recent Advances in Spatio‐Temporal Methodology

Abstract

This special issue consists of a collection of articles that describe innovations in spatio-temporal methodology. Spatio-temporal statistics has been developing at a rapid pace over the past 25 years. The topic is briefly covered in Cressie's (1993) comprehensive book on spatial statistics. Subsequently, Cressie and Wikle (2011) provided the first comprehensive book on spatio-temporal statistics, but it focused primarily on linear, univariate, and Gaussian methods. More recently, there have been numerous significant advancements in non-linear, multivariate, and non-Gaussian spatio-temporal methods, particularly those suited for ‘big’ data problems. Yet, each of these topic areas is relatively underdeveloped, and there are still many research challenges. Historically, spatio-temporal statistics methodology has developed more as an extension of spatial statistics rather than time series. That is, the emphasis has been on specification of models through their second-order structure, typically within a Gaussian process framework. Alternatively, dynamic spatio-temporal models (DSTMs) have been used to model processes for which it is more realistic to think of spatial processes evolving through time, that is, when it is more reasonable to think of the process conditionally (in time) rather than marginally (as with the Gaussian process framework). DSTMs often have model forms as in classical multivariate time series models, but they present unique challenges in that the types of relationships between space and time are often driven by mechanistic processes, and the associated statistical models must attempt to accommodate these relationships. In addition, the dimensionality of the spatial components of these models often prohibits the use of classical multivariate time series methods. Although much of the development of spatio-temporal methodology has been driven by environmental, epidemiological, and ecological applications (e.g. pollution monitoring, weather forecasting, climate, oceanography, disease mapping, invasive species, animal movement, etc.), there is an increasing number of novel methodologies that are motivated by the biological sciences (e.g. brain science), federal statistics (e.g. multivariate surveys, non-Gaussian change of support), sociological statistics (e.g. crime analysis), and econometric (e.g. multivariate panel) applications. Indeed, these processes are often multivariate, non-linear, and/or non-Gaussian. The articles in this special issue provide a representative snapshot of innovative work in these areas. Specifically, the articles selected for this issue highlight non-Gaussian spatio-temporal models, computational efficiency, and/or improving parameterizations of DSTMs. In their article ‘Scalable Inference for Space-Time Gaussian Cox Processes’, Shirota and Banerjee show how one can use an efficient data augmentation approach in conjunction with nearest-neighbor log-Gaussian processes to efficiently model count (crime event) data via spatio-temporal Gaussian Cox processes. In ‘Estimating Spatial Changes Over Time of Artic Sea Ice Using Hidden 2 × 2 Tables’, Zhang and Cressie consider non-Gaussian (Bernoulli) data on the presence/absence of sea ice. The model is cast in an efficient manner by using dimension-reduced spatio-temporal processes in an EM algorithm, cleverly describing the process as time-varying 2 × 2 tables. Tagle, Castruccio, Crippa, and Genton, in their article ‘A Non-Gaussian Spatio-Temporal Model for Daily Wind Speeds Based on a Multivariate Skew-T Distribution’, show how to build an efficient and realistic ‘weather generator’ for daily wind speeds that is able to simulate the type of skewed distributions that are often found in weather variables. In their article ‘On a Semiparametric Data-Driven Nonlinear Model with Penalized Spatio-Temporal Lag Interactions’, Al-Sulami, Jiang, Lu, and Zhu consider a non-linear (semiparametric) regression spatio-temporal model that also includes a dynamic interaction term and consider an adaptive lasso approach for selecting the space–time lag interactions that are most useful (in their example, to model US housing price data). Their methodology does not rely on a Gaussian error assumption. In the spirit of efficient modeling of the spatio-temporal terms beyond a trend and seasonality, Gao and Tsay present an efficient structured factor approach for multivariate time series and spatio-temporal data (e.g. PM2.5 pollutant observations) in their article ‘A Structural-Factor Approach to Modeling High-Dimensional Time Series and Space-Time Data’. Finally, in their article ‘Spatio-Temporal Models for Big Multinomial Data Using the Conditional Multivariate Logit-Beta Distribution’, Bradley, Wikle and Holan develop a novel efficient conjugate Bayesian algorithm to model high-dimensional spatio-temporal multinomial data, which includes a spatio-temporal dynamic process. They apply this model to public-use Quarterly Workforce Indicators from the Longitudinal Employer Household Dynamics program of the US Census Bureau. These articles provide excellent examples of how spatio-temporal statistical models can be applied to address complex non-Gaussian, non-linear, and multivariate data with efficient computational algorithms. These problems are by no means ‘solved’, but it is our hope that the readers of the Journal of Time Series Analysis may see connections to their own work that can be applied to this rich set of problems and this growing and important area of statistics. Finally, we would like to end this Editorial by thanking Prof. A. M. R. Taylor for encouraging us to edit this special issue.