Spatio-temporal Dependence Structure Research Articles

Change-detection-assisted multiple testing for spatiotemporal data

This paper considers a large-scale multiple testing problem for spatiotemporal data with multiple change points. A data-driven procedure that aims to fully utilize the clustering information is proposed. Specifically, we first develop a new change-point detection algorithm that integrates the kernel-based aggregation of spatial observations with a global loss function at the temporal level to group data into several sets, and then derive an FDR control scheme for set-wise multiple testing. Under some mild conditions on the spatiotemporal dependence structure, FDR is shown to be strongly controlled. Theoretical analysis and numerical studies demonstrate the advantages of the algorithm over competing methods.

Spatio-Temporal Patterns in Portuguese Regional Fertility Rates: A Bayesian Approach for Spatial Clustering of Curves

Abstract It is important for demographic analyses and policy-making to obtain accurate models of spatial diffusion, so that policy experiments can reflect endogenous spatial spillovers appropriately. Likewise, it is important to obtain accurate estimates and forecasts of demographic variables such as age-specific fertility rates, by regions and over time, as well as the uncertainty associated with such estimation. Here, we consider Bayesian hierarchical models with separable spatio-temporal dependence structure that can be estimated by borrowing strength from neighbouring regions and all years. Further, we do not consider the adjacency structure as a given, but rather as an object of inference. For this purpose, we use the local similarity of temporal patterns by developing a spatial clustering model based on Bayesian nonparametric smoothing techniques. The Bayesian inference provides the uncertainty associated with the clustering configurations that is typically lacking in classical analyses of large data sets in which a unique clustering representation can be insufficient. The proposed model is applied to 16-year data on age-specific fertility rates observed over 28 regions in Portugal, and provides statistical inference on the number of clusters, and local scaling and shrinkage levels. The corresponding central clustering configuration is able to capture spatial diffusion that has key demographic interpretations. Importantly, the exercise aids identification of peripheral regions with poor demographic prospects and development of regional policy for such places.

Analysis of spatio-temporal dependence of inflow time series through Bayesian causal modelling

This paper aims to assess fully the spatio-temporal dependence dimensions of inflow across two adjacent and parallel basins and among different time steps through Causality. This is addressed from the perspective of Causal Reasoning, supported by Bayesian modelling, under a novel framework named Bayesian Causal Modelling (BCM). This is applied, through a “concept-proof”, to the Jucar River Basin (the second largest basin of Eastern Spain, characterized by long and severe drought conditions). In this “concept-proof” a double goal is evaluated; first dedicated to a lumped analysis of dependence and second a specific one over dry periods focused on time-horizon of the Jucar basin typical drought (3 years). These challenges comprise the development of two fully connected Bayesian Networks (BNs), one for each challenge populated/trained from historical-inflow records. BNs were designed at a season-scale and consequently, time was upscaled and grouped into Irrigation and Non-Irrigation periods, according to Jucar River Basin Authority operational practices. Results achieved showed that BCM framework satisfactorily captured the spatio-temporal dependencies of systems. Furthermore, BCM is able to answer to some key questions over interdependencies between adjacent and parallel subbasins. Those questions may comprise, the amount of spatial dependences among time series, the temporarily conditionality among subbasins and the spatio-temporal dependence among basins. This provides a relevant insight on the intrinsic spatio-temporal dependence structure of inflow time series in complex basins systems. This approach could be very valuable for water resources planning and management, due to its application power for predicting extreme events (e.g. droughts) as well as improving and optimizing the reservoirs operation rules.

Turbine-specific short-term wind speed forecasting considering within-farm wind field dependencies and fluctuations

The unprecedented scale and sophistication of wind turbine technologies call for wind forecasts of high spatial resolution, i.e. turbine-tailored forecasts, to inform several operational decisions at the turbine level. Towards that, this paper is concerned with leveraging the hub-height measurements collected from a fleet of turbines on a farm to make turbine-specific short-term wind speed and power predictions. We find that the wind propagation across a dense grid of turbines induces strong spatial and temporal dependencies in the within-farm wind field, but also gives rise to high-frequency high-magnitude fluctuations which may compromise the predictive accuracy of several data-driven forecasting methods. To capture both aspects, we propose to model the total variability in the within-farm wind speed field as a combination of two independent stochastic process terms. The first term reconstructs and extrapolates the wind speed field by learning the complex spatio-temporal dependence structure using hub-height turbine-level data. The second term accounts for high-frequency high-magnitude fluctuations that are not informed by near-term spatio-temporal dependencies. The two terms are coupled to make probabilistic wind speed forecasts at each turbine, which are then translated into turbine-specific power predictions via wind power curves. Evaluation on more than 3,000,000 data points from a wind farm dataset provides a strong empirical evidence in favor of the proposed method’s forecasting accuracy. On average, our proposed method achieves 9% accuracy improvement relative to persistence forecasts, and 7–9% relative to a set of widely recognized forecasting methods such as autoregressive-based models and Gaussian Processes.

Clear-sky index space-time trajectories from probabilistic solar forecasts: Comparing promising copulas

Short-term probabilistic solar forecasts are an important tool in decision-making processes in which uncertainty plays a non-negligible role. Purely statistical models that produce temporal or spatiotemporal probabilistic solar forecasts are generally trained individually, and the combined forecasts therefore lack the temporal or spatiotemporal correlation present in the data. To recover the spatiotemporal dependence structure, a copula can be employed, which constructs a multivariate distribution from which spatially and temporally correlated uniform random numbers can be sampled, which in turn can be used to generate the so-called space-time trajectories via the inverse probability integral transform. In this study, we employ the recently introduced ultra-fast preselection algorithm to leverage the spatiotemporal information present in a pyranometer network and compare its accuracy to that of quantile regression forecasts that only consider temporal information. We show that the preselection algorithm improves both the calibration and sharpness of the predictive distributions. Furthermore, we employ four copulas, i.e., (1) Gaussian, (2) Student-t, (3) Clayton, and (4) empirical, to generate space-time trajectories. The results highlight the necessity to rigorously assess the calibration of the space-time trajectories and the correct modeling of the spatiotemporal dependence structure, which we show through techniques introduced in atmospheric sciences. The code used to generate the results in this study can be found at https://github.com/DWvanderMeer/SpaceTimeTrajectories.

Asymptotic behavior of the cross-dependence measures for bidimensional AR(1) model with $\alpha $-stable noise

In this paper, we consider a bidimensional autoregressive model of order 1 with $\alpha-$stable noise. Since in this case the classical measure of dependence known as the covariance function is not defined, the spatio-temporal dependence structure is described using the alternative measures, namely the codifference and the covariation functions. Here, we investigate the asymptotic relation between these two dependence measures applied to the description of the cross-dependence of the bidimensional model. We demonstrate the case when the dependence measures are asymptotically proportional with the coefficient of proportionality equal to the parameter $\alpha$. The theoretical results are supported by illustrating the asymptotic behavior of the dependence measures for two exemplary bidimensional $\alpha-$stable AR(1) systems.

Sparse network estimation for dynamical spatio-temporal array models

Neural field models represent neuronal communication on a population level via synaptic weight functions. Using voltage sensitive dye (VSD) imaging it is possible to obtain measurements of neural fields with a relatively high spatial and temporal resolution. The synaptic weight functions represent functional connectivity in the brain and give rise to a spatio-temporal dependence structure. We present a stochastic functional differential equation for modeling neural fields, which leads to a vector autoregressive model of the data via basis expansions of the synaptic weight functions and time and space discretization. Fitting the model to data is a practical challenge as this represents a large scale regression problem. By using a 1-norm penalty in combination with localized basis functions it is possible to learn a sparse network representation of the functional connectivity of the brain, but still, the explicit construction of a design matrix can be computationally prohibitive. We demonstrate that by using tensor product basis expansions, the computation of the penalized estimator via a proximal gradient algorithm becomes feasible. It is crucial for the computations that the data is organized in an array as is the case for the three dimensional VSD imaging data. This allows for the use of array arithmetic that is both memory and time efficient. Theproposed method is implemented and showcased in the R package dynamo available from CRAN.

Corrective receding horizon EV charge scheduling using short-term solar forecasting

Abstract Forecast errors can cause sub-optimal solutions in resource planning optimization, yet they are usually modeled simplistically by statistical models, causing unrealistic impacts on the optimal solutions. In this paper, realistic forecast errors are prescribed, and a corrective approach is proposed to mitigate the negative effects of day-ahead persistence forecast error by short-term forecasts from a state-of-the-art sky imager system. These forecasts preserve the spatiotemporal dependence structure of forecast errors avoiding statistical approximations. The performance of the proposed algorithm is tested on a receding horizon quadratic program developed for valley filling the midday net load depression through electric vehicle charging. Throughout one month of simulations the ability to flatten net load is assessed under practical forecast accuracy levels achievable from persistence, sky imager and perfect forecasts. Compared to using day-ahead persistence solar forecasts, the proposed corrective approach using sky imager forecasts delivers a 25% reduction in the standard deviation of the daily net load. It is demonstrated that correcting day-ahead forecasts in real time with more accurate short-term forecasts benefits the valley filling solution.

Spatiotemporal variability and empirical Copula-based dependence structure of modeled and observed coupled water and energy fluxes

AbstractThe spatial variations of water and energy budgets are highly influenced by the heterogeneity of land-surface characteristics. We investigate the spatiotemporal variability and dependence structure patterns of water and energy fluxes along an elevation gradient. Our analysis is based on the application of the GEOtop model and empirical Copulas. It is performed for the Rott (∼55 km2) and Upper-Ammer (∼300 km2) catchments in the TERrestrial ENvironmental Observatories prealpine region over two recent summer episodes, as a test case. We found that GEOtop is capable of quantifying the spatiotemporal variability of the water and energy budgets with consideration for the elevation-gradient effect of this heterogeneous landscape, which is confirmed by the linear statistical metrics. Furthermore, the empirical Copula-based function reveals that the dependence structures between the measured and simulated hydrometeorological variables are similar either at upper or lower density maxima. This suggests a reasonable performance of the model, as the interaction of variables is described properly; however, the model shows poorer performance in the middle ranks of the data. It is concluded that the presented Copula-based model performance analysis is a valuable complement to traditional global performance model analyses.

Using Meteorological Analogues for Reordering Postprocessed Precipitation Ensembles in Hydrological Forecasting

AbstractMeteorological ensemble forecasts are nowadays widely used as input of hydrological models for probabilistic streamflow forecasting. These forcings are frequently biased and have to be statistically postprocessed, using most of the time univariate techniques that apply independently to individual locations, lead times and weather variables. Postprocessed ensemble forecasts therefore need to be reordered so as to reconstruct suitable multivariate dependence structures. The Schaake shuffle and ensemble copula coupling are the two most popular methods for this purpose. This paper proposes two adaptations of them that make use of meteorological analogues for reconstructing spatiotemporal dependence structures of precipitation forecasts. Performances of the original and adapted techniques are compared through a multistep verification experiment using real forecasts from the European Centre for Medium‐Range Weather Forecasts. This experiment evaluates not only multivariate precipitation forecasts but also the corresponding streamflow forecasts that derive from hydrological modeling. Results show that the relative performances of the different reordering methods vary depending on the verification step. In particular, the standard Schaake shuffle is found to perform poorly when evaluated on streamflow. This emphasizes the crucial role of the precipitation spatiotemporal dependence structure in hydrological ensemble forecasting.

Visualization and assessment of spatio-temporal covariance properties

Spatio-temporal covariances are important for describing thespatio-temporal variability of underlying random fields in geostatistical data. For second-order stationary random fields, there exist subclasses of covariance functions that assume a simpler spatio-temporal dependence structure with separability and full symmetry. However, it is challenging to visualize and assess separability and full symmetry from spatio-temporal observations. In this work, we propose a functional data analysis approach that constructs test functions using the cross-covariances from time series observed at each pair of spatial locations. These test functions of temporal lags summarize the properties of separability or symmetry for the given spatial pairs. We use functional boxplots to visualize the functional median and the variability of the test functions, where the extent of departure from zero at all temporal lags indicates the degree of non-separability or asymmetry. We also develop a rank-based nonparametric testing procedure for assessing the significance of the non-separability or asymmetry. Essentially, the proposed methods only require the analysis of temporal covariance functions. Thus, a major advantage over existing approaches is that there is no need to estimate any covariance matrix for selected spatio-temporal lags. The performances of the proposed methods are examined by simulations with various commonly used spatio-temporal covariance models. To illustrate our methods in practical applications, we apply it to real datasets, including weather station data and climate model outputs.

A spatiotemporal dengue fever early warning model accounting for nonlinear associations with hydrological factors: a Bayesian maximum entropy approach

Dengue fever is identified as one of the most widespread vector-borne diseases in the world. In the last decade, high incidence of dengue fever has been observed in southern Taiwan on an annual basis. There is an urgent need to develop a dengue fever early warning model for the area. Previous studies showed that dengue fever transmission has complex space–time dynamics highly depending upon the activities of human and vectors and their interactions, as well as hydrological processes. This study developed a 1-week-ahead dengue fever warning system in southern Taiwan considering weekly-based nonlinear temporal lagged associations between dengue cases and hydrological factors across space and time by investigating the disease database during 1998–2011. The proposed model is based on an integration of distributed lag nonlinear model and spatiotemporal dependence structure under an epistemic framework of Bayesian maximum entropy method. This study identified that minimum temperature and maximum 24-h rainfall are the most significant to dengue fever incidences. Their associations to dengue fever risks are presented with respect to both hydrological measurement levels and temporal lags. A nested spatiotemporal covariance of transmissions was used to account for the disease diffusion across space and time. Results show that the proposed approach can provide early warnings of the dengue fever occurrences in both initial and peak epidemic stages in 2012, and obtain the spatiotemporal distribution of dengue fever epidemics. These features can be useful for local governmental agencies to seek more effective strategies for dengue fever prevention and control.

The Anisotropic Spatiotemporal Estimation of Housing Prices

This paper develops a method to identify three-dimensional anisotropic spatiotemporal autocorrelation with an application to real estate markets. A large literature modeling spatiotemporal autocorrelation in house prices assumes that the spatiotemporal dependence structure is isotropic: a function of only distances between observations, and therefore the direction effect is dismissed. If the importance of direction is dismissed or understated, an estimation result would be biased and therefore less precise unless the distribution of observations is in rare case of being directional homogeneous. This paper thus proposes a local anisotropic spatiotemporal approach to improve estimation performance. The methodology is illustrated by using data on single-family house transactions in the San Francisco Bay Area. The empirical results suggest that the proposed three-dimensional anisotropic modeling technique can reduce both in-sample estimation and out-of-sample forecast errors.

Joint Composite Estimating Functions in Spatiotemporal Models

SummaryModelling of spatiotemporal processes has received considerable attention in recent statistical research. However, owing to the high dimensionality of the data, the joint modelling of spatial and temporal processes presents a great computational challenge, in both likelihood-based and Bayesian approaches. We propose a joint composite estimating function approach to estimating spatiotemporal covariance structures. This substantially reduces the computational complexity and is more efficient than existing composite likelihood methods. The novelty of the proposed joint composite estimating function is rooted in the construction of three sets of estimating functions from spatial, temporal and spatiotemporal cross-pairs, which results in overidentified estimating functions. Thus, we form a joint inference function in a spirit that is similar to Hansen’s generalized method of moments. We show that under practical scenarios the estimator proposed is consistent and asymptotically normal. Simulation studies prove that our method performs well in finite samples. Finally, we illustrate the joint composite estimating function method by estimating the spatiotemporal dependence structure of airborne particulates (PM10) in the north-eastern USA over a 32-month period.

A practical approach for assessing the effect of grouping in hierarchical spatio-temporal models

Hierarchical spatio-temporal models allow for the consideration and estimation of many sources of variability. A general spatio-temporal model can be written as the sum of a spatio-temporal trend and a spatio-temporal random effect. When spatial locations are considered to be homogeneous with respect to some exogenous features, the groups of locations may share a common spatial domain. Differences between groups can be highlighted both in the large-scale, spatio-temporal component and in the spatio-temporal dependence structure. When these differences are not included in the model specification, model performance and spatio-temporal predictions may be weak. This paper proposes a method for evaluating and comparing models that progressively include group differences. Hierarchical modeling under a Bayesian perspective is followed, allowing flexible models and the statistical assessment of results based on posterior predictive distributions. This procedure is applied to tropospheric ozone data in the Italian Emilia–Romagna region for 2001, where 30 monitoring sites are classified according to environmental laws into two groups by their relative position with respect to traffic emissions.

Maxima of moving maxima of continuous functions

Maxima of moving maxima of continuous functions (CM3) are max-stable processes aimed at modelling extremes of continuous phenomena over time. They are defined as Smith and Weissman’s M4 processes with continuous functions rather than vectors. After standardization of the margins of the observed process into unit-Frechet, CM3 processes can model the remaining spatio-temporal dependence structure. CM3 processes have the property of joint regular variation. The spectral processes from this class admit particularly simple expressions given here. Furthermore, depending on the speed with which the parameter functions tend toward zero, CM3 processes fulfill the finite-cluster condition and the strong mixing condition. Processes enjoying these three properties also enjoy a simple expression for their extremal index. Next a method to fit CM3 processes to data is investigated. The first step is to estimate the length of the temporal dependence. Then, by selecting a suitable number of blocks of extremes of this length, clustering algorithms are used to estimate the total number of different profiles. The parameter functions themselves are estimated thanks to the output of the partitioning algorithms. The full procedure only requires one parameter which is the range of variation allowed among the different profiles. The dissimilarity between the original CM3 and the estimated version is evaluated by means of the Hausdorff distance between the graphs of the parameter functions.