We propose a parsimonious spatiotemporal model for time series data on a spatial grid. Our model is capable of dealing with high-dimensional time series data that may be collected at hundreds of locations and capturing the spatial non-stationarity. In essence, our model is a vector autoregressive model that utilizes the spatial structure to achieve parsimony of autoregressive matrices at two levels. The first level ensures the sparsity of the autoregressive matrices using a lagged-neighborhood scheme. The second level performs a spatial clustering of the non-zero autoregressive coefficients such that nearby locations share similar coefficients. This model is interpretable and can be used to identify geographical subregions, within each of which, the time series share similar dynamical behavior with homogeneous autoregressive coefficients. The model parameters are obtained using the penalized maximum likelihood with an adaptive fused Lasso penalty. The estimation procedure is easy to implement and can be tailored to the need of a modeler. We illustrate the performance of the proposed estimation algorithm in a simulation study. We apply our model to a wind speed time series dataset generated from a climate model over Saudi Arabia to illustrate its usefulness. Limitations and possible extensions of our method are also discussed.
The classical multilevel model fails to capture the proximity effect in epidemiological studies, where subjects are nested within geographical units. Multilevel Conditional Autoregressive models are alternatives to help explain the spatial effect better. They have been developed for cross-sectional studies but not for longitudinal studies so far. This paper has two goals. Firstly, it further develops the multilevel (growth) models for longitudinal data by adding existing area level random effect terms with CAR prior specification, whose structure is changing over time. We name these models MLM…
Interval-valued data receives much attention due to its wide applications in the fields of finance, econometrics, meteorology and medicine. However, most regression models developed for interval-valued data assume observations are mutually independent, not adapted to the scenario that individuals are spatially correlated. We propose a new linear model to accommodate to areal-type spatial dependency existed in interval-valued data. Specifically, spatial correlation among centers of responses are considered. To improve the new model's prediction accuracy, we add three inequality constrains. Para…
The objective of disease mapping is to model data aggregated at the areal level. In some contexts, however, (e.g. residential histories, general practitioner catchment areas) when data is arising from a variety of sources, not necessarily at the same spatial scale, it is possible to specify spatial random effects, or covariate effects, at the areal level, by using a multiple membership principle (MM) (Petrof et al. 2020, Gramatica et al. 2021). A weighted average of conditional autoregressive (CAR) spatial random effects embeds spatial information for a spatially-misaligned outcome and estimat…
Gridded data products, for example interpolated daily measurements of precipitation from weather stations, are commonly used as a convenient substitute for direct observations because these products provide a spatially and temporally continuous and complete source of data. However, when the goal is to characterize climatological features of extreme precipitation over a spatial domain (e.g., a map of return values) at the native spatial scales of these phenomena, then gridded products may lead to incorrect conclusions because daily precipitation is a fractal field and hence any smoothing techni…
We develop a test of normality for spatially indexed functions. The assumption of normality is common in spatial statistics, yet no significance tests, or other means of assessment, have been available for functional data. This paper aims at filling this gap in the case of functional observations on a spatial grid. Our test compares the moments of the spatial (frequency domain) principal component scores to those of a suitable Gaussian distribution. Critical values can be readily obtained from a chi-squared distribution. We provide rigorous theoretical justification for a broad class of weakly…
The demand for e-hailing services is growing rapidly, especially in large cities. Uber is the first and popular e-hailing company in the United Stated and New York City. A comparison of the demand for yellow-cabs and Uber in NYC in 2014 and 2015 shows that the demand for Uber has increased. However, this demand may not be distributed uniformly either spatially or temporally. Using spatio-temporal time series models can help us to better understand the demand for e-hailing services and to predict it more accurately. This paper analyzes the prediction performance of one temporal model (vector au…
