GSTAR Model Research Articles

Prediksi Risiko Emisi Karbon Dioksida Melalui Pemodelan GSTAR Kriging di Wilayah Asia

This study analyzes the variability of carbon dioxide emissions across Asia, revealing that China, India, and Indonesia are the primary contributors with extremely high average emissions and standard deviations. The GSTAR(3;1,1,1) model has been shown to be optimal for forecasting future emissions, based on lower RMSE and MAPE values. Ordinary Kriging analysis using the isotropic spherical semivariogram model provides the most accurate predictions for unobserved areas, with contour maps indicating that the northeastern region of Asia will continue to face high emission concentrations until 2027. While countries such as Brunei and Armenia have managed to keep emission levels low, the instability of emission trends across Asia underscores the need for emission reduction strategies tailored to the specific context of each country.

Looking at GDP from a Statistical Perspective: Spatio-Temporal GSTAR(1;1) Model

The gross domestic product (GDP) is a significant indicator for evaluating the performance of an economy. The GDP of a nation can be used to get a sense of the size and health of that nation's economy. Indonesia is the only nation from Southeast Asia to be represented in the G20. All G20’s countries play vital roles in creating the economic landscape of the region, the world, and everything in between. This research is focused on the increase of the GDP in Indonesia, Malaysia, Singapore, Thailand, and Brunei Darussalam. The spatial influence of GDP can be seen in the growth of each nation's infrastructure and industrial sector, for example. at the regional level, the increase of a country's GDP can also have an effect on the countries that are its neighbors. Using the GSTAR model, the aim of this study is to investigate the spatial and temporal influences on the GDP statistics of five different countries. The GSTAR model is distinguished by the presence of a weight matrix, which is one of its distinguishing features. In addition, the aim of this research is to select the most appropriate weight matrix for the purpose of representing the spatial effect on GDP statistics. Uniform, queen contiguity, and inverse distance weight matrices are the types of weight matrices that are utilized. Calculating each weight matrix, estimating relevant parameters, and performing diagnostic tests are the primary activities involved in this investigation. As a consequence of this, a weight matrix that is uniform in its distribution is the one that performs the best. The spatial and temporal correlations of GDP data may be accurately represented by the GSTAR model when it is equipped with a uniform weight matrix. This model is applied to five different countries.

Generalized Space-Time Autoregressive Modeling of the Vertical Distribution of Copper and Gold Grades with a Porphyry-Deposit Case Study

We examined the first-order application of the generalized space-time autoregressive GSTAR (1;1) model. The autoregressive model was used and was performed simultaneously in multiple drill-hole locations. The GSTAR model was applied to data with absolute time parameter units, such as hours, days, months, or years. Here a new perspective on modeling space-time data is raised. We used the relative time parameter index as a discretization of the same drilling depth of mineralization through a porphyritic deposit. Random variables were the copper and gold grades derived from the hydrothermal fluid that passed through the rock fractures in a porphyry copper deposit in Indonesia. This research aims to model the vertical distribution of copper and gold grades through backcasting the GSTAR (1;1) model. Such results could help geologists to predict copper and gold grades in deeper zones in an ore deposit. Two spatial weight matrices were used in the GSTAR (1;1) model, and these were based on a Euclidean distance and kernel function. Both weight matrices were constructed from different perspectives. The Euclidean distance approach gave a fixed weight matrix. Meanwhile, the kernel function approach gave the possibility to be random since it is based on real observations. It is obtained that the estimated (in-sample) and predicted (out-sample) kernel weight approach was accurate. Copper and gold grades data could recommend the GSTAR (1;1) model with a spatial kernel weight for modeling the vertical continuity case.

AN ITERATIVE PROCEDURE FOR OUTLIER DETECTION IN GSTAR(1;1) MODEL

Outliers are observations that differ significantly from others that can affect the estimation results in the model and reduce the estimator's accuracy. To deal with outliers is to remove outliers from the data. However, sometimes important information is contained in the outlier, so eliminating outliers is a misinterpretation. There are two types of outliers in the time series model, Innovative Outlier (IO) and Additive Outlier (AO). In the GSTAR model, outliers and spatial and time correlations can also be detected. We introduce an iterative procedure for detecting outliers in the GSTAR model. The first step is to form a GSTAR model without outlier factors. Furthermore, the detection of outliers from the model's residuals. If an outlier is detected, add an outlier factor into the initial model and estimate the parameters so that a new GSTAR model and residuals are obtained from the model. The process is repeated by detecting outliers and adding them to the model until a GSTAR model is obtained with no outliers detected. As a result, outliers are not removed or ignored but add an outlier factor to the GSTAR model. This paper presents case studies about Dengue Hemorrhagic Fever cases in five locations in West Kalimantan Province. These are the subject of the GSTAR model with adding outlier factors. The result of this paper is that using an iterative procedure to detect outliers based on the GSTAR residual model provides better accuracy than the regular GSTAR model (without adding outliers to the model). It can be solved without removing outliers from the data by adding outlier factors to the model. This way, the critical information in the outlier id is not lost, and an accurate ore model is obtained.

SPATIO-TEMPORAL ANALYSIS OF RUPIAH LOANS PROVIDED BY COMMERCIAL BANKS AND RURAL BANKS

According to SEKI data in 2020, DKI Jakarta is the province that has the highest average monthly value of rupiah loans provided by commercial banks and rural banks. Many factors can affect the size of the value. The amount of rupiah loans provided by commercial banks and rural banks in the previous months can affect the current value. The geographical conditions of an area can have an impact on the surrounding area. Likewise, the number of rupiah loans in DKI Jakarta Province is suspected of having mutual influence with surrounding provinces. The provinces that are directly adjacent to DKI Jakarta are Banten Province and West Java Province. The purpose of this study is to conduct spatio-temporal analysis of the amount of loans provided by commercial banks and rural banks. The data used is the monthly amount of rupiah loans provided by commercial banks and rural banks in DKI Jakarta, West Java, and Banten Provinces in a time period between January 2012 to July 2021. The GSTAR method has been used to analyze the spatio-temporal relationship. The GSTAR model formed is GSTAR(3,6,12) with differencing order of 1. Based on the model formed, it was concluded that the amount of loans provided by commercial banks and rural banks in the three provinces is related to each other spatially and temporally. The RMSE value for each of the models formed is 1.871 for Banten Province, 13.701 for DKI Jakarta, and 2.919 for West Java Province.

Application of GSTARI (1,1,1) Model for Forecasting the Consumer Price Index (CPI) in Three Cities in Central Java

Economic development is affected by several factors, one of which is the inflation rate. One indicator used to measure the inflation rate is Consumer Price Index (CPI). The CPI data is recorded simultaneously at several locations over time, produces space-time data. In Central Java Province, CPI is calculated in six regency/cities, so the CPI is affected by the time and other locations named space-time effect. The forecasting methods involve space and time effect simultaneously is GSTAR. This study used the GSTAR model to forecasting the CPI in 3 cities in Central Java, assuming that autoregressive and space-time parameters differ for each location. This study aims to obtain the best GSTAR model to forecast the CPI in three cities in Central Java by using the IDW and NCC weighting. The results indicated that the best GSTAR model for forecast the CPI in three cities (Surakarta, Semarang, and Tegal) was the GSTARI (1,1,1) model. The GSTARI (1,1,1) model fulfils the assumption of homoscedasticity, white noise, and multivariate normal. The MAPE values obtained using the IDW and NCC weighting are 0.2922% and 0.2914%, respectively. From these results, it can be concluded that the best GSTARI (1,1,1) model to forecast the CPI data in three cities in Central Java is NCC weights, as they have a minimum MAPE value . The results of this research can be used as consideration for the government in making economic policies at the present and in the future.

Application of GSTAR(1,1) model for layer peat soil predicted based on resistivity log data

In this study, GSTAR modeling was carried out with the inverse of distance weight matrix obtained from Geoelectrical Resistivity data at several peatland locations around the Universitas Tanjungpura, Pontianak. This data can identify the subsurface layer of the soil through the electric current that binds into the soil. However, due to the limitation of the tool to measure the resistivity value, it can only measure 1/5 of the depth of the observation length. To overcome this problem, predictions are made at the next depth using the GSTAR model. The study began by measuring the resistivity value of the land using the geoelectric method and mapping it. Through this GSTAR modeling, predictions are made for the unobserved subsurface to determine the type of soil layer. Knowing the type of deeper soil layer can help contractors build plant concrete stakes to keep buildings safe on peatland. The results of the GSTAR(1.1) model are not accurate enough to estimate the resistivity value data. This is possible because the correlation between rock ages is not the same, so further analysis is required.

Identifikasi Model Generalized Space-time Autoregressive (GSTAR) untuk Nilai Inflasi di Pulau Sulawesi

This study aims to identify a forecast model for the value of inflation at seven locations on the island of Sulawesi, namely Palu, Makassar, Gorontalo, Kendari, Manado, Mamuju and Palopo. Estimation of the parameters of the GSTAR model is carried out using the Ordinary Least Square (OLS) method with uniform location weights. The analysis results show that the GSTAR model (1,1) can be used to predict the value of inflation in Sulawesi Island.

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.

Global Cities and Local Challenges: Booms and Busts in the London Real Estate Market

In this paper we investigate the dynamic features of house prices in London. Using a generalized smooth transition model (GSTAR) we show that dynamic symmetry in price cycles in the London housing market is strongly rejected. We also show that the GSTAR model is able to replicate the features of the observed cycle in the simulated data. Further, our results show that the proposed model performs well when compared to other linear and nonlinear specifications in a out-of-sample forecasting exercise.

A Generalized Space-Time Autoregressive Moving Average (GSTARMA) Model for Forecasting Air Pollutant in Surabaya

The GSTAR model is a multivariate time series model that has time and location dependencies. The implementation of the GSTAR model was developed using the GSTARMA model by referring to the Autoregressive Moving Average (ARMA) model. This research provides the early warning stage of air pollution in Surabaya by forecasting the content of pollutant, especially the CO (Carbon monoxide). The data used in this research are CO data are taken from three monitoring stations in Surabaya with a period from January, 1st to December 31st, 2018. There are two stages in this research, the first stage is time series regression with a dummy variable from the data pattern, and the second step is modeling residual time series regression with GSTAR and GSTARMA. This research is using two weights, uniform and inverse weight the distances, with two-parameter estimates, namely OLS and SUR. The results given the RMSE values tend to be small by using GSTARMAX(21,[7]1:) model with an inverse weight the distance and OLS parameter estimation for SUF 1, GSTAR(21) model with an inverse weight the distance using SUR parameter estimation on SUF 6, and GSTARMA(21,[7]1) model using an inverse weight the distance and SUR parameter estimation on SUF 7. Based on the results of this research, the GSTARMA model can correct prediction errors from the GSTAR model on CO data.

Global Cities and Local Challenges: Booms and Busts in the London Real Estate Market

In this paper we investigate the dynamic features of house prices in London. Using a generalized smooth transition model (GSTAR) we show that dynamic symmetry in price cycles in the London housing market is strongly rejected. We also show that the GSTAR model is able to replicate the features of the observed cycle in the simulated data. Further, our results show that the proposed model performs well when compared to other linear and nonlinear specifications in a out-of-sample forecasting exercise.

Modeling Dengue Fever Cases by Using GSTAR(1;1) Model with Outlier Factor

Dengue fever is an endemic disease transmitted through the Aedes Aegypti mosquitos. Dengue virus can be transmitted from human hosts who have been infected by the virus to the mosquitoes to be transmitted back to other humans. So that, it is possible for the virus to be transmitted to several surrounding locations. Aedes Aegypti is one of the dengue mosquitoes that likes a warm climate and not too wet or dry. In addition, many un-expected factors can cause a significant increase in the number of dengue fever cases. So that the number of dengue fever cases can increase significantly far different from other data. An observation data that has different characteristics from others is called outlier. The existence of outliers can indicate individuals or groups that have very different behavior from the most of the individuals of the dataset. Outlier data in a data set are often encountered in various kinds of data analysis. Frequently, outliers are removed to improve accuracy of the estimators. But sometimes the presence of an outlier has a certain meaning, which explanation can be lost if the outlier is removed. In this paper, modeling dengue fever cases using GSTAR(1;1) with outlier factors was firstly proposed.

Generalized space time autoregressive (gstar)-artificial neural network (ann) model with multilayer feedforward networks architecture

The GSTAR model is one linear space time model used to model time series data with inter-location linkages. One of the weaknesses of the GSTAR model is that the model has not been able to capture any nonlinear patterns that may arise. The ANN is one model of nonlinear artificial intelligence that has a flexible functional form and is a supervised engine learning that provides a good framework to represent a relationship in time series data. Due to the advantages of such ANN, it can be combined with GSTAR model. In this research conducted study of GSTAR-ANN model and its network architecture. The model is constructed in 3 layers namely input, hidden and output. The GSTAR model is used as input in the training process. Each input will receive an input signal and forward the signal to the hidden layer, then to the output layer. The GSTAR-ANN model has network architecture with one neuron unit at the output layer, p input neuron, q neuron in hidden layer (multilayer feedforward networks).

G-STAR Model for Forecasting Space-Time Variation of Temperature in Northern Ethiopia

Among many indicators of climate change, the temperature is a key indicator to take remedial action for world global warming. This finding provides application of space-time models for temperature data, which is selected in three meteorology stations (Mekelle, Adigrat and Adwa) of Northern Ethiopia. The objectives of this research are to see the space-time variations of temperature and to find better forecasting model. The steps for building this model starting from order selection of space and autoregressive order, parameters estimation, a diagnostic check of errors and finally forecasting for the long term. The preliminary model is identified by VAR (vector autoregressive) model and tentatively selects the order by using MIC (minimum information criteria) and uses the autoregressive order for the model and fixes the spatial effect, model parameters are estimated using the least square method. Weighted matrix computed by using queen contiguity criteria. It is found that the model STAR(1,1) and GSTAR(1,1) are two options, finally the best-fitted model is GSTAR(1,1) which has high forecasting performance and smallest RMSEF. The outcome of the forecast indicated that in northern Ethiopia, the weather conditions especially temperature of future is increasing trend in dry seasons in all 3 stations in similar fashion but more consistent and has less variation across the region, and less consistent and high variation within the region and the researcher found that spatial effect has high impact on prediction of models.

Spatial Weight Determination of GSTAR(1;1) Model by Using Kernel Function

The stochastic process models with the index parameters such as time and location were investigated in this paper. The model used was GSTAR (1;1), and it was applied to the Gamma ray log data. The important thing to be assessed in this model is the determination of the space weight matrix. Commonly, the spatial weight matrix was determined based on the Euclidean distance, but not based on data. In this work, we use the kernel function approach to determine the spatial weighting function whose domain was in the form of data observation. In addition, we also study the influence of this weight matrix to the stationary condition of GSTAR (1;1) model, and we use the inverse of auto-covariance matrices or IAcM methods. The results showed that the kernel weights matrix approach still being met influence on stationary of this model.

Ensemble averaging and stacking of ARIMA and GSTAR model for rainfall forecasting

Unpredictable rainfall changes can affect human activities, such as in agriculture, aviation, shipping which depend on weather forecasts. Therefore, we need forecasting tools with high accuracy in predicting the rainfall in the future. This research focus on local forcasting of the rainfall at Jember in 2005 until 2016, from 77 rainfall stations. The rainfall here was not only related to the occurrence of the previous of its stations, but also related to others, it’s called the spatial effect. The aim of this research is to apply the GSTAR model, to determine whether there are some correlations of spatial effect between one to another stations. The GSTAR model is an expansion of the space-time model that combines the time-related effects, the locations (stations) in a time series effects, and also the location it self. The GSTAR model will also be compared to the ARIMA model that completely ignores the independent variables. The forcested value of the ARIMA and of the GSTAR models then being combined using the ensemble forecasting technique. The averaging and stacking method of ensemble forecasting method here provide us the best model with higher acuracy model that has the smaller RMSE (Root Mean Square Error) value. Finally, with the best model we can offer a better local rainfall forecasting in Jember for the future.

Comparison between GSTAR and GSTAR-Kalman Filter models on inflation rate forecasting in East Java

Up to now, we often find data which have correlation between time and location. This data also known as spatial data. Inflation rate is one type of spatial data because it is not only related to the events of the previous time, but also has relevance to the other location or elsewhere. In this research, we do comparison between GSTAR model and GSTAR-Kalman Filter to get prediction which have small error rate. Kalman Filter is one estimator that estimates state changes due to noise from white noise. The final result shows that Kalman Filter is able to improve the GSTAR forecast result. This is shown through simulation results in the form of graphs and clarified with smaller RMSE values.

Error Assumptions on Generalized STAR Model

For GSTAR models, the least squares estimation method is commonly used since errors are assumed be uncorrelated. However, this method is not appropriate when errors are correlated, either in time or spatially. For these cases, the generalized least squares (GLS) method can be applied. GLS is more powerful since it has an error parameter that can act as a controller of the model to produce an efficient estimator. In this study, R Software was used to estimate GSTAR parameters. The resulted model was applied to real data, i.e. the monthly tea production of five plantations in West Java, Indonesia. The best model for forecasting was the GSTAR(1;1) model with temporally correlated error assumption.

Optimal Production of Paddy Fields Using Modified GSTAR Models

The optimal paddy harvested in paddy fields of Boyolali is discussed here. The given data are varied by increasing the number of data by random normal generator. Basic model of GSTAR is evaluated and the model must be improved due to the error greater than 20%. The same time is used to model of critical region and the amount of rainfalls instead of using previous data in the usual GSTAR model. The errors are reduced. The amount of paddy is model as a function of critical region and rainfalls from different 2 surrounding locations. This model contains 7 variables. An other modification is done by reducing the number of variables. As a result, a simpler optimization problem arises which is beneficial for computational point of view. Based on the given data, the amount of paddy in Selo and Ampel are possible to improve for future.