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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika)
Umairah, Tarisa
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Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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ARIMA MODEL VERIFICATION WITH OUTLIER FACTORS USING CONTROL CHART Umairah, Tarisa; Imro'ah, Nurfitri; Huda, Nur'ainul Miftahul
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 1 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss1pp0579-058

Abstract

Control charts are often used in quality control processes, especially in the industrial sector because of their significant benefits in increasing industrial production. However, control charts can also be used throughout the field of time series modeling to evaluate measures of accuracy represented by a particular time series model. The application of control charts in this research meets the criteria for evaluating accuracy. However, it is not certain that the time series model will have a high level of accuracy. There are various factors that can influence this phenomenon, one of which is the potential for outliers. Therefore, it is very important to perform time series modeling by adding an outlier factor. The residuals of the time series model obtained are used to create a control chart for model verification. The aim of this research is to evaluate the validity of time series models by looking at the influence of outlier characteristics to improve their accuracy. This research studies the accuracy of a time series model built using Gross Domestic Product (GDP) data in Indonesia. There are two different models, namely the ARIMA model without outlier factors and the ARIMA model with outlier factors which are used for research purposes. Both models were performed using the same data set. The results of this study indicate that the ARIMA model with outlier factors has better accuracy than the ARIMA model without outlier factors. This conclusion can be drawn based on the observation that the residual value is within the predetermined control limits, thus indicating that the process is in a state of statistical control.
Control Chart for Correcting the ARIMA Time Series Model of GDP Growth Cases Imro'ah, Nurfitri; Huda, Nur'ainul Miftahul; Utami, Dewi Setyo; Umairah, Tarisa; Arini, Nani Fitria
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 1 (2024): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i1.19612

Abstract

The essential prerequisite for attending the G20 conference is a country's GDP because G20 members can significantly boost the economy and preserve the nation's financial stability. Time series data can be thought of as a country's Gross Domestic Product (GDP) at a particular point in time. In this research, the GDP numbers from five Southeast Asian nations that are attending the G20 fulfilling are used. The total was 47 observations made yearly, which extended from 1975 to 2001. A time series analysis was performed on the data gathered. The correctness of time series models is also evaluated using control charts based on this research. The control chart is constructed using the time series model's residuals as observations. After applying the IMR control chart for verification, the results revealed that the residuals, specifically the models for GDP in Malaysia, Singapore, and Thailand, are out of control. The white noise assumption is fulfilled by the time series model obtained for Brunei and Indonesia's GDP, but the residuals are out of control. Whether controlled residuals are used depends on the accuracy with which the time series model predicts the future. If the amount of residuals is under control, then the time series model produced is accurate and good enough for prediction. After using the IMR control chart to verify the residuals, the results indicate that the residuals, namely the models for GDP in Malaysia, Singapore, and Thailand, are not under control. The assumption of white noise is proved correct by the time series model obtained for the GDP of Brunei Darussalam and Indonesia. With that being said, the residuals are entirely out of control. The model must improve its ability to forecast various future periods. It is a consequence of the unmanageable residuals that the model contains. Even if the best available model has been obtained based on the criteria that have been defined, it is anticipated that the research findings will improve the theories that have previously been developed and raise knowledge regarding the usefulness of testing the time series model. In addition to all of that, it is intended that the research will produce a summary of cases of an increase in GDP from five Southeast Asian countries participating in the G20 conference. 
Looking at GDP from a Statistical Perspective: Spatio-Temporal GSTAR(1;1) Model Huda, Nur'ainul Miftahul; Imro'ah, Nurfitri; Arini, Nani Fitria; Utami, Dewi Setyo; Umairah, Tarisa
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 7, No 4 (2023): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v7i4.16236

Abstract

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.
Co-Authors Arini, Nani Fitria Huda, Nur'ainul Miftahul Imro'ah, Nurfitri Utami, Dewi Setyo