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All Journal BIMASTER Jurnal Gaussian CAUCHY: Jurnal Matematika Murni dan Aplikasi Journal of the Indonesian Mathematical Society BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Jurnal Matematika UNAND Jambura Journal of Biomathematics (JJBM) Journal of Mathematics Education and Science Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi Jurnal Forum Analisis Statistik
Huda, Nur'ainul Miftahul
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Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Energy Engineering Mathematics Mechanical Engineering Physics Transportation Other

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Analysis of Multi-Input ARIMA Interventions with Additive Outlier for Forecasting Price of Crude Oil West Texas Intermediate Nabil, Ilhan Nail; Satyahadewi, Neva; Huda, Nur'ainul Miftahul
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 8, No 3 (2024): July
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v8i3.22147

Abstract

Crude oil is a liquid characterized by a thick texture and blackish color. It is composed of complex hydrocarbon compounds with various benefits that are spread around the world. Crude oil derived from fossil fuels can be used as primary fuels, such as gasoline, and is the most important of the energy resources. Based on that, crude oil play a crucial role in the global economy movement because can be used as the main sources of energy all over the world. However, one of the benchmarks for crude oil from the USA is West Texas Intermediate (WTI). Known to produce high-quality oil, the price of crude oil of WTI fluctuates. In addition, fluctuations occur because of several factors, such as the availability of oil supplies, the embargo on oil imports, and the COVID-19 pandemic. The research aims to analyze price forecasting that occurs over the next five months and the accuracy level of the method used. The data that exists outliers is usually removed from forecasting that contains outliers, but that can affect the estimation result in the model. So, in this research intervention and outlier factors are added to the research to overcome the constraints In this study, the Multi-Input ARIMA Intervention and Additive Outlier (AO) method are used by modelling ARIMA pre-intervention and then. After that, the procedure is adding intervention factorsand additive outlier with iterative procedures. Multi-Input ARIMA Intervention and Additive Outlier (AO) are used to determine the magnitude of fluctuations that occur. Data shocks causing outlier data can be used by adding AO factors. WTI oil price data was retrieved from investing.com with monthly data from January 2011 to June 2023. Based on the results of Mmulti-Iinput ARIMA intervention with Additive Outlier method, it has been determined that the movement of WTI oil prices in the next five months will increase compared to the last five periods of actual data. Because of incrased price of crude oil, it will impact of the economic growth all over the world. So, the government better controlled the price of crude oil at lower price. . withMulti-Input ARIMA interventions resulting in AIC, MAPE, and RMSE model each 941.490, 6.979%, and 5.913 . So, Multi-Input and AO proven can be used to forecast data with fluctuate that data occur. 
A Hybrid ARIMA-Intervention Modelling for Forest Fire Risk in The Dry Season Imro'ah, Nurfitri; Huda, Nur'ainul Miftahul; Pratiwi, Hesty; Ayyash, Muhammad Yahya
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v10i2.36741

Abstract

This study explores the time-related patterns of forest fires and assesses the impact of measures implemented during the dry season. Special focus is directed towards the effects of these interventions on the frequency and intensity of fires. This study highlights the importance of combining temporal analysis with spatial data to identify high-risk locations and optimize resource allocation for fire prevention. This study develops an ARIMA model to forecast fire risk before intervention. The findings indicate that integrating intervention factors into the ARIMA model will enhance the model's accuracy. The satisfactory MAPE values and the value data plots effectively demonstrate the data patterns. This method establishes a solid basis for predicting and reducing the risk of forest fires in the dry season, thereby enhancing the fire resilience of ecosystems considered at risk. The findings indicate that the onset of the dry season significantly elevates the risk of forest fires, especially in areas near bodies of water.
The MODWT-ARIMA Model in Forecasting The COVID-19 Cases Imro'ah, Nurfitri; Huda, Nur'ainul Miftahul
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.v7i4.16465

Abstract

The Maximal Overlap Discrete Wavelet Transform-Autoregressive Integrated Moving Average (MODWT-ARIMA) is a forecasting method that uses the ARIMA model generated from MODWT data. The purpose of this study is to analyze an investigation into the MODWT-ARIMA model with regard to the total number of COVID-19 cases in DKI Jakarta. For this study, daily data on cases of Covid-19COVID-19 in DKI Jakarta were obtained. The model is trained with data from April 3, 2022, to June 11, 2022 (referred to as the "in-sample"), and the outcomes of the prediction are tested with data from June 12, 2022, to June 18, 2022 (referred to as the "out-sample"). These data exhibit trends and are organizedorganised into four data series using MODWT. The ARIMA modelling technique is applied to each of the produced sequences. When using the MODWT-ARIMA approach, the RMSE value obtained from the in-sample data is found to be lower than the RMSE value obtained from the out-sample data. In light of the findings, Iit t became clear that MODWT-ARIMA is better suited for estimation than prediction. The fact that the RMSE value for the data acquired from the in-sample is lower than the RMSE value for the data collected from the out-sample demonstrates that this is the case. 
Interpolation of Fire Radiative Power in West Kalimantan using Ordinary Kriging Fitriyana, Gita; Imro'ah, Nurfitri; Huda, Nur'ainul Miftahul; Zuleha, Zuleha
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 4 (2025): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i4.32643

Abstract

Forest fires are recurring environmental disasters with severe ecological and economic impacts, particularly in regions like West Kalimantan. One of the key indicators used to measure fire intensity is Fire Radiative Power (FRP). Accurate spatial prediction of FRP is essential to support early warning systems and mitigation strategies. This study is a quantitative descriptive research that applies a geostatistical spatial analysis technique, namely Ordinary Kriging interpolation, to predict FRP values in West Kalimantan for July, August, and September 2024. The data were obtained from satellite imagery (VIIRS NOAA-20), including latitude, longitude, and FRP values. Prior to modeling, data were tested for normality and found to follow a normal distribution. The spherical semivariogram model yielded the best fit for July and August with RMSE values of 0.046 and 0.011, respectively, while the Gaussian model was optimal for September (RMSE = 0.007). The results show spatial variation in FRP distribution across different regencies each month, with the highest estimated FRP values recorded in Kapuas Hulu (July: 63.56), Melawi (August: 69.00), and Ketapang (September: 55.27). Most areas demonstrated low fire intensity, as shown by the dominance of green zones on the prediction maps. However, localized red-yellow zones indicate areas with high fire potential, which shifted monthly. This study contributes by demonstrating the application of Ordinary Kriging in forest fire intensity mapping and highlights the importance of choosing an appropriate semivariogram model to enhance predictive accuracy. The resulting FRP prediction maps can serve as a valuable tool for policy planning and targeted fire prevention efforts.
ARIMA Time Series Modeling with the Addition of Intervention and Outlier Factors on Inflation Rate in Indonesia Utami, Dewi Setyo; Huda, Nur'ainul Miftahul; Imro'ah, Nurfitri
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.v8i1.17487

Abstract

Extreme events in a time series model can be detected when the precise timing of the event, known as the intervention, is known. When the exact timing of an event is unknown, it is referred to as an outlier.  If these factors are neglected, the model's accuracy will be affected. To overcome this situation, it is possible to add the intervention or outlier factor into the time series model. This study proposes the combination of intervention and outlier analysis in time series models, especially ARIMA. It is intended to minimize the residuals and increase the accuracy of the model so that it is suitable for forecasting. Using the data of inflation rate in Indonesia, the conflict between Russia and Ukraine was used as an intervention factor in this case. Pre-intervention data (before February 2022) is used to construct the ARIMA model (1st  model). After that, the modeling process continued by adding the intervention factor to the ARIMA model. The effect caused by the intervention allows an outlier to appear, so the process is continued by adding the outlier factor, called an additive outlier, into the model before (2nd model). The MAPE for the first and second models is 7.96% and 7.57%, respectively. The finding of this research shows that the ARIMA model with intervention and outlier factors, named as the 2nd model, is the best model. This study shows that combining the intervention and outlier factors into ARIMA model can improve the accuracy. The forecasting of the inflation rate in Indonesia for one period ahead in 2023 is in the range of 2.06%.
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.
Penerapan Model Harga Opsi Black Scholes dalam Penentuan Premi Asuransi Jiwa Dwiguna Unit Link Seftiani, Seftiani; Satyahadewi, Neva; Huda, Nur'ainul Miftahul
Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi EULER: Volume 11 Issue 2 December 2023
Publisher : Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/euler.v11i2.23049

Abstract

Unit-linked life insurance is one of the most popular insurance products. This product connects the element of protection with investment assets in a product. Regarding option pricing, the Black Scholes model is one method that can be used. The advantage of this model is that it is a call option valuation model and is in great demand among financial associations because the option rate obtained from the calculation of this model is an accurate value. This research aims to determine the premium value of unit-linked endowment life insurance by applying the Black Scholes option pricing model. This research begins by selecting the stocks used and completing the information needed, including the insured's age, gender, insurance period, and life expectancy based on TMI in 2011. The return value and stock volatility can be calculated based on the stock data used. Furthermore, applying the Black Scholes option pricing model on customer data with male gender, age 25 years, a selected interest rate of 5.75%, and an insurance period of 5 years obtained a unit link insurance premium value of Rp123,058,412. The results showed that the Black Scholes option price model is determined by stock prices, interest rates, insurance periods, and volatility. When the longer period of insurance taken causes the premium value to be higher, and for different ages, with increasing age, the value of premiums paid will also increase.
GREY MARKOV (1,1) MODEL FOR FORECASTING THE PERCENTAGE OF THE POPULATION THAT EXPERIENCED HEALTH COMPLAINTS IN INDONESIA Huda, Nur'ainul Miftahul; Imro'ah, Nurfitri
Jurnal Matematika UNAND Vol. 12 No. 2 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.2.108-120.2023

Abstract

In mathematics, in addition to the time series model, Autoregressive, Moving Average, or Autoregressive Moving Average, the Grey-Markov (1,1) model can be employed for forecasting. One of the gains of this model is that it may cover a minimum quantity of data, which is beneficial in situations when the amount of data that is available is restricted but is not excessively vast. This model works well with data that does not exhibit a great deal of variability. The Grey model was further developed into the Grey-Markov model by including the idea of a Markov chain into the original model. In this particular investigation, the processes consist of first forming a sequence using a 1-Accumulated Generating Operation (1-AGO), then forming a sequence using an MGO, and finally predicting using an AGO. The procedure that came before it is actually a modeling procedure for the Grey model. In addition, in order to model Grey- Markov(1,1), it is necessary to initially compute the relative inaccuracy of the forecast that came before it. The following step is to partition the outcome of the relative error into numerous states, one for each interval of the relative error. After that, each error is categorized based on a state that has been specified in advance. The state that is defined within the class is used as the basis for making predictions. The percentage of the population in Indonesia that reports having health difficulties on a yearly basis was chosen as the case study for this research because it is relevant to the topic at hand. The data came from the Central Statistics Agency in the United Kingdom. The period covered by the data is from 1996 to 2021. The purpose of this research is to investigate the structure of the Grey-Markov Model (1,1) and provide a forecast regarding the proportion of the general population that will be affected by health issues in the year 2022. According to the findings of this research project, the forecast of the proportion of the population in Indonesia that suffered health complaints in 2022 produced predictive data that was 30.36%, with a very good accuracy value of 2.43%.
AN ANALYSIS OF CLUSTER TIMES SERIES FOR THE NUMBER OF COVID-19 CASES IN WEST JAVA Imro'ah, Nurfitri; Huda, Nur'ainul Miftahul
Jurnal Matematika UNAND Vol. 12 No. 3 (2023)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.12.3.203-212.2023

Abstract

The government may be able to develop more effective strategies for dealing with COVID-19 cases if it groups districts and cities according to the features of the number of Covid-19 cases being reported in each district or city. The data can be more easily summarized with the help of cluster analysis, which organizes items into groups according to the degree of similarity between members. Since it is possible to group more than one period together, the generation of clusters based on time series is a more efficient method than clusters that are created for each individual unit. Using a time series cluster hierarchical technique that has complete linkage, the purpose of this study is to categorize the number of instances of Covid-19 that have been found in West Java by district or city. The data that was used comes from monthly reports of Covid-19 instances compiled by West Java districts from 2020 to 2022. The Autocorrelation Function (ACF) distance cluster was utilized in this investigation to determine how closely cluster members are related to one another. According to the findings, there could be as many as seven separate clusters, each including a unique assortment of districts and cities. Cluster 3, which is comprised of three different cities and regencies, including Bandung City, West Bandung Regency, and Sumedang Regency, has an average number of cases that is 66, making it the cluster with the highest number of cases overall. A value of 0.2787590 is obtained for the silhouette coefficient as a result of the established grouping. This value suggests that the structure of the newly created cluster is quite fragile.The government may be able to develop more eective strategies fordealing with COVID-19 cases if it groups districts and cities according to the featuresof the number of Covid-19 cases being reported in each district or city. The data canbe more easily summarized with the help of cluster analysis, which organizes items intogroups according to the degree of similarity between members. Since it is possible togroup more than one period together, the generation of clusters based on time series isa more ecient method than clusters that are created for each individual unit. Using atime series cluster hierarchical technique that has complete linkage, the purpose of thisstudy is to categorize the number of instances of Covid-19 that have been found in WestJava by district or city. The data that was used comes from monthly reports of Covid-19 instances compiled by West Java districts from 2020 to 2022. The AutocorrelationFunction (ACF) distance cluster was utilized in this investigation to determine howclosely cluster members are related to one another. According to the ndings, there couldbe as many as seven separate clusters, each including a unique assortment of districtsand cities. Cluster 3, which is comprised of three dierent cities and regencies, includingBandung City, West Bandung Regency, and Sumedang Regency, has an average numberof cases that is 66, making it the cluster with the highest number of cases overall. Avalue of 0.2787590 is obtained for the silhouette coecient as a result of the establishedgrouping. This value suggests that the structure of the newly created cluster is quitefragile.
Cluster Analysis Of Cities/Districts In West Kalimantan Based On Stunting Response Indicators Using The Calinski Harabasz Index Priyatna, Tegar Rama; yundari, yundari; Huda, Nur'ainul Miftahul
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.34510

Abstract

The stunting rate in West Kalimantan has reached 27%, mainly due to the government's inability to prioritise regions for essential services and education, especially for adolescents and pregnant women. This study aims to explain the role of modified K-Means and CHI methods in forming optimal clusters and interpreting their conditions. Eight research variables, sourced from BPS and SIGA in 2023, were used: number of adolescents receiving counselling, informed consents, complication cases, aslokon expenditure, aslokon stock, population growth rate, population density, and life expectancy. These variables were validated using PCA with the Kaiser and PVE approaches. Clustering was done by analysing the data for each variable and the characteristics of the objects using the Euclidean distance, determining the centroid values, and iterating until the results stabilised. The clusters were evaluated from one to seven to find the optimal amount using CHI. The results identified five clusters: cluster 1 (relatively poor, three objects), cluster 2 (inferior, four objects), cluster 3 (good, three objects), cluster 4 (exquisite, three objects) and cluster 5 (good, one object).
Co-Authors Arini, Nani Fitria Aulia, Alwa Ayyash, Muhammad Yahya Fikadila, Lisa Fitriyana, Gita Fran, Fransiskus Imro'ah, Nurfitri Kartika Sari Mauditia, Lyra Mujiarti, Eka May Nabil, Ilhan Nail Neva Satyahadewi Pratiwi, Hesty Priyatna, Tegar Rama Rachmawati, Febby Rahmi Hidayati Rofatunnisa, Sifa Safira, Shafa Alya Safitri, Fauziah Seftiani, Seftiani Umairah, Tarisa Utami, Dewi Setyo Utriweni Mukhaiyar Yundari, Yundari Zuleha, Zuleha