Generalized Space Time Autoregressive Research Articles

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

Development of the GSTARIMA(1,1,1) model order for climate data forecasting

The space-time model combines spatial and temporal elements. One example is the Generalized Space-Time Autoregressive (GSTAR) Model, which improves the Space-Time Autoregressive (STAR) model. The GSTAR model assumes that each location has heterogeneity characteristics, and that the data is stationary. In this research, the moving average component is calculated by involving the relationship between variable values at a certain time and residual values at a previous time, and it is assumed that the data is not stationary, so the model used is the Generalized Space-Time Autoregressive Integrated Moving Average (GSTARIMA) Model. The model order for GSTARIMA is determined through the Space-Time Autocorrelation Function (STACF) and Space-Time Partial Autocorrelation Function (STPACF) to ensure accurate forecasting. Previous research only discussed the GSTARIMA(1,1,1) model, so in this research, the GSTARIMA(3,1,1) model will be addressed as a form of development of the GSTARIMA(1,1,1) model and applied to climate data. The climate data used in this research is sourced from NASA POWER and consists of rainfall variables with large data sizes, requiring the use of the data analytics lifecycle method to analyse Big Data. The lifecycle includes six phases: discovery, data preparation, model planning, model building, communicating results, and operationalization. Based on the data processing results with Python software, the GSTARIMA(3,1,1) model has a MAPE value of 9% for out-sample data and 11% for in-sample data. In contrast, the GSTARIMA(1,1,1) model has a MAPE value of 11% for out-sample data and 12% for in-sample data. So the GSTARIMA(3,1,1) model provides more accurate forecasting results. Therefore, selecting the correct model order is crucial for accurate forecasting.

The Implementation of the Generalized Space-Time Autoregressive (GSTAR) Model for Inflation Prediction

The macroeconomic indicator used to measure a country’s economic balance is inflation. The increase in the price of goods and services causes an increase in inflation, which impacts the decrease in the value of money so that people’s purchasing power for goods and services will decrease and result in slow economic growth. One way to determine future inflation is by forecasting. The Generalized Space-Time Autoregressive (GSTAR) model is a time series model involving time and location. This study aims to predict future inflation using the GSTAR model, which uses differencing without uniform location weights, inverse distance, and normalized cross-correlation. The results showed that the models obtained were the GSTAR (2,1) and GSTAR (5,1)I(1) models. The best model to predict inflation is the GSTAR (5,1)I(1) model with the normalized cross-correlation weight, which had Root Mean Square Error (RMSE) value of 0.5743, which was smaller than the GSTAR (2,1) model.

Literature Review on Integrating Generalized Space-Time Autoregressive Integrated Moving Average (GSTARIMA) and Deep Neural Networks in Machine Learning for Climate Forecasting

The issue of climate change holds immense significance, affecting various aspects of life, including the environment, the interaction between soil conditions and the atmosphere, and agriculture. Over the past few decades, a range of spatio-temporal and Deep Neural Network (DNN) techniques had been proposed within the field of Machine Learning (ML) for climate forecasting, using spatial and temporal data. The forecasting model in this paper is highly complex, particularly due to the presence of nonlinear data in the residual modeling of General Space-Time Autoregressive Integrated Moving Average (GSTARIMA), which represented nonstationary data with time and location dependencies. This model effectively captured trends and seasonal data with time and location dependencies. On the other hand, DNNs proved reliable for modeling nonlinear data that posed challenges for spatio-temporal approaches. This research presented a comprehensive overview of the integrated approach between the GSTARIMA model and DNNs, following the six-stage Data Analytics Lifecycle methodology. The focus was primarily on previous works conducted between 2013 and 2022. The review showed that the GSTARIMA–DNN integration model was a promising tool for forecasting climate in a specific region in the future. Although spatio-temporal and DNN approaches have been widely employed for predicting the climate and its impact on human life due to their computational efficiency and ability to handle complex problems, the proposed method is expected to be universally accepted for integrating these models, which encompass location and time dependencies. Furthermore, it was found that the GSTARIMA–DNN method, incorporating multivariate variables, locations, and multiple hidden layers, was suitable for short-term climate forecasting. Finally, this paper presented several future directions and recommendations for further research.

FORECASTING THE CONSUMER PRICE INDEX WITH GENERALIZED SPACE-TIME AUTOREGRESSIVE SEEMINGLY UNRELATED REGRESSION (GSTAR-SUR): COMPROMISE REGION AND TIME

Economic success will provide benefits for improving people’s welfare. An important indicator to determine economic success can be seen through inflation by calculating the Consumer Price Index (CPI). CPI is a time series data that is influenced by elements between locations. The GeneralizedSpace-Time Autoregressive (GSTAR) method is a suitable method to be applied to CPI data because it involves elements of time and location (spatiotemporal). The problem is that the GSTAR model cannot detect any correlated residuals. The GSTAR model was developed into the GSTAR-SUR model to estimate parameters with correlated residuals so produce more efficient estimates. The purpose of this study was to determine the best GSTAR-SUR model to predict the CPI of six cities in Central Java, namely Cilacap, Purwokerto, Kudus, Surakarta, Semarang, and Tegal. The data that used is secondary data sourced from BPS Central Java Province. Based on the results of the analysis, the best model formed is the GSTAR-SUR (11)-I(1) model with an RMSE value of 6.213. Forecasting results show that the CPI value for the next 6 months will increase every month for each city

MODIFIED WEIGHT MATRIX USING PRIM’S ALGORITHM IN MINIMUM SPANNING TREE (MST) APROACH FOR GSTAR(1;1) MODEL

The Generalized Space-Time Autoregressive (GSTAR) model is able to utilize modeling of both space and time simultaneously. The existence of a weight matrix is one of the aspects that established this model. The matrix illustrates the spatial impact that occurs between locations. In this research, a modified weight matrix is presented using the Minimum Spanning Tree approach of graph theory. Prim's algorithm is utilized for calculation here. Not only does the modified weight matrix depend distance, but also highlights the correlation. It makes the modified weight matrix unique. Before starting Prim's algorithm, the correlation is first utilized as an input in forming the initial graph. Following that, find the graph with the least of MST weight. Afterwards, the graph is described utilizing weight matrix, which is applied to the normalization process. Following this, the GSTAR(1;1) modelling process is carried out, beginning with estimating the parameters and then forecasting. The case study is Covid-19 cases that occurred on Java Island between July 2020 (when early Covid-19 entered Indonesia) and the beginning of January 2021. The aim of the research is to model the Covid-19 cases using modified weights and to predict the following five times. The outcome is a GSTAR(1;1) model with modified weights can captures both temporal and spatial patterns. The accuracy of the model is achieved for both the training data and the testing data by the MAPE computations, which yielded of 11.40% and 21.57%, respectively. Predictions are also obtained for each province in the next five times.

ESTIMATING AND FORECASTING COVID-19 CASES IN SULAWESI ISLAND USING GENERALIZED SPACE-TIME AUTOREGRESSIVE INTEGRATED MOVING AVERAGE MODEL

A range of spatio-temporal models has been used to model Covid-19 cases. However, there is only a small amount of literature on the analysis of estimating and forecasting Covid-19 cases using the Generalized Space-Time Autoregressive Integrated Moving Average (GSTARIMA) model. This model is a development of the GSTARMA model which has non-stationary data. This paper aims to estimate and forecast the daily number of Covid-19 cases in Sulawesi Island using GSTARIMA models. We compared two models namely GSTARI and GSTIMA considering the root mean square error (RMSE). Data on a daily number of Covid-19 cases (from April 10, 2020, to May 07, 2021) were used. The location weight used is the inverse distance weight based on the distance between airports in the capital cities of each province. The appropriate models obtained based on the data are the GSTARIMA (1;0;1;1) model and the GSTARIMA (1;1;1;0) model. The results showed that the forecast for the number of new Covid-19 cases is accurate and reliable only for the short term.

Generalized Space-Time Autoregressive Integrated Moving Average (GSTARIMA) Modeling in Forecasting Covid-19 Cases in Indonesia

Covid-19 is an infectious disease caused by Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2). The spread of Covid-19 in Indonesia has grown rapidly that the World Health Organization (WHO) has declared Covid-19 a pandemic. Covid-19 cases have spread to 34 provinces in Indonesia. Covid-19 data in Indonesia involves space and time so the appropriate modeling is the space-time model. Space-time modeling of the Covid-19 case in 34 provinces in Indonesia using the Generalized Space-Time Autoregressive Integrated Moving Average (GSTARIMA) model has not been carried out. The purpose of this research is to get the best GSTARIMA model and forecat the Covid-19 case for the next several times. This model incorporates time and location interdependence with different parameters for each location. Identification of the order of the AR and MA was carried out through the STACF and STPACF plots. For simplicity of interpretation, the spatial order is chosen first order. In this study, the queen contiguity and the inverse distance location weighting matrix were used. The parameter estimation used is Ordinary Least Square (OLS). The results show that the best model for predicting Covid-19 cases in 34 provinces in Indonesia is the GSTARIMA model (1,1,0)1 using an inverse distance weighting matrix with the smallest RMSE value of 1.22.Keywords: Covid-19, GSTARIMA, Queen Contiguity, Inverse Distance, OLS.

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.

Determination of the best weight matrix for the Generalized Space Time Autoregressive (GSTAR) model in the Covid-19 case on Java Island, Indonesia

One factor that goes into the construction of a space–time model, in this case, the Generalized Space–Time Autoregressive (GSTAR) model, is the weight matrix, which acts as a spatial representation and illustrates the relationship that exists between different locations. The temporal and spatial correlations are both accounted for in this model simultaneously. The accuracy with which the weight matrix is chosen significantly impacts the prediction results. The distance inverse and uniform weight matrices are two examples of weight matrices utilized frequently. A recent study on the adjustment of the weight matrix uses distance with rail transit, queen contiguity matrices, and techniques with graph theory. This research aims to find a weight matrix that closely resembles the real-world spatial context by analyzing and contrasting the five weight matrices presented earlier. Afterward, the weight matrix is fed into the GSTAR model as an input variable. In this article, each weight matrix’s various properties will be broken down and analyzed in detail. The case study used in preparation for the Christmas and New Year’s celebrations in 2023 focused on the daily increase in Covid-19 cases across six provinces on Java Island, Indonesia. The Java island was selected as Indonesia’s capital because it serves as the country’s economic hub and connects all provinces to one another. This enables large-scale spatial links between sites with the same time lag or different time delays. According to the findings that were uncovered, the MST weight matrix is the one that should be utilized, and it should have a prediction error tolerance of 19%.

PENERAPAN MODEL GENERALIZED SPACE TIME AUTOREGRESSIVE (GSTAR) UNTUK MERAMALKAN PENERBANGAN DOMESTIK PADA TIGA BANDAR UDARA DI PULAU JAWA

The number of flights is a thing to measure the marketing performance of aviation services. Forecasting the number of flights is done so that airlines can make decisions in increasing the number of passengers and revenue. Forecasting the number of flights at various airports has relationship between time and location. The suitable method for forecasting the number of flights is Generalized Space Time Autoregressive (GSTAR) method. GSTAR is a method that used for forecasting time series data that has a relationship between time and location and has heterogeneous characteristics. This study applied the GSTAR method to model and forecast the number of domestic flights at three airports in Java, namely Husein Sastranegara Airport Bandung, Ahmad Yani Semarang, and Juanda Surabaya. The research chose those three airports because the impact of Covid-19 is very severe in that area. The weight used in this study is the distance inverse weight. The resulting model is a model with differencing 1, autoregressive order 1, and spatial order limited to 1 so that the model formed is the GSTAR model (11)-I(1). The GSTAR (11)-I(1) meets the assumptions of residual white noise and normal multivariate. The model also has sMAPE values for each airport: 2.60%, 4.18%, and 9.89%. Therefore, it can be concluded that the forecasting results of Husein Sastranegara Airport Bandung, Ahmad Yani Airport Semarang, and Surabaya Juanda Airport are very accurate.

GSTARI-X-ARCH Model with Data Mining Approach for Forecasting Climate in West Java

The spatiotemporal model consists of stationary and non-stationary data, respectively known as the Generalized Space–Time Autoregressive (GSTAR) model and the Generalized Space–Time Autoregressive Integrated (GSTARI) model. The application of this model in forecasting climate with rainfall variables is also influenced by exogenous variables such as humidity, and often the assumption of error is not constant. Therefore, this study aims to design a spatiotemporal model with the addition of exogenous variables and to overcome the non-constant error variance. The proposed model is named GSTARI-X-ARCH. The model is used to predict climate phenomena in West Java, obtained from National Aeronautics and Space Administration Prediction of Worldwide Energy Resources (NASA POWER) data. Climate data are big data, so we used knowledge discovery in databases (KDD) in this study. The pre-processing step is collecting and cleaning data. Then, the data mining process with the GSTARI-X-ARCH model follows the Box–Jenkins procedure: model identification, parameter estimation, and diagnostic checking. Finally, the post-processing step for visualization and interpretation of forecast results was conducted. This research is expected to contribute to developing the spatiotemporal model and forecast results as recommendations to the relevant agencies.

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

The Space-Time Autoregressive Modelling with Time Correlated Errors for The Number of Vehicles in Purbaleunyi Toll Gates

The space-time modelling considers the observations dependence based on time and spatial simultaneously. One of popular models used is the Generalized Space-Time Autoregressive (GSTAR). Most of the GSTAR class models assumed that the errors are uncorrelated and normal distributed. In fact, the dependence of errors is exist. In this paper, the GSTAR model is assumed to have the time correlated errors. The convergence of the parameter estimators is evaluated and the weak consistency is obtained. The illustration is performed by using the number of vehicles passed through Purbaleunyi toll gates. For this data, the GSTAR models be applied and compared between the uncorrelated and time correlated errors assumption of modeling. It is obtained that the GSTAR(1;1) model with time correlated errors, is more appropriate model to predict the number of vehicles passed through the Purbaleunyi toll gates. This appropriate model is well performed when the minimum number of time observations is more than sixty observations.

Evolving Hybrid Generalized Space-Time Autoregressive Forecasting with Cascade Neural Network Particle Swarm Optimization

Background: The generalized space-time autoregressive (GSTAR) model is one of the most widely used models for modeling and forecasting time series and location data. Methods: In the GSTAR model, there is an assumption that the research locations are heterogeneous. In addition, the differences between these locations are shown in the form of a weighting matrix. The novelty of this paper is that we propose the hybrid time-series model of GSTAR uses the cascade neural network and obtains the best parameters from particle swarm optimization. Results and conclusion: This hybrid model provides a high accuracy value for forecasting PM2.5, PM10, NOx, and SO2 with high accuracy forecasting, which is justified by a mean absolute percentage error (MAPE) accuracy of around 0.01%.

PEMODELAN INDEKS HARGA PROPERTI RESIDENSIAL DI INDONESIA MENGGUNAKAN METODE GENERALIZED SPACE TIME AUTOREGRESSIVE

Generalized Space Time Autoregressive (GSTAR) is a model used for space time data analysis. Space time data is data related to events at previous times and different locations. GSTAR is an expansion of the Space Time Autoregressive (STAR) method. The STAR method is only suitable for homogeneous locations while GSTAR can be used for heterogeneous locations. This research uses Residensial Property Price Index (IHPR) data. IHPR data is in the form of a multivariate time series consisting of 18 cities/regions with a certain time span. In this study, the analysis of IHPR data is carried out by looking at the relationship between the previous time and other cities/regions. Therefore, the method that can be used is GSTAR method. Analysis of IHPR data in each city/region can help increase the supply of housing, thereby reducing the number of backlogs. The backlog of houses in Indonesia is still relatively high. Backlog is an indicator that is often used by the government to measure the number of housing needs in Indonesia. Based on the fulfillment of the assumptions and the smallest MSE value, the best model obtained is GSTAR(4;1,1,1,1) using cross-correlation normalized weight. The largest IHPR data on forcasting results is in the cities of Makassar, Manado, and Surabaya while the smallest IHPR data is in the city of Balikpapan. The GSTAR method produces forcasted data that is close to the actual data so it is good to use.Keywords : GSTAR, OLS, IHPR

The Generalized STAR Modeling with Heteroscedastic Effects

In general, the Generalized Space Time Autoregressive (GSTAR) model of space-time assumes constant error variance. In this study, a GSTAR model was built with an error variance that was not constant or had a heteroscedasticity effect, namely the combination of GSTAR–Autoregressive Conditional Heteroskedasticity (ARCH). The parameters of the GSTAR–ARCH model were estimated using the Generalized Least Square (GLS) method to obtain an efficient parameter estimation. As a case study, the GSTAR–ARCH model was applied to the daily mean wind speed data of New Orleans, Florida and Mississippi to predict the occurrence of Hurricane Katrina that occurred in 2005. The results obtained show that the GSTAR model (3;0,0,1)–ARCH(1) predicts Hurricane Katrina very well.

THE APPLICATION OF THE SEMIPARAMETRIC GSTAR MODEL IN DETERMINING GAMMA-RAY LOG DATA ON SOIL LAYERS

This research examines the semiparametric Generalized Space-Time Autoregressive (GSTAR) spacetime modeling and determines its spatial weight. In general, the spatial weights used are uniform, binary weights, and based on the distance, the result is a fixed weight. The GSTAR model is a stochastic model that takes into account its random variables. Thus, it is necessary to study the random spatial weights. This study introduced a new method to estimate the observed value of the GSTAR model semiparametric with a uniform kernel. The data involved the Gamma Ray (GR) log data on four coal drill holes. The semiparametric GSTAR modeling aimed to predict the amount of log GR in the unobserved soil layer based on the observation data information on the layer above it and its surrounding location. The results revealed that semiparametric GSTAR modeling could predict the presence of coal seams and their thickness of drill holes. The results also highlight the validity test on the out-sample data that the error in each borehole results in a small error. In addition, the error tends to approach the actual observed value at a depth of 1 meter down.

GSTARI-ARCH MODEL AND APPLICATION ON POSITIVE CONFIRMED DATA FOR COVID-19 IN WEST JAVA

Time series model that is commonly used is the Box-Jenkins based time series model. Time series data phenomena based on Box-Jenkins can be combined with spatial data, it is called the space time model One model based on Box-Jenkins model with heterogeneous location characteristics is the Generalized Space Time Autoregressive Integrated (GSTARI) model for a model that assumes data is not stationary or has a trend. This paper discusses the development of the GSTARI model with the assumption that the error variance is not constant which is applied to positive data confirmed by Covid-19 in West Java Province, especially in 4 regencies/cities that have cases in the high category from 6 March 2020 until 31 December 2020. Four regencies/cities are Depok City, Bekasi City, Bekasi Regency, and Karawang Regency. Parameter estimation method for the assumption of non-constant error variance can use Autoregressive Conditional Heteroscedasticity (ARCH) method. GSTARI-ARCH modeling procedure followed three Box-Jenkins stages, namely the identification process, parameter estimation and checking diagnostic. Application of the GSTARI-ARCH Model to Covid-19 positive confirmed data in 4 regencies/cities has a minimum value of RMSE in Bekasi City. The plot of forecast results for the four regencies/cities has a similar pattern to the actual data only applicable for a short time for 1-2 days.

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.