Space Time Autoregressive Model Research Articles

PERAMALAN NILAI TUKAR RUPIAH TERHADAP DOLAR SINGAPURA, BAHT, DAN PESO MENGGUNAKAN METODE GSTAR

The Generalized Space-Time Autoregressive (GSTAR) model is an extension of the Space-Time Autoregressive (STAR) model. The difference between the two models lies in the parameter assumptions. In the STAR model, the parameters are assumed to be independent of location, so this model is only suitable for data with homogeneous locations. Meanwhile in the GSTAR model, the parameters are assumed to change for each different location. This research aims to develop the best model for forecasting the Rupiah exchange rate against the Singapore Dollar, Thai Baht, and Philippine Peso. The appropriate model used for the Rupiah exchange rate data is the GSTAR(51)I(1) model. The weights used in this study are uniform location weights and inverse distance. The modeling results show that the best model is the model with inverse distance weighting, which has an MSE value of 371.8907 with MAPE values for each of the Rupiah exchange rate data against the Singapore Dollar, Thai Baht, and Philippine Peso of 0.3154214%, 0.8369436%, and 0.6237245%, respectively.

Shallot Price Forecasting in Three Locations in Indonesia Using Generalized Space-Time Autoregressive Model

Shallot Price Forecasting in Three Locations in Indonesia Using Generalized Space-Time Autoregressive Model

PEMODELAN GENERALIZED SPACE TIME AUTOREGRESSIVE (GSTAR) PADA DATA INDEKS HARGA KONSUMEN (IHK) 5 IBUKOTA PROVINSI DI PULAU KALIMANTAN

Generalized Space Time Autoregressive (GSTAR) model is a development model from the generalized STAR (Space Time Autoregressive) model. GSTAR model have autoregressive order to see the effect of the time element and location weighting matrix to see the effect of the location element. Unlike the STAR model, it can assume that each location research has different characteristics. The purpose of this research is to apply the Generalized Space Time Autoregressive (GSTAR) model to the Consumer Price Index (CPI) data in Kalimantan Island, especially in the capital city of each province in Kalimantan Island to find out the best estimation model with the best location weight. The location weights used the distance inverse location weights and the normalized cross-correlation location weights by estimating the parameters of the GSTAR model using the Ordinary Least Square (OLS) method. The best estimated model can be seen from the smallest Akaikae’s Information Criterion (AIC) and Root Mean Square Error (RMSE) value. From the research results, it was found that the best GSTAR prediction model for CPI data for 5 cities in Kalimantan Island was the GSTAR(1,1)-I(1). These results are based on the GSTAR prediction model with the smallest AIC value and the data is differencing 1 time. The best location weight based on the smallest RMSE value for the GSTAR(1,1)-I(1) model is the normalized cross-correlation location weight.

Generalized Space Time Autoregressive Integrated Moving Average (GSTARIMA) dalam Peramalan Data Curah Hujan di Kota Makassar

Modeling of rainfall data using time series data involving location elements has not been widely carried out. One model that involves elements of time and location is Space Time Autoregressive (STAR). The development of the STAR model which assumes that each location has heterogeneous characteristics is the Generalized Space Time Autoregressive Integrated Moving Average (GSTARIMA) model. The purpose of this research is to get the best GSTARIMA model and forecast rainfall data in Makassar City based on the best GSTARIMA model. This model incorporates time and geographic dependencies with different parameters for each location. The data used is Makassar city's monthly rainfall data at the Bawil IV/Panaikang, Biring Romang/Panakkukang and Stammar Paotere rain stations from January 2017 to September 2021. Autoregressive (AR) and Moving Average (MA) orders were identified using the Space Time Autocorrelation plot. Function (STACF) and Space Time Partial Autocorrelation Function (STPACF). The spatial order used in this study is spatial order 1 with an inverse distance weighting matrix and normalized cross-correlation. Parameters were estimated using the Generalized Least Squares (GLS) method. The best model for predicting rainfall in the city of Makassar is the GSTARIMA (1,0,0) (1,1,0)12 model using an inverse distance weighting matrix with the smallest average Root Mean Square Error (RMSE) of 132.9661.

PEMODELAN JUMLAH WISATAWAN DI JAWA TENGAH MENGGUNAKAN METODE GENERALIZED SPACE TIME AUTOREGRESSIVE - SEEMINGLY UNRELATED REGRESSION (GSTAR-SUR)

Space-time model is a model that can explain data with spatial and time characteristics. The Generalized Space Time Autoregressive (GSTAR) model is one of the generalized space-time models from the Space Time Autoregressive (STAR) model. The GSTAR model is more flexible when dealing with areas that have heterogeneous characteristics than the STAR model. The GSTAR model models time series data in multiple regions at once. This model can then be used to model data on the number of tourists in four regions in Central Java, namely Semarang, Jepara, Magelang and Semarang district for the 2014 to 2019 period. in Central Java. On the residual model, the Lagrange Multiplier Test is carried out and it is known that there is a correlation between the residuals. The modeling was continued by using the Generalized Space Time Autoregressive – Seemingly Unrelated Regression (GSTAR-SUR) model. GSTAR-SUR is one of the more efficient models used to model GSTAR with correlated residuals. Residual through the white-noise assumption test, it is found that the appropriate model is the GSTAR-SUR(2,1) model. This model can then be used in forecasting data on the number of tourists in Semarang, Jepara, Magelang and Semarang district in the next period

Robust space–time modeling of solar photovoltaic deployment

Solar photovoltaic (PV) has established itself as a fairly promising, fast-growing renewable energy source. The main determinants of solar PV deployment are thought to be physical and climatic factors – such as latitude and solar irradiance, not to mention terrain and built environment features – as well as socio-economic drivers — such as population density, household size, and education level. Besides, peer effects and neighborhood effects are found to affect the willingness to adopt solar photovoltaic systems strongly. This study aims to set up robust space–time models, which enable us to investigate the drivers of solar PV deployment using fine-grained spatial and temporal data. We use space–time auto-regressive models (STAR) with several exogenous covariates that are expected to explain the installed solar PV capacity. STAR models require the specification of spatial weight matrices (W). As in regular lattice data, we select causal (lower triangular) W matrices so that the consistency of least-squares (LS) estimators is warranted. We show that they can be extended to robust LS estimators, which are necessary because of strong outlier contamination. Models are tested on the Italian municipal data of residential and industrial PV plants installed under the support schemes in force between 2006 and 2011. Empirical results confirm the important role played by the space–time dynamic components. Significant exogenous predictors are found in the domains of the physical features (elevation and land area), demography (population), built environment (residential buildings), and socio-economic aspects (income, employment rate, commuter workers).

Community mobility in the European regions during COVID-19 pandemic: A partitioning around medoids with noise cluster based on space–time autoregressive models

In this paper we propose a robust fuzzy clustering model, the STAR-based Fuzzy C-Medoids Clustering model with Noise Cluster, to define territorial partitions of the European regions (NUTS2) according to the workplaces mobility trends for places of work provided by Google with reference to the whole COVID-19 pandemic period. The clustering model takes into account both temporal and spatial information by means of the autoregressive temporal and spatial coefficients of the STAR model. The proposed clustering model through the noise cluster is capable of neutralizing the negative effects of noisy data. The main empirical results regard the expected direct relationship between the Community mobility trend and the lockdown periods, and a clear spatial interaction effect among neighboring regions.

Evaluation of COVID-19 Mitigation Policies in Australia Using Generalised Space-Time Autoregressive Intervention Models.

In handling the COVID-19 pandemic, various mitigation policies aiming at slowing the spread and protecting all individuals, especially the vulnerable ones, were implemented. A careful evaluation of the effectiveness of these policies is necessary so that policy-makers can implement informed decisions if another wave of COVID-19 or another pandemic happens in the future. This paper reports an assessment of some policies introduced by the Australian governments using a generalised space-time autoregressive model which incorporates multiple exogenous variables and delay effects. Our results show that the number of daily new cases from the states and territories are influenced by both temporal and spatial aspects. Business and border restrictions are found helpful in reducing the number of new cases a few days after implementation while gathering restrictions may not be effective.

Invertibility of Generalized Space-Time Autoregressive Model with Random Weight

The generalized linear process accomplishes stationarity and invertibility properties. The invertibility property must be having a series of convergence conditions of the process parameter. The generalized Space-Time Autoregressive (GSTAR) model is one of the stationary linear models therefore it is necessary to reveal the invertibility through the convergence of the parameter series. This article studies the invertibility of model GSTAR(1;1) with kernel random weight. The result shows that the model GSTAR(1;1) under kernel random weight fulfills the invertibility property and obtains a finite order of Generalized Space-Time Moving Average (GSTMA) process. The other result obtained is the time order of the finite orde . On the Triangular kernel resulted in the relatively great value n, so that it does not apply to the kernel with a finite value n.

Forecasting the amount of rainfall in West Kalimantan using Generalized Space-time Autoregressive model

The generalized space-time autoregressive or GSTAR is a space-time model which can be used to analyze time-series data in several locations considered to be correlated. In this research, the GSTAR model is applied to forecast the amount of rainfall in West Kalimantan, especially at Sintang Station, Melawi Station, and Ketapang Station. The data used for modeling is data of the amount of rainfall for the period January 2013-December 2017, while the data used for model validation is data for the period January 2018-December 2018. The spatial weights used are uniform weights, inverse distance weights, and normalized cross-correlation weights, and the estimation method used is the ordinary least square or OLS estimation. The best model is selected based on the smallest RMSE (root mean square error). The results showed that all spatial weights gave the same good GSTAR(1:1) model because they had almost the same RMSE value. Thus, this model can be used to forecast the amount of rainfall for the period January 2019-December 2019. The forecast results show that for Sintang Station and Melawi Station, the highest amount of rainfall is estimated to occur in March 2019 and the lowest will occur in August 2019. Meanwhile, for Ketapang Station, the highest amount of rainfall is estimated to occur in January 2019 and the lowest will occur in September 2019.

Application of Generalized Space Time Autoregressive Model on Farmer Exchange Rate Data in Three Provinces of The Sumatera Island

The agricultural sector has a big role in the development of the Gross Regional Domestic Product (GDP). Therefore the agricultural sector is very important. Besides the agricultural sector, the farmer's welfare also needs to be considered because the agricultural sector will be good if the welfare of farmers is good also. In measuring the level of farmers' welfare, the method used is the farmer's exchange rate. The farmer's exchange rate has a location relationship and a previous time relationship. The Generalized Space-Time Autoregressive (GSTAR) model is a good method of forecasting data that contains time series and location relationships by assuming that the data has heterogeneous characteristics. The purpose of this study is to model the farmer exchange rate data with GSTAR using normalization of cross-correlations weighting and inverse distance in three provinces namely West Sumatra, Bengkulu and Jambi Provinces. Based on data analysis, the best GSTAR model obtained by using the best weighting with the model is GSTAR (11) − I(1) using normalization of cross-correlations because the assumption of normal white noise and multivariate are fulfilled with an RMSE value of 1.097775. The best GSTAR model explains that the exchange rate of West Sumatra farmers is only the previous time, Bengkulu farmers' exchange rate is the previous time and is the exchange rates of farmers of West Sumatra and Jambi, whereas for the exchange rate of farmers of Jambi is the exchange rates of farmers of Bengkulu and West Sumatra and influenced by previous times.Keywords: GSTAR, RMSE, farmers exchange rate, normalization of cross-correlations, inverse distance.

First Order Space Time Autoregressive Stationary Model on Petroleum Data

First order Space-Time Autoregressive model is one of the models which involves location and time. STAR(1;1) model stationary can be used to forecast future observation at a location based on one previous time of its own location and the spatial neighborhood. STAR(1;1) model on petroleum productivity data in Balongan, Indramayu, West Java with eigenvalue less than 1. It indicates that STAR (1;1) model on petroleum productivity data in Balongan, Indramayu, West Java meets the stationary requirement

A generalised linear space–time autoregressive model with space–time autoregressive disturbances

We present a solution to problems where the response variable is a count, a rate or binary using a generalised linear space–time autoregressive model with space–time autoregressive disturbances (GLSTARAR). The possibility to test the fixed effect specification against the random effect specification of the panel data model is extended to include space–time error autocorrelation or a space–time lagged dependent variable. Space-time generalised estimating equations are used to estimate the spatio-temporal parameters in the model. We also present a measure of goodness of fit, and show the pseudo-best linear unbiased predictor for prediction purposes. Additionally, we propose a joint space–time modelling of mean and dispersion to give a solution when the variance is not constant. In the application, we use social, economic, geographic and state presence variables for 32 Colombian departments in order to analyse the relationship between the number of armed actions (AAs) per 1000 km committed by the guerrillas of the FARC-EP and ELN during the years 2003–2009, and a set of covariates given by attention rate to victims of violence, forced displacement-households expelled, forced displacement-households received, total armed confrontations per year, number of AAs by military forces and percentage of people living in urban area.

Modeling Interval Time Series with Space–Time Processes

We consider interval-valued time series, that is, series resulting from collecting real intervals as an ordered sequence through time. Since the lower and upper bounds of the observed intervals at each time point are in fact values of the same variable, they are naturally related. We propose modeling interval time series with space–time autoregressive models and, based on the process appropriate for the interval bounds, we derive the model for the intervals’ center and radius. A simulation study and an application with data of daily wind speed at different meteorological stations in Ireland illustrate that the proposed approach is appropriate and useful.

Space–time autoregressive models and forecasting national, regional and state crime rates

Abstract The recently advanced space–time autoregressive (ST-AR) model is used to forecast US, regional and state rates of violent and property crime. The disaggregate state (Florida) violent crime model includes murder, rape, robbery, and assault, while the property crime model includes burglary, larceny, and motor vehicle theft. In experimental forecasts, ST-AR RMSEs are compared to those for aggregate univariate AR(p) models, vector autoregressions (VAR), Bayesian VARs (BVAR), and two naive models that predict future crime rates either as the most recent rate or according to the most recent change in rates. The ST-AR model is of particular interest, given its efficient use of data, much like panel-data estimation. The ST-AR, BVAR, and AR(p) models outperform the other three approaches, but the ST-AR models are generally superior.

Hierarchical Bayesian autoregressive models for large space–time data with applications to ozone concentration modelling

Increasingly large volumes of space–time data are collected everywhere by mobile computing applications, and in many of these cases, temporal data are obtained by registering events, for example, telecommunication or Web traffic data. Having both the spatial and temporal dimensions adds substantial complexity to data analysis and inference tasks. The computational complexity increases rapidly for fitting Bayesian hierarchical models, as such a task involves repeated inversion of large matrices. The primary focus of this paper is on developing space–time autoregressive models under the hierarchical Bayesian setup. To handle large data sets, a recently developed Gaussian predictive process approximation method is extended to include autoregressive terms of latent space–time processes. Specifically, a space–time autoregressive process, supported on a set of a smaller number of knot locations, is spatially interpolated to approximate the original space–time process. The resulting model is specified within a hierarchical Bayesian framework, and Markov chain Monte Carlo techniques are used to make inference. The proposed model is applied for analysing the daily maximum 8‐h average ground level ozone concentration data from 1997 to 2006 from a large study region in the Eastern United States. The developed methods allow accurate spatial prediction of a temporally aggregated ozone summary, known as the primary ozone standard, along with its uncertainty, at any unmonitored location during the study period. Trends in spatial patterns of many features of the posterior predictive distribution of the primary standard, such as the probability of noncompliance with respect to the standard, are obtained and illustrated. Copyright © 2012 John Wiley & Sons, Ltd.

Application of Generalized Space-Time Autoregressive Model on GDP Data in West European Countries

This paper provides an application of generalized space-time autoregressive (GSTAR) model on GDP data in West European countries. Preliminary model is identified by space-time ACF and space-time PACF of the sample, and model parameters are estimated using the least square method. The forecast performance is evaluated using the mean of squared forecast errors (MSFEs) based on the last ten actual data. It is found that the preliminary model is GSTAR(2;1,1). As a comparison, the estimation and the forecast performance are also applied to the GSTAR(1;1) model which has fewer parameter. The results showed that the ASFE of GSTAR(2;1,1) is smaller than that of the order (1;1). However, thet-test value shows that the performance is significantly indifferent. Thus, due to the parsimony principle, the GSTAR(1;1) model might be considered as a forecasting model.

Modeling spatio-temporal relationships: retrospect and prospect

Interest in space–time modeling is experiencing a resurgence, in part because more and more sizeable space–time datasets are becoming readily available. Currently techniques to describe these data, many of which have existed for years, are being utilized and improved. This paper surveys general categories of these techniques (i.e., autoregressive-integrated-moving-average models, space–time autoregressive models, three-dimensional geostatistical models, and panel data models), in retrospect, demonstrates a future prospect (i.e., spatial filtering models), and suggests important topics for incorporation into a research agenda, including ones pertaining to non-normal random variables, panel data models, space–time heterogeneity, missing data, and distributional properties of space–time filters.

Simulated village locations in Thailand: a multi-scale model including a neural network approach

The simulation of rural land use systems, in general, and rural settlement dynamics in particular has developed with synergies of theory and methods for decades. Three current issues are: linking spatial patterns and processes, representing hierarchical relations across scales, and considering nonlinearity to address complex non-stationary settlement dynamics. We present a hierarchical simulation model to investigate complex rural settlement dynamics in Nang Rong, Thailand. This simulation uses sub-models to allocate new villages at three spatial scales. Regional and sub-regional models, which involve a nonlinear space-time autoregressive model implemented in a neural network approach, determine the number of new villages to be established. A dynamic village niche model, establishing pattern-process link, was designed to enable the allocation of villages into specific locations. Spatiotemporal variability in model performance indicates the pattern of village location changes as a settlement frontier advances from rice-growing lowlands to higher elevations. Experiments results demonstrate this simulation model can enhance our understanding of settlement development in Nang Rong and thus gain insight into complex land use systems in this area.

Consistency and asymptotic normality of least squares estimators in generalized STAR models

Space–time autoregressive (STAR) models, introduced by Cliff and Ord [Spatial autocorrelation (1973) Pioneer, London] are successfully applied in many areas of science, particularly when there is prior information about spatial dependence. These models have significantly fewer parameters than vector autoregressive models, where all information about spatial and time dependence is deduced from the data. A more flexible class of models, generalized STAR models, has been introduced in Borovkovaet al. [Proc. 17th Int. Workshop Stat. Model. (2002), Chania, Greece] where the model parameters are allowed to vary per location. This paper establishes strong consistency and asymptotic normality of the least squares estimator in generalized STAR models. These results are obtained under minimal conditions on the sequence of innovations, which are assumed to form a martingale difference array. We investigate the quality of the normal approximation for finite samples by means of a numerical simulation study, and apply a generalized STAR model to a multivariate time series of monthly tea production in west Java, Indonesia.