Generalized Space Time Autoregressive Model Research Articles

Application of GSTAR kriging model in forecasting and mapping coffee berry borer attack in Probolinggo district

Generalized Space Time Autoregressive (GSTAR) is one of multivariate time series modeling that considers aspects of location with heterogeneous location characteristics. The GSTAR model normally can only be used in forecasting an event in the future at the observed locations. The problem that often occurs in some cases is that there are locations to be modeled that do not have sufficient or incomplete data as data in other locations. For this reason, several alternatives can be done, and one of them is by combining the GSTAR model with the kriging interpolation technique. This modeling is known as GSTAR Kriging modeling. In this research, GSTAR Kriging modeling is applied in predicting and mapping coffee berry borer attacks in Probolinggo District. The model parameters are estimated using the GLS method in the SUR equation system. Forecasting results indicate that the GSTAR Kriging model has a high forecasting accuracy and is not much different from the GSTAR model. Meanwhile, based on the forecasting map, it can be seen that the peak of coffee berry borer attack is predicted to occur in July 2019 with the attack center located in Tiris Sub-district.

Integration of GSTAR-X and Uniform location weights methods for forecasting Inflation Survey of Living Costs in Central Java

Inflation is a tendency to increase prices of goods and services that take place continuously. Inflation is a monthly time series data that is thought to be influenced by location elements. Modeling for inflation forecasting that involves time and location (spatio temporal) can use the Generalized Space Time Autoregressive (GSTAR) method. To increase accuracy in modeling and forecasting, the GSTAR model was developed into the GSTARX model by involving exogenous variables. Exogenous Variavel used in GSTARX modeling for forecasting Inflation is a variation of the Eid calendar. This GSTARX modeling is applied for inflation forecasting in six cities Cost of Living Survey (SBH) in Central Java, namely Cilacap, Purwokerto, Semarang, Kudus, Magelang and Surakarta. The purpose of this study is to get the best GSTARX model for inflation forecasting for six SBH cities in Central Java. The selection of the best model from the GSTARX method is seen with the smallest RMSE value of each model. Obtained that the GSTARX model with uniform weights is the best model because it has a smaller RMSE compared to the GSTARX model with inverse distance weights, the RMSE values are 0.6122 and 0.6137, respectively. It can be concluded that the GSTARX method with Uniform weighting can provide better performance and can be used to predict the inflation of the six SBH cities in Central Java in the next 12 periods.

Poisson GSTAR model: spatial temporal modeling count data follow generalized linear model and count time series models

This paper discusses the formation of one temporal spatial model, the Generalized Space Time Autoregressive (GSTAR) model, if the data of model is count data. The development of the GSTAR model is an update or problem completion of the count data which tends to be stationary and non-normal / Gaussian data, because GSTAR model is assumed normal distributed and stationarity. GSTAR modelling for count data refers to the Time series model for count data, which are the Generalized Autoregressive Moving Average (GARMA) model and modeling Count Time Series which has the Generalized Linear Model (GLM) concept. The model formed is called the Poisson GSTAR model

Determination of consumer price index with generalized space-time autoregressive

Customer Price Index is one way to analyze the level of consumption needs of people for goods and services within a certain time. The development of the current Customer Price Index determination besides being influenced by time is also influenced by spatial heterogeneity between regions. In this study, the determination of the Customer Price Index was carried out in three cities in Probolinggo, Surabaya, and Kediri using the Generalized Space-Time Autoregressive (GSTAR) approach. The GSTAR model is a time-series data analysis model that shows the existence of spatial heterogeneity between time and between regions. Based on the test results of the Matrix Autocorrelation Function and the Matrix Partial Autocorrelation Function, the best model is GSTAR with order 1 with the smallest Akaike Information Criterion value found in lag 1 which is 90.924.

Short time PM2.5 prediction model for Beijing-Tianjin-Hebei region based on Generalized Space Time Autoregressive (GSTAR)

In recent years, with the rapid development of China’s economy and urbanization, the irrational industrial structure, large energy consumption, and increased car ownership have made China’s air pollution increasingly serious, especially in Beijing-Tianjin-Hebei, Yangtze River Delta, and the Pearl River Delta. As the primary pollutant affecting the air quality in the Beijing-Tianjin-Hebei region, the accurate prediction of PM2.5 concentration is of great significance for predicting heavy pollution weather, formulating the start-up mechanism of emergency plan and optimizing the production of enterprises. This study used the online hourly data of conventional pollutants from 80 national control stations in Beijing, Tianjin and Hebei from May 1, 2015 to May 31, 2019. Considering the influence of time and space, the GSTAR model of PM2.5 prediction is established. Comparing the prediction results of GSTAR model with ARMA and STAR, the validity of GSTAR model is verified by applying relevant accuracy evaluation indicators.

Generalized STAR (1;1) Model with Outlier - Case Study of Begal in Medan, North Sumatera

This study was aimed to compare generalized space time autoregressive (GSTAR) (1;1) model with its modification. The modification of GSTAR (1;1) model was done by adding the outlier factor which gained by outlier detection procedure. A case study was done towards the amount of monthly crime activity-begal at seven police sectors in Medan, North Sumatera. By using three steps of Box-Jenkins, Autoregressive (1) model was applied to each location and resulted West Medan as fifth location with additive outlier (AO) in the third data of time which weighted -57.5247. The comparison of model was done by calculating the root mean square of error (RMSE) in each model. Since GSTAR (1:1) model has larger RMSE (8.1728) rather than its modification (7.9700), then GSTAR (1;1) model with outlier is the best model in this case study. This invention shows that the model of space time with outlier model is useable to find precise result rather than space time model only.

GSTAR-X-SUR Model with Neural Network Approach on Residuals

One of the models that combine time and inter-location elements is Generalized Space Time Autoregressive (GSTAR) model. GSTAR model involving exogenous variables is GSTARX model. The exogenous variables which are used in GSTAR model can be both metrical and non-metrical data. Exogenous variable that can be applied into the forecasting of precipitation is non-metrical data which is in a form of precipitation intensity of a certain location. Currently, precipitation possesses patterns and characteristics difficult to identify, and thus can be interpreted as non-linear phenomenon. Non-linear model which is much developed now is neural network. Parameter estimation method employed is Seemingly Unrelated Regression (SUR) model approach, which can solve the correlation between residual models. This current research employed GSTARX-SUR modelling with neural network approach on residuals. The data used in this research were the records of 10-day precipitations in four regions in West Java, namely Cisondari, Lembang, Cianjur, and Gunung Mas, from 2005 to 2015. The GSTARX-SUR NN modelling resulted in precipitation deviation average of the forecast and the actual data at 4.1385 mm. This means that this model can be used as an alternative in forecasting precipitation.

Forecasting of Rainfall in Central Java using Hybrid GSTAR-NN-PSO Model

Forecasting of rainfall trends is essential for several fields, such as airline and ship management, flood control and agriculture. The rainfall data were recorded several time simultaneously at a number of locations and called the space-time data. Generalized Space Time Autoregressive (GSTAR) model is one of space-time models used to modeling and forecasting the rainfall. The aim of this research is to propose the nonlinear space-time model based on hybrid of GSTAR, Feed Forward Neural Network (FFNN) and Particle Swarm Optimization (PSO) and it called GSTAR-NN-PSO. In this model, input variable of the FFNN was obtained from the GSTAR model. Then use PSO to initialize the weight parameter in the FFNN model. This model is applied for forecasting monthly rainfall data in Jepara, Kudus, Pati and Grobogan, Central Java, Indonesia. The results show that the proposed model gives more accurate forecast than the linear space-time model, i.e. GSTAR and GSTAR-PSO. Moreover, further research about space-time models based on GSTAR and Neural Network is needed to improving the forecast accuracy especially the weight matrix in the GSTAR model.

GSTARIX Model for Forecasting Spatio-Temporal Data with Trend, Seasonal and Intervention

Generalized Space-Time Autoregressive (GSTAR) is a statistics model that usually applied for forecasting data that have both spatial and temporal dependency. The monthly tourist arrival data in some locations are example of spatio-temporal data. Most of previous researches in GSTAR model only focused on stationary data. Otherwise, tourist arrival data in Indonesia mostly contain trend, seasonal, and some extreme values caused by interventions or outliers. The objective of this study is to apply and develop GSTAR model for forecasting spatio-temporal data with trend, seasonal, and interventions or outliers. This model is then known as GSTAR with exogeneous variables or GSTARIX model. Then, the forecast accuracy of GSTARIX model are compared to VAR with exogenous variables or VARIX model. Monthly data about number of tourist arrivals to Jakarta, Surakarta, Surabaya, and Denpasar are used as case study. Moreover, two methods are used for parameter estimation, i.e. Ordinary Least Square (OLS) and Generalized Least Square (GLS). The criteria for selecting the best model is Root Mean Square Error (RMSE). The results showed that the best model for forecasting tourist arrivals in each location are different. The best model for forecasting number of tourist arrivals to Jakarta and Surabaya is GSTARIX with OLS method or GSTARIX-OLS. Whereas, the best model for Denpasar and Surakarta data are VARIX and GSTARIX-GLS, respectively.

The Geographical Clustering of The Rainfall Stations on Seasonal GSTAR Modeling for Rainfall Forecasting

Recent research in time series shows that the data not only have inter-relations with events in the previous time, but also have inter-location linkages. This type of time series data with elements of time and location dependencies are modeled with the Space-Time model. The Space-Time model with heterogeneous research sites is the Generalized Space Time Autoregressive (GSTAR) model. The data that has a seasonal pattern is modeled with seasonal GSTAR by including seasonal elements in the non-seasonal model. In this case, Jember District has 77 rain stations with various regional topography. Based on various characteristics, K-Means cluster analysis is used to obtain optimal rainfall rain stations clusters. This clustering is expected to give better rainfall forecasting result compared with clustering conducted by the Statistics Central of Jember (BPS). The RMSE value can be minimized by including seasonal elements in the model, both in BPS and K-Means clustering. In addition, the K-Means clustering in this study may also reduce the RMSE value of model, both on non-seasonal and seasonal models. The best model for this case is GSTARK-Seasional (1;1), ie Seasonal GSTAR model on K-Means clustering.

Rainfall model on area of rice production in Sragen, Karanganyar and Klaten by using Generalized Space Time Autoregressive (GSTAR)

ABSTRACTThe planning of planting period became non-optimal due to the uncertain rainfall fluctuation condition in the past few years. To anticipate food insecurity caused by such a matter, the development of rainfall prediction models in several rice production areas in Central Java, which represent the center for rice production, is required. This paper provides the application of GSTAR model on the rainfall data in Sragen Regency, Karanganyar Regency, and Klaten Regency with considering time and location conditions. The weighting applied in the model was normalized cross-correlation. By applying the least square method and stepwise procedure, GSTAR model for six, seven in Sragen, seven areas in Karanganyar, and seven areas in Klaten respectively was obtained. The validity of the model was tested by applying RMSE.

SOME COMMENTS ON THE THEOREM PROVIDING STATIONARITY CONDITION FOR GSTAR MODELS IN THE PAPER BY BOROVKOVA et al.

Generalized Space-Time Autoregressive (GSTAR) model is one of the models that usually used for modeling and forecasting space and time series data. The aim of this paper is to study further about the stationarity conditions for parameters in the GSTAR model and the relation to Vector Autoregressive (VAR) model. We focus on the theoretical study about stationarity condition in GSTAR(11) and the relation tothe stationarity condition of parameters in VAR(1). Then, we do an empirical study to give counter examples for the theorem of stationarity condition proposed by Borovkovaet al. The results show that the theorem of stationarity condition of parameters in GSTAR(11) model given by Borovkova et al. is incorrect. Additionally, the empirical results also show that GSTAR(11) model could always be represented in VAR(1) model by applying matrix operation to the space and time parameters. Hence, we can also conclude that VAR model, particularly VAR(1), is an extension of GSTAR(11) model with any possibility values of space and time parameters.DOI : http://dx.doi.org/10.22342/jims.13.1.90.115-122

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.

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.