Spatiotemporal Autoregressive Research Articles

Adaptive Gaussian Markov random field spatiotemporal models for infectious disease mapping and forecasting

Recent disease mapping literature presents adaptively parameterized spatiotemporal (ST) autoregressive (AR) or conditional autoregressive (CAR) models for Bayesian prediction of COVID-19 infection risks. These models were motivated to capture complex spatiotemporal dynamics and heterogeneities of infection risks. In the present paper, we synthesize, generalize, and unify the ST AR and CAR model constructions for models augmented by adaptive Gaussian Markov random fields, with an emphasis on disease forecasting. A general convolution construction is presented, with illustrative models motivated to (i) characterize local risk dependencies and influences over both spatial and temporal dimensions, (ii) model risk heterogeneities and discontinuities, and (iii) predict and forecast areal-level disease risks and occurrences. The broadened constructions allow rich options of intuitive parameterization for disease mapping and spatial regression. Illustrative parameterizations are presented for Bayesian hierarchical models of Poisson, zero-inflated Poisson, and Bernoulli data models, respectively. They are also discussed in the context of quantifying time-varying or time-invariant effects of (omitted) covariates, with application to prediction and forecasting areal-level COVID-19 infection occurrences and probabilities of zero-infection. The model constructions presented herein have much wider scope in offering a flexible framework for modelling complex spatiotemporal data and for estimation, learning, and forecasting purposes.

Buyer behaviour and price expectations: a spatial analysis of the Athens residential market

PurposeThis paper examines the price setting behaviour over time and space in the Athens residential market. In periods of house price inflation asking prices are often based upon the last observed highest selling price achieved for a similar property in the same micro-location. However, in a falling market, prices may be rigid downwards and less sensitive to the most recent transaction prices, weakening spatial effects. Furthermore, the paper considers whether future price expectations affect price setting behaviour.Design/methodology/approachThe paper employs a dataset of approximately 24,500 property values from 2007 until 2014 in Athens incorporating characteristics and locational variables. The authors begin by estimating a baseline hedonic price model using property characteristics, neighbourhood amenities and location effects. Following this, a spatio-temporal autoregressive (STAR) model is estimated. Running separate models, the authors account for spatial dependence from historic valuations, contemporaneous peer effects and expectations effects.FindingsThe initial STAR model shows significant spatial and temporal effects, the former remaining important in a falling market contrasting with previous literature findings. In the second STAR model, whilst past sales effects remain significant although smaller, contemporaneous and price expectations effects are also found to be significant, the latter capturing anchoring and slow adjustment heuristics in price setting behaviour.Research limitations/implicationsAs valuations used in the database are based upon comparable sales, then in the recessionary periods covered in the dataset, finding comparables may have become more difficult, and hence this, in turn, may have impacted on valuation accuracy.Practical implicationsIn addition to past effects, contemporaneous transactions and expected future values need to be taken in consideration in analysing spatial interactions in housing markets. These factors will influence housing markets in different cities and countries.Social implicationsThe information content of property valuations should more carefully consider the relative importance of different components of asking prices.Originality/valueThis is the first paper to use transactions data over a period of falling house prices in Athens and to consider current and future values in addition to past values in a spatio-temporal context.

ONE DAY AHEAD PREDICTION OF PM2.5 SPATIAL DISTRIBUTION USING MODIS 3 KM AOD AND SPATIOTEMPORAL MODEL OVER BEIJING-TIANJIN-HEBEI, CHINA

Abstract. Accurate prediction of PM2.5 concentration is the premise and guarantees to effectively control PM2.5 concentration and avoid the adverse effects of high PM2.5 concentration on human health. However, given the existing statistical models can only predict the pollutant concentration at the monitoring sites, the spatial distribution of PM2.5 concentration cannot be predicted, which greatly limits the application of the model in PM2.5 concentration prediction. This study combined the PM2.5 spatial distribution data predicted using the Moderate Resolution Imaging Spectroradiometer 3 km aerosol optical depth (AOD) and meteorological factors into a spatiotemporal autoregressive (STAR) model to predict the regional PM2.5 concentration and quantify the short-term spatial distribution change of PM2.5 in Beijing–Tianjin–Hebei region (JingJinJi) one day in advance. Five simulation functions were used to simulate the STAR model, and the 2014 data of JingJinJi were used to verify its accuracy. Results showed that the STAR model had the best prediction performance when gradient boosting decision tree was used as the simulation function compared with other simulation functions. The coefficient of determination (R2), root mean square prediction error (RMSE), index of agreement (IA), and mean absolute error (MAE) of the STAR model were 0.85, 27.08 µg/m3, 0.96, and 20 µg/m3, respectively. The spatial distribution prediction results of PM2.5 showed that the +1-day PM2.5 spatial distribution prediction results were in good agreement with the PM2.5 spatial distribution results predicted by AOD to provide accurate spatiotemporal distribution data for reducing air pollution and air pollution early warning.

Modeling and monitoring of a multivariate spatio-temporal network system

With the development of information technology, various network systems are created to connect physical objects and people by sensor nodes or smart devices, providing unprecedented opportunities to realize automated interconnected systems and revolutionize people’s lives. However, network systems are vulnerable to attacks, due to the integration of physical objects and human behaviors as well as the complex spatio-temporal correlated structures of the network systems. Therefore, how to accurately and effectively model and monitor a network system is critical to ensure information security and support system automation. To address this issue, this article develops a multivariate spatio-temporal modeling and monitoring methodology for a network system by using multiple types of sensor signals collected from the network system. We first propose a Multivariate Spatio-Temporal Autoregressive (MSTA) model by integrating a Gaussian Markov Random Field and a vector autoregressive model structure to characterize the spatio-temporal correlation of the network system. In particular, we develop an iterative model learning algorithm that integrates the Bayesian inference, least squares, and a sum square error-based optimization method to learn the network structure and estimate parameters in the MSTA model. Then, we propose two spatio-temporal control schemes to monitor the network system based on the MSTA model. Numerical experiments and a real case study of an IoT network system are presented to validate the performance of the proposed method.

Matrix Autoregressive Spatio-Temporal Models

Matrix-variate time series are now common in economic, medical, environmental, and atmospheric sciences, typically associated with large matrix dimensions. We introduce a structured autoregressive (AR) model to characterize temporal dynamics in a matrix-variate time series by formulating the AR matrices in a bilinear form. This bilinear parameter structure reduces the model dimension and highlights dynamic interaction among columns and rows in the AR matrices, making the model highly explainable. We further incorporate spatial information and explore sparsity in the AR coefficients by introducing spatial neighborhoods. In addition, we consider a nonstationary multi-resolution spatial covariance model for innovation errors. The resulting spatio-temporal AR model is flexible in capturing heterogeneous spatial and temporal features while maintaining a parsimonious parameterization. The model parameters are estimated by maximum likelihood (ML) with a fast algorithm developed for computation. We conduct a simulation study and present an application to a wind-speed dataset to demonstrate the merits of our methodology. Supplementary files for this article are available online.

Channel Prediction in High-Mobility Massive MIMO: From Spatio-Temporal Autoregression to Deep Learning

While massive multiple-input multiple-output (MIMO) has achieved tremendous success in both theory and practice, it faces a crisis of sharp performance degradation in moderate or high-mobility scenarios (e.g., 30 km/h), due to the breach of uplink-downlink channel duality. Such a “curse of mobility” has spurred the research on channel prediction in high-mobility scenarios. Instead of predicting channel response matrix in the space-frequency domain, we investigate it in the angle-delay domain by utilizing the high angle-delay resolution of wideband massive MIMO systems. Specifically, we study the general angle-delay domain channel characterization and obtain that: 1) the correlations between the angle-delay domain channel response matrix (ADCRM) elements are decoupled significantly; 2) when the number of antennas and bandwidth are limited, the decoupling is insufficient and residual correlations between the neighboring ADCRM elements exist. Then focusing on the ADCRM, we propose two channel prediction methods: a spatio-temporal autoregressive (ST-AR) model-driven unsupervised-learning method and a deep learning (DL) based data-driven supervised-learning method. While the model-driven method provides a principled way for channel prediction, the data-driven method is generalizable to various channel scenarios. In particular, ST-AR exploits the residual spatio-temporal correlations of the channel element with its most neighboring elements, and DL realizes element-wise angle-delay domain channel prediction utilizing a complex-valued neural network (CVNN). Simulation results under the 3GPP non-line-of-sight (NLOS) scenarios indicate that, compared to the state-of-the-art Prony-based angular-delay domain (PAD) prediction method, both the proposed ST-AR and the CVNN-based channel prediction methods can enhance the channel prediction accuracy.

High-Resolution PV Forecasting from Imperfect Data: A Graph-Based Solution

Operating power systems with large amounts of renewables requires predicting future photovoltaic (PV) production with fine temporal and spatial resolution. State-of-the-art techniques combine numerical weather predictions with statistical post-processing, but their resolution is too coarse for applications such as local congestion management. In this paper we introduce computing methods for multi-site PV forecasting, which exploit the intuition that PV systems provide a dense network of simple weather stations. These methods rely entirely on production data and address the real-life challenges that come with them, such as noise and gaps. Our approach builds on graph signal processing for signal reconstruction and for forecasting with a linear, spatio-temporal autoregressive (ST-AR) model. It also introduces a data-driven clear-sky production estimation for normalization. The proposed framework was evaluated over one year on both 303 real PV systems under commercial monitoring across Switzerland, and 1000 simulated ones based on high-resolution weather data. The results demonstrate the performance and robustness of the approach: with gaps of four hours on average in the input data, the average daytime NRMSE over a six-hour forecasting horizon (in 15 min steps) and over all systems is 13.8% and 9% for the real and synthetic data sets, respectively.

Impact of bus rapid transit on residential property prices in Auckland, New Zealand

Dubbed ‘The City of Cars’, congestion is a prominent issue in Auckland, New Zealand. Auckland's first Bus Rapid Transit (BRT) system - the Northern Busway - was implemented in 2008. The 6.2-km (km) busway network services the northern suburbs and provides a link to the Central Business District (CBD). This research aims to assess the impact of the Northern Busway on nearby residential property values. Spatio-temporal autoregressive (STAR) modelling is used to examine the accessibility impacts of the BRT under the difference – in – differences (DID) framework alongside a typical OLS and a strictly spatial model. We have observed two main findings. Firstly, the average sale price for properties in the treatment group (within 800 m of the Northern Busway) increased by approximately 3.69% as a result of the opening of the Northern Busway. Second, consistent with previous literature, we find that OLS estimates suffer from high spatial autocorrelation bias, while co-integrating spatial and temporal dependencies within a STAR model improves the precision of estimation. While the models produced a relatively modest accessibility premium on house prices, given traditional importance of private cars coupled with high income levels in the case study area, it would take a generational shift to make a significant impact on house prices as the area becomes more desirable due to reduced traffic congestion/travel time.

Estimating hourly PM2.5 concentrations using MODIS 3 km AOD and an improved spatiotemporal model over Beijing-Tianjin-Hebei, China

The spatiotemporal distribution of PM2.5 during heavy pollution is a short-term dynamic change process, and quantifying the dynamic change process of PM2.5 is the premise and guarantee for short-term PM2.5 exposure research. However, given the low temporal resolution of polar-orbiting satellites and late launch time of geostationary satellites, the application of remote sensing aerosol optical depth (AOD) data in hourly PM2.5 spatial distribution prediction is greatly limited, which brings uncertainty to short-term PM2.5 exposure research. This study introduces the PM2.5 concentration predicted by Moderate Resolution Imaging Spectroradiometer (MODIS) 3 km AOD data and the PM2.5 concentration of monitoring stations into a spatiotemporal autoregressive (STAR) model to generate hourly PM2.5 spatial distribution and quantify the short-term dynamic change process of PM2.5. The monitoring data in the Beijing–Tianjin–Hebei (JingJinJi) region of 2014 were used to test the model performance. Time-based 10-fold cross-validation (CV) R2 was 0.82, and the root-mean-square prediction error (RMSE) was 37.37 μg/m3. The CV R2 and RMSE were higher by 0.04 and lower by 3.4 μg/m3 than the STAR model without monitoring station PM2.5 concentration as predictors, which indicated that the monitoring station PM2.5 concentration could improve the performance of the model. Hourly performance statistics results showed that the model's accuracy increased when the time was closer to the MODIS transit time compared with that at other hours. The farther away from the MODIS transit time, the greater the monitoring stations' PM2.5 concentration improved the performance of the model. The predicted results of the spatial distribution of PM2.5 showed that the spatial distribution of the average PM2.5 concentration in each hour varied greatly in JingJinJi, and the maximum difference reached 30 μg/m3. The model in this paper not only demonstrates high prediction accuracy but also provides high spatiotemporal resolution of PM2.5 for short-term PM2.5 exposure studies.

Spatio-temporal modeling of yellow taxi demands in New York City using generalized STAR models

The spatio-temporal variation in the demand for transportation, particularly taxis, in the highly dynamic urban space of a metropolis such as New York City is impacted by various factors such as commuting, weather, road work and closures, disruptions in transit services, etc. This study endeavors to explain the user demand for taxis through space and time by proposing a generalized spatio-temporal autoregressive (STAR) model. It deals with the high dimensionality of the model by proposing the use of LASSO-type penalized methods for tackling parameter estimation. The forecasting performance of the proposed models is measured using the out-of-sample mean squared prediction error (MSPE), and the proposed models are found to outperform other alternative models such as vector autoregressive (VAR) models. The proposed modeling framework has an easily interpretable parameter structure and is suitable for practical application by taxi operators. The efficiency of the proposed model also helps with model estimation in real-time applications.

Spatiotemporal Tracking of Ocean Current Field With Distributed Acoustic Sensor Network

A distributed networked underwater sensor (DNUS) system can provide ocean measurements over a wide area with a large number of sensors. This paper studies the estimation of the ocean current field observed by a DNUS system. Considering that the current field is correlated in time and space, we present a statistically-based acoustic travel time difference tomography method based on a Kalman filter (KF) to reconstruct and track the ocean current field. A spatiotemporal autoregressive (AR) model is used to describe the time evolution of the current field. In the spatiotemporal AR model, the observation region is divided into subtriangle grids. The subtriangles are partitioned into clusters and each cluster is assigned with one AR coefficient. Moreover, the AR coefficients are updated adaptively with the past estimated current velocities. The proposed method is verified with the synthetic observational data generated by a barotropic ocean model. Compared with the regular distributed processing method, the proposed ocean current field reconstruction and tracking method achieves a lower region-integrated root-mean-square error (RMSE). In addition, by making use of the spatiotemporal correlation, the proposed method is robust to the measurement link failure and burst errors in the DNUS system.

Current field tracking based on spatiotemporal evolution model with distributed networked underwater sensor system

Distributed networked underwater sensor (DNUS) system can provide ocean measurements over a wide area with a large number of sensors. This paper studies the estimation of the two-dimensional ocean current field with acoustic travel time difference data observed by a DNUS system. Considering that the current field is correlated in time and space, we present a statistical-based tomography method based on Kalman filter to reconstruct and track the ocean current field. A spatiotemporal autoregressive (AR) model is used to describe the evolution of the current field. In the spatiotemporal AR model, the observation region is divided into sub-triangle grids. The sub-triangles are partitioned into clusters by distance and each cluster is assigned with one AR coefficient. The AR coefficients are updated adaptively with the past estimated current velocities. The proposed method is verified with the synthetic observational data generated by a barotropic ocean model and the tomography experiment conducted near Zhoush...

The role of spatial and temporal structure for residential rent predictions

This paper examines the predictive power of five linear hedonic pricing models for the residential market with varying levels of complexity in their spatial and temporal structures. Unlike similar studies, we extend the out-of-sample forecast evaluation to one-day-ahead predictions with a rolling estimation window, which is a reasonable setting for many practical applications. We show that the in-sample fit and cross-validation prediction accuracy improve significantly when we account for spatial heterogeneity. In particular, for one-day-ahead forecasts, the spatiotemporal autoregressive (STAR) model demonstrates its superiority over model specifications with alternating spatial and temporal heterogeneity and dependence structures. In addition, sub-market fixed effects, constructed on the basis of statistical TREE methods, improve the results of predefined local rental markets further.

The Impact of LEED Neighborhood Certification on Condo Prices

The U.S. Green Building Council offers LEED certification for existing and new neighborhood developments that meet sustainable urban development standards. Features of sustainable urban development have been found to positively affect residential sales prices. We investigate whether the intangible labeling effects of LEED neighborhood certification add a premium to the sales prices of LEED and non‐LEED–certified condos. Using a quasi‐experiment, transaction data from Portland, Oregon, and a spatio‐temporal autoregressive (STAR) model, we find no evidence that the intangible labeling effects of LEED neighborhood certification directly or indirectly affect sales prices. Our results suggest that, contrary to LEED building certification, which we find adds a premium to condo sales prices, the LEED neighborhood label by itself fails to add value for condo buyers. Explanations for our findings include market acceptance, neighborhood delineation issues and the free rider problem as it relates to public goods.

The Role of Spatial and Temporal Structure for Residential Rent Predictions

This paper examines the predictive power of five linear hedonic pricing models for the residential market with varying complexity in their spatial and temporal structure. In contrast to similar studies, we extend the out-of-sample forecast evaluation to one-day-ahead predictions with a rolling estimation window, which is a reasonable setting for many practical applications. We can show that in-sample fit and cross-validation prediction accuracy improve significantly when we account for spatial heterogeneity. In particular, for one-day-ahead forecasts, the spatiotemporal autoregressive (STAR) model demonstrates its superiority compared to model specifications with alternating spatial and temporal heterogeneity and dependence structures. In addition, sub-market fixed-effects, constructed on the basis of statistical TREE methods, further improve the results of predefined local rental markets.

Retrospective Analysis of the Dwelling Price by Means of STAR Models with Neighborhood Effects

The need of retrospective predictions arises in situations such as litigations, inheritances or fiscal purposes to provide the fair market value of a dwelling of given characteristics and specific location. In this paper, a Bayesian method to carry out this retrospective analysis is proposed by using a Spatio-Temporal Autoregressive (STAR) model with neighborhood effects and heteroscedastic errors. Moreover, the developed methodology allows the construction of a retrospective price index that shows the evolution of the dwelling price level in a specific geographical area. The methodology is illustrated with an application to the real estate market in the Spanish city of Zaragoza.

The role of borders, languages, and currencies as obstacles to labor market integration

Based on a modified spatiotemporal autoregressive (STAR) model, we analyze whether borders still constitute significant impediments to labor market integration in the European Union, despite the formal law of free movement of labor. Using regional data from the EU-15 countries over 21 years, we find that this is the case. We further investigate whether the abolishment of border checks through the Schengen agreement or the introduction of the Euro improved our measure of labor market integration across borders, and do not find evidence in favor. Last, we investigate the role of languages, and potentially cultures, as obstacles to labor market integration. We find that indeed language borders play a larger role than country borders in explaining the lack of labor market integration across borders.

Forecasting intentional wildfires using temporal and spatiotemporal autocorrelations

We report daily time series models containing both temporal and spatiotemporal lags, which are applied to forecasting intentional wildfires in Galicia, Spain. Models are estimated independently for each of the 19 forest districts in Galicia using a 1999–2003 training dataset and evaluated out-of-sample with a 2004–06 dataset. Poisson autoregressive models of order P – PAR(P) models – significantly out-perform competing alternative models over both in-sample and out-of-sample datasets, reducing out-of-sample root-mean-squared errors by an average of 15%. PAR(P) and static Poisson models included covariates deriving from crime theory, including the temporal and spatiotemporal autoregressive time series components. Estimates indicate highly significant autoregressive components, lasting up to 3 days, and spatiotemporal autoregression, lasting up to 2 days. Models also applied to predict the effect of increased arrest rates for illegal intentional firesetting indicate that the direct long-run effect of an additional firesetting arrest, summed across forest districts in Galicia, is –139.6 intentional wildfires, equivalent to a long-run elasticity of –0.94.

Variable selection in STAR models with neighbourhood effects using genetic algorithms

In this paper we deal with the problem of variable selection in spatiotemporal autoregressive (STAR) models with neighbourhood effects. We propose a procedure to carry out the selection process, taking into account the uncertainty associated with estimation of the parameters and the predictive behaviour of the compared models, in order to give more realism to the analysis. We set up a multi-objective programming problem that combines the use of different criteria to measure both these aspects. We use genetic algorithms which are very flexible and suitable for our multicriteria decision problem. In particular, the procedure allows us to estimate the number of spatial and temporal nearest neighbours as well as their relative effects. The methodology is illustrated through an application to the real estate market of Zaragoza. Copyright © 2010 John Wiley & Son, Ltd.

A Spatio-Temporal Auto Regressive Model for Frame Rate Upconversion

This paper proposes a spatio-temporal auto regressive (STAR) model for frame rate upconversion. In the STAR model, each pixel in the interpolated frame is approximated as the weighted combination of a sample space including the pixels within its two temporal neighborhoods from the previous and following original frames as well as the available interpolated pixels within its spatial neighborhood in the current to-be-interpolated frame. To derive accurate STAR weights, an iterative self-feedback weight training algorithm is proposed. In each iteration, first the pixels of each training window in the interpolated frames are approximated by the sample space from the previous and following original frames and the to-be-interpolated frame. And then the actual pixels of each training window in the original frame are approximated by the sample space from the previous and following interpolated frames and the current original frame with the same weights. The weights of each training window are calculated by jointly minimizing the distortion between the interpolated frames in the current and previous iterations as well as the distortion between the original frame and its interpolated one. Extensive simulation results demonstrate that the proposed STAR model is able to yield the interpolated frames with high performance in terms of both subjective and objective qualities.