Space-time Autoregressive Moving Average Research Articles

Enhanced Spatio-Temporal Modeling for Rainfall Forecasting: A High-Resolution Grid Analysis

Rainfall serves as a lifeline for crop cultivation in many agriculture-dependent countries including India. Being spatio-temporal data, the forecasting of rainfall becomes a more complex and tedious process. Application of conventional time series models and machine learning techniques will not be a suitable choice as they may not adequately account for the complex spatial and temporal dependencies integrated within the data. This demands some data-driven techniques that can handle the intrinsic patterns such as non-linearity, non-stationarity, and non-normality. Space–Time Autoregressive Moving Average (STARMA) models were highly known for its ability to capture both spatial and temporal dependencies, offering a comprehensive framework for analyzing complex datasets. Spatial Weight Matrix (SWM) developed by the STARMA model helps in integrating the spatial effects of the neighboring sites. The study employed a novel dataset consisting of annual rainfall measurements spanning over 50 (1970–2019) years from 119 different locations (grid of 0.25 × 0.25 degree resolution) of West Bengal, a state of India. These extensive datasets were split into testing and training groups that enable the better understanding of the rainfall patterns at a granular level. The study findings demonstrated a notable improvement in forecasting accuracy by the STARMA model that can exhibit promising implications for agricultural management and planning, particularly in regions vulnerable to climate variability.

An estimation method for switching points of multimode spatiotemporal data based on SFSTAR

Various traditional methods, including statistical and spatial map-based approaches, are employed to model spatiotemporal data. However, the lack of explicit descriptions of spatial and temporal dependencies leads to unnecessarily intensive and uninterpretable relationships among the variables. To address this problem, space–time autoregressive moving average (STARMA)-type models that can depict temporal and spatial dependencies in a parametric manner are adopted in this study. However, such models may not be applicable to unlabeled multimode spatiotemporal data. In this study, we propose a switching flexible space–time autoregressive (SFSTAR) model to describe multimode spatiotemporal data. Considering the coupling between the parameter estimation of each mode and determination of the switching points, an estimation method is proposed to identify the mode switching points to partition the multimode data into different segments. First, the proposed estimation method identifies the number of segments by locating the transition regions that enclose the switching points based on the spatiotemporal feature extraction proposed herein. Second, with the estimated number of segments that is actually the number modes and the constraints on the locations of the switching points given by the transition regions, the proposed method jointly estimates the switching points and the SFSTAR model parameters in each mode through Bayesian optimization. The effectiveness of the proposed method is evaluated using a numerical example and a fiber optic temperature measurement dataset.

Comparison of modelling and prediction of export values in West Java, Banten, and Central Java using the STIMA and GSTIMA (1,1,1)

Export is the delivery and sale of goods from a country to abroad. The growth of export values can be seen from time to time and it differs between locations which are influenced by spatial interactions. The Space-Time Autoregressive Moving Average (STARMA) model is a model that combines the interdependence of time and location. However, the STARMA model is sometimes seen unrealistic as it assumes all parameters in all locations to be the same. Meanwhile, The Generalized Space-Time Autoregressive Moving Average (GSTARMA) model is more realistic because it produces different parameters for each location. This study aims to compare the STIMA and GSTIMA models and to forecast export values. The STIMA and GSTIMA models are the models with zero-order for AR and apply First Difference. In this study, the STIMA and GSTIMA models with weighted inverse distance are used to predict the value of exports in three interacting provinces that have dominant superior sectors in the industrial sector, namely the Provinces of West Java, Banten, and Central Java. The data used is export values from January 2014 – December 2018. The identification of the model revealed the 1st order cut-off on lag 1 of the STACF plot with the first data differencing. The selected order of spatial lag is lag 1 because these three provinces are located on the same island. This is confirmed through the VARMA approach where the AR(0) and MA(1) models have the smallest AIC values so that the models constructed are the STIMA(1,1,1) and GSTIMA(1,1,1). The results of this study indicated that the GSTIMA(1,1,1) model produce better prediction than the STIMA(1,1,1) as it has a smaller MAPE value, where each MAPE value is 14.23% for STIMA and 11.38% for GSTIMA. This result indicates the fulfillment of different parameter assumptions at each location under the existing phenomenon that the export management of each location has different characteristics.

Two-Stage Spatiotemporal Time Series Modelling Approach for Rice Yield Prediction & Advanced Agroecosystem Management

A robust forecast of rice yields is of great importance for medium-to-long-term planning and decision-making in cereal production, from regional to national level. Incorporation of spatially correlated adjacent effects in forecasting models in general, results in accurate forecast. The Space Time Autoregressive Moving Average (STARMA) is the most popular class of model in linear spatiotemporal time series modelling. However, STARMA cannot process nonlinear spatiotemporal relationships in datasets. Alternately, Time Delay Neural Network (TDNN) is a most popular machine learning algorithm to model the nonlinear pattern in data. To overcome these limitations, two-stage STARMA approach was developed to predict rice yield in some of the most intensive national rice agroecosystems in India. The Mean Absolute Percentage Errors value of proposed STARMA-II approach is lower compared to Autoregressive Moving Average (ARIMA) and STARMA model in all examined districts, while the Diebold-Mariano test confirmed that STARMA-II model is significantly different from classical approaches. The proposed STARMA-II approach is promising alternative to classical linear and nonlinear spatiotemporal time series models for estimating mixed linear and nonlinear patterns and can be advanced tool for mid-to-long-term sustainable planning and management of crop yields and patterns in agroecosystems, i.e., food supply and demand from local to regional levels.

Generalized Space Time Autoregressive Integrated Moving Average with Exogenous (GSTARIMA-X) Models

Space time data is data that relates to events at previous times and locations. One of the models that used to analyze space time data is the Generalized Space Time Autoregressive Moving Average (GSTARMA) model. GSTARMA model uses parameters p and λk to represent the time order and spatial order respectively. Hence, this model can be called GSTARMA(p, λk ). Because in fact there are more models with different parameters for different locations, GSTARMA(p, λk ) model is more realistic. If space time data is not stationary, a different order is added so that the model becomes GSTARIMA(p, d, λk ). In modelling sometimes the accuracy of the model can increase by other influence variables. These variables are named exogenous variables. The GSTARIMA model with exogenous variables is named the GSTARIMA-X(p, d, λk ) model. This research aims to examine the model and its estimation of parameters. Model parameters are estimated using the Generalized Least Square (GLS) method. The method in this writing is literature study obtained from several articles, journals, and books that support in achieving research. The results of the study show that with the GLS method, parameter estimates can be obtained with the assumption of time order 1 and spatial order 1.

A hybrid spatio-temporal modelling: an application to space-time rainfall forecasting

Efficient and reliable forecasting techniques for various climatic conditions are indispensable in agricultural dependent country like India. In this context, rainfall forecasting is one of the most challenging tasks because of the existence of three patterns, viz., temporal, spatial, and non-linear, simultaneously. Space-Time Autoregressive Moving Average (STARMA) model is one of the promising and popular approaches for modelling spatio-temporal time series data. However, the observed features of many space-time rainfall data comprise complex non-linear dynamics and modelling these patterns often go beyond the capability of conventional STARMA model. Moreover, despite the popularity of artificial neural network (ANN) and support vector machine (SVM) for modelling complex non-linear dynamics, they are not capable to deal with spatial patterns. To overcome the problem, a new spatio-temporal hybrid modelling approach has been proposed by integrating STARMA, ANN, and SVM as well. The proposed approach has been empirically illustrated on annual precipitation data of six districts of northern part of West Bengal, India. The study reveals that proposed spatio-temporal hybrid approach has better modelling and forecasting precision over conventional STARMA as well as most widely used Autoregressive Integrated Moving Average (ARIMA) model.

Testing for poolability of the space-time autoregressive moving-average model

We consider the impacts of spatial aggregation on the model parameters and forecasts of the space-time autoregressive moving-average (STARMA) model. In particular, we focus on poolability, the equality of mean squared forecast error of the aggregate variable from both the non-aggregate and aggregate models, where the same model order is assumed because a model order is often unchanged under spatial aggregation, which is different from temporal aggregation. For VARMA models, there exists conditions for poolability with known parameters and a test for poolability when parameters are not known. However, this test does not apply to STARMA models due to the restricted form of their parameter matrices. In focusing on the STARMA model, we show how the aggregate model parameters are functions of the non-aggregate model parameters under poolability. In addition, we develop three poolability tests that apply to any STARMA model. We demonstrate these tests through an empirical example involving urban crime data.

A GIS-Based Spatial-Temporal Autoregressive Model for Forecasting Marine Traffic Volume of a Shipping Network

Research on the forecasting of marine traffic flows can provide a basis for port planning, planning the water area layout, and ship navigation management and provides a practical background for sustainable development evaluation of shipping. Most of the traditional marine traffic volume forecasting studies focus on the variation of the traffic volume of a single port or section in time dimension and less research on traffic correlation of associated ports in shipping networks. To reveal the spatial-temporal autocorrelation characteristics of the shipping network and to establish a suitable space-time forecasting model for marine traffic volume, this paper uses the AIS data from 2011 to 2016 for the South China Sea to construct a regional shipping network. The adjacent discrimination rule based on network correlation is proposed, and the traffic demand between ports is estimated based on the gravity model. On this basis, STARMA (space-time autoregressive moving average) model was introduced for deducing the interaction between he traffic volumes of adjacent ports in shipping network. The experimental results show that (1) there is a significant positive correlation between time and space in the South China Sea shipping network, and this spatial-temporal correlation has the characteristics of time dynamics and spatial heterogeneity; (2) the forecasting accuracy of the marine traffic volume based on the spatial-temporal model is better than the traditional time-series-based forecasting model, and the spatial-temporal model can better portray the spatial-temporal autocorrelation of maritime traffic.

공간시계열 자료에 대한 STARMA 모형과 STBL 모형의 예측력 비교

본 논문은 공간시계열 자기회귀 이동평균(STARMA) 모형과 공간 시계열 중선형(STBL) 모형에 대해 식별, 추정, 예측 등의 통계적 절차와 특징들을 논하고, 두 모형을 비교하는데 목적이 있다. 사례 연구를 위 해 2001년부터 2006년까지 8개 지역으로부터 보고된 월별 Mumps 자료를 사용했고, 예측오차제곱합(SSF)을 활용하여 두 모형의 적합도를 비교하였다. The major purpose of this article is to formulate a class of Space Time Autoregressive Moving Average(STARMA) model and Space Time Bilinear model(STBL), to discuss some of the their statistical properties such as model, identification approaches, some procedure for estimation and the predictions, and to compare the STARMA model with the STBL model. For illustration, The Mumps data reported from eight city & provinces monthly over the years 2001-2006 are used and the result from STARMA and STBL model are compared with using SSF(Sum of Square Prediction Error).

A Generalized Space-Time ARMA Model with an Application to Regional Unemployment Analysis in Italy

The STARMA (space-time autoregressive moving average) model class was introduced in the mid-1970s as a spatio-temporal extension to the ARMA time series model class. To enhance the model’s ability in dealing with spatial dependence and heterogeneity of observations, the article extends the STARMA model specification by augmenting the set of explanatory variables with simultaneous spatial lags of the observed process and unobservable shocks and by letting model parameters vary with location in space. Having introduced the extended specification,the space time impulse response function is subsequently presented as a useful tool in addressing structural issues. The article then deals with maximum likelihood estimation and hypothesis testing; in particular, Lagrange multiplier tests are proposed for spatial heterogeneity in the intercept, conditional variance and ARMA coefficients. The article closes with an application to the analysis of the series of the regional unemployment rate in Italy, aimed at evaluating the extent of the spatial propagation of regional specific shocks to unemployment and the degree of spatial heterogeneity in the process parameters.

Spatial and space–time correlations in ecological models

Space–time autoregressive moving average (STARMA) processes can be used to represent a wide range of theoretical models of ecological variation and statistical models for analyzing ecological data. Many discrete-time, discrete-space ecological processes can be analyzed using STARMA theorems. As an example, one focus is on population genetic models, and using STARMA we obtain not only the usual spatial variance and correlations, but also the space–time correlations. Examples show how this allows one to characterize general space–time population genetic processes in a new and more detailed way. STARMA processes include migration-drift models with general patterns of migration among populations. They also include processes with features that are more realistic for many natural population systems, including various forms of stochastic migration. The space–time correlations are particularly important because they allow us to connect data to theoretical processes, and they can be used for estimating migration rates, model-fitting, testing, and forecasting the future behavior of real systems. The space–time correlations also specify the relationship between spatial correlations at different spatial distances, thus bridging gaps between observations on spatial correlations and inferences about dispersal and selection, and other aspects of the underlying space–time process.

Spatial interaction between the truck flows through the Mexico–Texas border

This paper presents an analysis of the spatial and temporal interactions between truck flows across the Texas–Mexico border. The system of flows is modeled as a multivariate stochastic process with interactions both in time and space dimensions. A novel modeling approach, the space time autoregressive moving average (STARMA) model, is applied to capture the autocorrelations between the flows. These autocorrelations are the base to compute direct and crossed demand elasticities between the flows. The demand elasticities are used to estimate the degree of dependence between the truck flows both southbound and northbound, revealing that uneven adjustments take place in the truck flows pattern for southbound and northbound traffic. In fact, the southbound flows are more sensitive to changes in their own demand over time than the corresponding spatial changes. On the other hand, the northbound flows are more sensitive to changes in the demand for the main flow (Laredo's bridge) rather than their own variations in previous periods.

Spatio-temporal precipitation modelling in rural watersheds

Abstract The natural variability of precipitation in agricultural regions both in time and space is modelled using extensions of Box & Jenkins (1976) methodology based on the ARMA procedure. This broad class of aggregate regional models belongs to the general family of Space-Time Autoregressive Moving Average (STARMA) processes. The paper develops a three-stage iterative procedure for building a ST ARMA model of multiple precipitation series. The identified model is STMA (13). The emphasis is placed on the three stages of the model building procedure, namely identification, parameter estimation and diagnostic checking. In the parameter estimation stage the polytope (or simplex) method and three further classical nonlinear optimization algorithms are used, namely two conjugate gradient methods and a quasi-Newton method. The polytope method has been adopted and the developed model performed well in describing the spatio-temporal characteristics of the multiple precipitation series. Application has been attempted in a rural watershed in southern Canada.

Spatial and Space-Time Correlations in Systems of Subpopulations with Stochastic Migration

The great majority of models of the population genetics of subdivided populations have made the simplifying assumption that the gene frequencies in migrant groups are deterministic. The present paper examines models which more closely mimic natural conditions, in which the gene frequencies in migrant groups are subject to stochastic effects. It is shown that some types of stochastic migration can cause dramatic changes in spatial correlations and variance. These changes depend on how the stochastic migration effects in the gene frequency recursion equations are shared among nearby subpopulations during the same generation. Only for cases where the effects are completely unshared are the equilibrium spatial and space-time correlations among adult subpopulations unaffected, but the variance is always inflated. The analyses here use novel methods, by recasting population genetic migration-drift models as space-time autoregressive moving average (STARMA) processes. Recent theorems for STARMA processes are employed for finding the spatial correlations, and for the first time in population genetics theory the complete set of space-time correlations, for systems with general patterns of migration rates and numbers of spatial dimensions. The space-time correlations provide a uniquely detailed description of a system, and thus form a link between observed spatial autocorrelation statistics and the underlying space-time population genetic process. STARMA theoretical processes have direct statistical analogues that can be applied for process identification, parameter estimation, model fitting, and forecasting in real systems.

The effect of space-time demand processes on the solution of transportation problems

Using a formulation of the transportation problem with a stochastic demand represented by a space-time autoregressive moving average (STARMA) model, a simulation study is presented whereby the consequences of ignoring space and/or time dependencies in the demand process are evaluated. It is found that the percentage change in total deliveries, x PCT , when space-time dependency is ignored varies linearly with space-time autoregressive (STAR) parameters. Furthermore, x PCT is larger when we ignore spatial dependency than temporal dependency. When both dependencies are ignored, x PCT may be larger than that for both spatial and temporal cases depending upon the signs of STAR parameters. Results for space-time moving average (STMA) are similar to that of STAR. However, for STARMA, when both the temporal and spatial dependencies in demand are ignored, x PCT is piecewise linear. The improvement in percentage change in total cost, PCT, is found to vary between 1–55% as the ratio of unit holding cost to unit product cost, H/P, varies from its minimum to its maximum, and 1–95% for the ratio of unit shortage cost to unit product cost, SH/P, when space-time dependencies are taken into account, depending upon the values of various parameters.

On the distribution of independence test for the residuals of space-time arma models

The procedure for building space-time autoregressive moving average (STARMA) models depends on the form of the variance-covariance matrix G of the underlying errors (see Pfeifer Deutsch (1980a,c)). In this paper the distribu¬tion of the statistic for testing the hypothesis that G is diagonal is obtained in a very convenient computational form. A table of critical values for the test is given Comparison is made with the approximate values obtained by Pfeifer Deutsch (1980c)

Independence and sphericity tests for the residuals of space-time arma models

The mechanics of the procedure for building space-time autoregressive moving average (STARMA) models is dependent upon the form of G, the variance-covariance matrix of the underlying errors.This paper presents large sample tests of the hypotheses that G is diagonal and that G equals o2 I. Tables of the critical values for these tests are constructed