Spatio-temporal Autoregressive Model Research Articles

The Spatio-Temporal Distribution of Suicide-related Emergency Calls in a European City: Age and Gender Patterns, and Neighborhood Influences.

Objective: The aim of this study was to conduct a comprehensive spatio-temporal analysis of suicide-related emergency calls in the city of Valencia (Spain) over a six-year period. To this end we first examined age and gender patterns and, second, the influence of neighborhood characteristics on general and gender-specific spatio-temporal patterns of suicide-related emergency calls. Method: Geocoded data on suicide-related emergency calls between 2017 and 2022 (N = 10,030) were collected from the 112 emergency service in Valencia. Data were aggregated at the census block group level, used as a proxy for neighborhoods, and trimesters were considered as the temporal unit. Two set of analyses were performed: (1) demographic (age and gender) and temporal descriptive analyses and (2) general and gender-specific Bayesian spatio-temporal autoregressive models. Results: Descriptive analyses revealed a higher incidence of suicide-related emergency calls among females and an increase in calls among the 18-23 age group from 2020 onwards. The general spatio-temporal model showed higher levels of suicide-related emergency calls in neighborhoods characterized by lower education levels and population density, and higher residential mobility, aging population, and immigrant concentration. Relevant gender differences were also observed. A seasonal effect was noted, with a peak in calls during spring for females and summer for males. Conclusions: These findings highlight the need for comprehensive mental health targeted interventions and preventive strategies that account for gender-specific disparities, age-related vulnerabilities, and the specific characteristics of neighborhoods.

A multivariate spatial and spatiotemporal ARCH Model

This paper introduces a multivariate spatiotemporal autoregressive conditional heteroscedasticity (ARCH) model based on a vec-representation. The model includes instantaneous spatial autoregressive spill-over effects, as they are usually present in geo-referenced data. Furthermore, spatial and temporal cross-variable effects in the conditional variance are explicitly modelled. We transform the model to a multivariate spatiotemporal autoregressive model using a log-squared transformation and derive a consistent quasi-maximum-likelihood estimator (QMLE). For finite samples and different error distributions, the performance of the QMLE is analysed in a series of Monte-Carlo simulations. In addition, we illustrate the practical usage of the new model with a real-world example. We analyse the monthly real-estate price returns for three different property types in Berlin from 2002 to 2014. We find weak (instantaneous) spatial interactions, while the temporal autoregressive structure in the market risks is of higher importance. Interactions between the different property types only occur in the temporally lagged variables. Thus, we see mainly temporal volatility clusters and weak spatial volatility spillovers.

Enhancing ENSO predictions with self-attention ConvLSTM and temporal embeddings

El Niño-Southern Oscillation (ENSO), a cyclic climate phenomenon spanning interannual and decadal timescales, exerts substantial impacts on the global weather patterns and ecosystems. Recently, deep learning has brought considerable advances in the accurate prediction of ENSO occurrence. However, the current models are insufficient to characterize the evolutionary behavior of the ENSO, particularly lacking comprehensive modeling of local-range and longrange spatiotemporal interdependencies, and the incorporation of calendar monthly and seasonal properties. To make up this gap, we propose a Two-Stage SpatioTemporal (TSST) autoregressive model that couples the meteorological factor prediction with ENSO indicator prediction. The first stage predicts the meteorological time series by leveraging self-attention ConvLSTM network which captures both the local and the global spatial-temporal dependencies. The temporal embeddings of calendar months and seasonal information are further incorporated to preserves repeatedly-occurring-yet-hidden patterns in meteorological series. The second stage uses multiple layers to extract higher level of features from predicted meteorological factors progressively to generate ENSO indicators. The results demonstrate that our model outperforms the state-of-the-art ENSO prediction models, effectively predicting ENSO up to 24 months and mitigating the spring predictability barrier.

Forecasting Money Flow in East Java Using The Generalized Space-Time Autoregressive With Exogenous Variable Method

The forecast is more accurate when involving an exogen, for example, the generalized spatio temporal autoregressive (GSTAR) model with exogenous variables (GSTARX). This study aims to obtain appropriate statistical values to identify autoregressive orders for time dependencies and order effects with exogenous variables such as Eid al-Fitr and the consumer price index (CPI) in the GSTARX model. Additionally, this study seeks to obtain a GSTARX model suitable for forecasting. The case study is the inflows and outflows in four locations in East Java. The simulation results show that the statistical values for identifying VAR order for time dependencies use the matrix partial cross-correlation function (MPCCF). Meanwhile, effect orders from exogenous variables in the two-level GSTARX model show CCF at level one. In addition, GLS (general least squares) produces a more efficient estimator than the OLS (ordinary least squares). The results of the case study show that the two-level GSTAR model forming inflow and outflow data are GSTARX (31) and GSTARX ([1,3]1) respectively. In addition, the comparison of forecast accuracy shows that, in general, the smallest root mean square error (RMSE) value in the two-level GSTARX model is the inverse distance weight.

Price competition and market concentration: Evidence from the land market in China

While localized price competition in many markets has been extensively analyzed, little empirical work has been undertaken in the land market. It is the intent of this paper, therefore, to investigate the nature of spatial price competition among land sellers that compete in concentrated markets within a specific geographical area. Applying spatio-temporal autoregressive model to data from the residential land market in China from 2007 to 2015, we find that, (1) the land market for residential development is highly localized, where land sellers (local governments) respond more strongly to the price changes by “close-by” sellers; (2) larger market share is significantly associated with less spatial price response and higher land price. Placebo analysis using the sample of land supply for industrial development reinforces a causal interpretation of our main findings. Results from this paper permit the conclusion that the supply of land for residential development is not a perfect competitive but a localized competitive market where land sellers controlling a larger share of the market exercise market power to maximize land revenue.

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.

Efficient Output Photovoltaic Power Prediction Based on MPPT Fuzzy Logic Technique and Solar Spatio-Temporal Forecasting Approach in a Tropical Insular Region

Photovoltaic (PV) energy source generation is becoming more and more common with a higher penetration level in the smart grid because of PV energy’s falling production costs. PV energy is intermittent and uncertain due to its dependence on irradiance. To overcome these drawbacks, and to guarantee better smart grid energy management, we need to deal with PV power prediction. The work presented in this paper concerns the study of the performance of the fuzzy MPPT approach to extract a maximum of power from solar panels, associated with PV power estimation based on short time scale irradiance forecasting. It is particularly applied to a case study of a tropical insular region, considering extreme climatic variability. To validate our study with real solar data, measured and predicted irradiance profiles are used to feed the PV system, based on solar forecasting in a tropical insular context. For that, a spatio-temporal autoregressive model (STVAR) is applied. The measurements are collected at three sites located on Guadeloupe island. The high variability of the tropical irradiance profile allows us to test the robustness and stability of the used MPPT algorithms. Solar forecasting associated with the fuzzy MPPT technique allows us to estimate in advance the produced PV power, which is essential for optimal energy management in the case of smart energy production systems. Simulation of the proposed solution is validated under Matlab/Simulink software. The results clearly demonstrate that the proposed solution provides good PV power prediction and better optimization performance: a fast, dynamic response and stable static power output, even when irradiation is rapidly changing.

Capacity of River Valleys to Retain Nutrients from Surface Runoff in Urban and Rural Areas (Southern Poland)

Studies on water quality are necessary, as catchments of small watercourses are exposed to anthropogenic influences associated with agricultural activities, settlement, transport and other undertakings, leading to water pollution. There has been insufficient research performed on the valley’s ability to retain nutrients during floods, contributing to water accumulation. The main object of the study was to identify the retention capacity of river valleys under various aspects of human urbanization. To represent soil water retention, the Soil Conservation Service Curve Number (SCS-CN) method was used. Spatiotemporal autoregressive models were exploited to investigate the relationship between pollutants in precipitation and surface water in rivers. In contrast, multivariate analysis was used to identify and reveal patterns of land use for specific chemical compounds in the headwaters. The canonical-correlation analysis (CCA) showed that Mg+2 and Ca+2 cations in rainwater and surface waters play the main roles in the geochemical cycle in urban and rural areas. In the urban catchment area, the strongest relations were found for NO3−, K+ and Na+. The average NO3− concentration in urban headwater was 8.3 mg·dm−3, the highest in the study area. The relationship between NO3− concentration in headwater and rainwater was found for all study catchments using spatial autoregression (SAR). High concentrations of SO42− in surface water have been identified in urban areas. Severe water erosion raises the risk of nutrient leaching in soils prone to surface runoff. As a consequence of low soil permeability and urbanization, retention capacity is significantly reduced in areas with low soil permeability. Land development plans should take spatial retention capacity into consideration. To ensure that large reservoirs can retain water in the face of climate change, riparian buffer zones (protective zones in valleys for small water bodies as well as Nature-based Solution) are important.

Estimation of the Spatial Weighting Matrix for Spatiotemporal Data under the Presence of Structural Breaks

ABSTRACT In this article, we propose a two-stage LASSO estimation approach for the estimation of a full spatial weight matrix of spatiotemporal autoregressive models. In addition, we allow for an unknown number of structural breaks in the local means of each spatial location. These locally varying mean levels, however, can easily be mistaken as spatial dependence and vice versa. Thus, the proposed approach jointly estimates the spatial dependence, all structural breaks, and the local mean levels. For selection of the penalty parameter, we propose a completely new selection criterion based on the distance between the empirical spatial autocorrelation and the spatial dependence estimated in the model. Through simulation studies, we will show the finite-sample performance of the estimators and provide practical guidance as to when the approach could be applied. Finally, the method will be illustrated by an empirical example of intra-city monthly real-estate prices in Berlin between 1995 and 2014. The spatial units will be defined by the respective postal codes. The new approach allows us to estimate local mean levels and quantify the deviation of the observed prices from these levels due to spatial spillover effects. In doing so, the entire spatial dependence structure is estimated on a data-driven basis. Supplementary materials for this article are available online.

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.

A Spatio-Temporal autocorrelation model for designing a carshare system using historical heterogeneous Data: Policy suggestion

As an emerging urban mobility service, carsharing has become increasingly popular worldwide. To understand customers’ needs and optimize the design of service networks, the usage of carsharing vehicles whose trips are recorded by the operators has been applied in research estimating carsharing demand. However, as a form of spatio-temporal correlated data, the underlying spatio-temporal information included in such carsharing records has not been investigated in existing models of carsharing demand. Meanwhile, due to the supply limitation of carsharing stations, some demand cannot be fulfilled and thus remains unrecorded in the operational data. Unrealized demand may lead to underestimation of carsharing demand and therefore an incorrect vehicle deployment strategy by the service providers. In view of these issues, this paper develops an innovative approach to estimating the actual demand at a carsharing station with operational data from GoGet, the largest carsharing company in Australia. The accuracy of the estimation is improved by adding spatio-temporal correlated variables as well as variables from emerging data sources such as social media. To explore the latent space-and-time correlated information, spatio-temporal autoregressive and moving-average models have been applied. Based on the results of the analysis, the paper also provides recommendations related to the operation policies of the service providers.

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.

A spatio-temporal autoregressive model for monitoring and predicting COVID infection rates

The COVID-19 epidemic has raised major issues with regard to modelling and forecasting outcomes such as cases, deaths and hospitalisations. In particular, the forecasting of area-specific counts of infectious disease poses problems when counts are changing rapidly and there are infection hotspots, as in epidemic situations. Such forecasts are of central importance for prioritizing interventions or making severity designations for different areas. In this paper, we consider different specifications of autoregressive dependence in incidence counts as these may considerably impact on adaptivity in epidemic situations. In particular, we introduce parameters to allow temporal adaptivity in autoregressive dependence. A case study considers COVID-19 data for 144 English local authorities during the UK epidemic second wave in late 2020 and early 2021, which demonstrate geographical clustering in new cases—linked to the then emergent alpha variant. The model allows for both spatial and time variation in autoregressive effects. We assess sensitivity in short-term predictions and fit to specification (spatial vs space-time autoregression, linear vs log-linear, and form of space decay), and show improved one-step ahead and in-sample prediction using space-time autoregression including temporal adaptivity.

Spatiotemporal prediction of COVID-19 cases using inter- and intra-county proxies of human interactions

Measurements of human interaction through proxies such as social connectedness or movement patterns have proved useful for predictive modeling of COVID-19, which is a challenging task, especially at high spatial resolutions. In this study, we develop a Spatiotemporal autoregressive model to predict county-level new cases of COVID-19 in the coterminous US using spatiotemporal lags of infection rates, human interactions, human mobility, and socioeconomic composition of counties as predictive features. We capture human interactions through 1) Facebook- and 2) cell phone-derived measures of connectivity and human mobility, and use them in two separate models for predicting county-level new cases of COVID-19. We evaluate the model on 14 forecast dates between 2020/10/25 and 2021/01/24 over one- to four-week prediction horizons. Comparing our predictions with a Baseline model developed by the COVID-19 Forecast Hub indicates an average 6.46% improvement in prediction Mean Absolute Errors (MAE) over the two-week prediction horizon up to 20.22% improvement in the four-week prediction horizon, pointing to the strong predictive power of our model in the longer prediction horizons.

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.

Spatio Temporal Modelling for Government Policy the COVID-19 Pandemic in East Java

COVID-19 has cursorily spread globally. Just in four months, its status altered into a pandemic. In Indonesia, the virus epicenter is identified in Java. The first positive case was identified in West Java and later spread in all Java. The Large-scale Social Restrictions are seemingly inefficient as the SARS-CoV-2 transmission remains. As such, the government is struggling to find anticipatory policies and steps best to mitigate the transmission. In this particular article, we used a Spatio-temporal model method for the total COVID-19 cases in Java and forecasted the total cases for the next 14 days, allowing the stakeholders to make more effective policies. The data we were using were the daily data of the cumulative number of COVID-19 cases taken from www.covid19.go.id. Data modelling was conducted using a generalized spatio-temporal autoregressive model. The model acquired to model the COVID-19 cases in Java was the GSTAR(1)(1,0,0) model.

Decentralized estimation of ocean current field using underwater acoustic sensor networks.

A decentralized method is proposed to estimate the two-dimensional horizontal ocean current field using the underwater acoustic sensor networks (UASNs), termed the "UASN-decentralized" method, which integrates the state-of-the-art ocean current field estimation techniques for UASNs: triangle-division-based travel time difference tomography and a spatiotemporal autoregressive model of ocean current dynamics. Moreover, the UASN-decentralized method employs a single-time scale consensus+innovations distributed estimator, called the "distributed information Kalman filter," to perform decentralized estimation and tracking. Given the redundancy of travel time differences when using UASN-based tomography, sensor nodes are classified into two types (i.e., type I and type II) to perform different tasks to reduce computations. A shortest-path-based consensus weight matrix is designed to accommodate fast-varying ocean dynamics. More communication rounds after each sensing are studied as an extension of the adopted single-time scale distributed estimator. Synthetic data are used to verify the decentralized method. Monte Carlo simulations show the feasibility of the proposed method and its robustness to measurement error related problems. With an increased number of communication rounds, the proposed method can also work well for fast-varying dynamics or a lowered sensor measurement rate.

Exploring the Dynamic Spatio-Temporal Correlations between PM2.5 Emissions from Different Sources and Urban Expansion in Beijing-Tianjin-Hebei Region.

Due to rapid urbanization globally more people live in urban areas and, simultaneously, more people are exposed to the threat of environmental pollution. Taking PM2.5 emission data as the intermediate link to explore the correlation between corresponding sectors behind various PM2.5 emission sources and urban expansion in the process of urbanization, and formulating effective policies, have become major issues. In this paper, based on long temporal coverage and high-quality nighttime light data seen from the top of the atmosphere and recently compiled PM2.5 emissions data from different sources (transportation, residential and commercial, industry, energy production, deforestation and wildfire, and agriculture), we built an advanced Bayesian spatio-temporal autoregressive model and a local regression model to quantitatively analyze the correlation between PM2.5 emissions from different sources and urban expansion in the Beijing-Tianjin-Hebei region. Our results suggest that the overall urban expansion in the study area maintained gradual growth from 1995 to 2014, with the fastest growth rate during 2005 to 2010; the urban expansion maintained a significant positive correlation with PM2.5 emissions from transportation, energy production, and industry; different anti-haze policies should be designated according to respective local conditions in Beijing, Tianjin, and Hebei provinces; and during the period of rapid urban expansion (2005–2010), the spatial correlations between PM2.5 emissions from different sources and urban expansion also changed, with the biggest change coming from the PM2.5 emissions from the transport sector.

A Bayesian spatiotemporal autoregressive model with constant and temporally varying coefficients: an application to hotspot detection of childhood tuberculosis in Bandung City, Indonesia

The health reported data shows that the risk of tuberculosis among children aged 0-14 years is still a significant health problem in developing countries such as Indonesia in terms of case detection, control, and effective treatment. However, some information is available about the burden of tuberculosis and its risk factors (e.g., malnutrition, population density, healthy behaviours, and AFB smear-positive tuberculosis) which can be very useful. This study aimed to identify the hotspot of tuberculosis among children aged 0-14 years in Bandung city, Indonesia. Using Bandung health profile database of tuberculosis notification for 2016 – 2018, we estimated the burden of tuberculosis among children aged 0-14 years by districts. We estimate that incidence rates vary over space and time, with the hotspots centred in the western and central regions of Bandung city. Population density has a significant effect on burden tuberculosis among aged 0-14 years over districts.