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All Journal Epsilon: Jurnal Matematika Murni dan Terapan CAUCHY: Jurnal Matematika Murni dan Aplikasi Jurnal Matematika UNAND
Nurfitri Imro'ah
Universitas Tanjungpura
Computer Science & IT Decision Sciences, Operations Research & Management Mathematics Transportation

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 1 
AN ANALYSIS OF CLUSTER TIMES SERIES FOR THE NUMBER OF COVID-19 CASES IN WEST JAVA Nurfitri Imro'ah; Nur'ainul Miftahul Huda
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.
A Two-Stage Kalman Filter and ARIMA Framework for High-Frequency Wind Speed Modeling in Equatorial Regions Nurfitri Imro'ah; Nur'ainul Miftahul Huda; Kartika Sari; Rahmi Hidayati
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 1 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i1.41753

Abstract

High-frequency wind speed data collected via environmental monitoring systems often contain significant stochastic noise that can obscure underlying patterns and degrade the reliability of statistical models. A two-stage modeling framework (integrating a Kalman Filter (KF) for signal purification and Autoregressive Integrated Moving Average (ARIMA) for predictive modeling) was developed and applied to five-minute interval wind speed data in Pontianak, West Kalimantan. The dataset, comprising 3,742 observations recorded from December 11 to 24, 2024, was utilized to evaluate the effectiveness of the KF in enhancing model fitting. The model quality was further assessed using Individual Moving Range (IMR) control charts to monitor residual stability and detect localized anomalies. Results demonstrate that the KF-ARIMA approach significantly improves performance, reducing the Root Mean Square Error (RMSE) from 1.123 m/s to 0.145 m/s, representing an 87.1\% improvement in precision compared to the standalone ARIMA model. The I-MR charts confirmed that the KF-ARIMA residuals remained consistently within the $3\sigma$ control limits, effectively identifying transient variations that standard diagnostic tests might overlook. This integrated framework proves that combining state-space filtering with traditional time-series models provides a robust approach for characterizing high-frequency meteorological data in equatorial regions.
A Hybrid ARIMA-Intervention Modelling for Forest Fire Risk in The Dry Season Nurfitri Imro'ah; Nur'ainul Miftahul Huda; Hesty Pratiwi; Muhammad Yahya Ayyash
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 10, No 2 (2025): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of 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.
VALUE AT RISK VARIAN KOVARIAN PADA PORTOFOLIO OPTIMAL MULTI INDEX MODEL Mely Amara Putri; Evy Sulistianingsih; Nurfitri Imro'ah
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 2 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i2.14924

Abstract

The construction of an optimal portfolio aims to minimize investment risk, with the Multi-Index Model being one method that accounts for multiple factors influencing stock returns. This study analyzes the optimal portfolio allocation and estimates potential losses using the variance-covariance Value at Risk (VaR) method. The study examines seven stocks from different sectors that have consistently been part of the IDX30 index from January 2019 to June 2024. The factors considered include the Jakarta Composite Index (JCI) and the exchange rate of the Indonesian Rupiah against the US Dollar (USD). The results indicate that the optimal portfolio consists of PT Adaro Energy Tbk. (ADRO), PT Bank Central Asia Tbk. (BBCA), and PT Kalbe Farma Tbk. (KLBF), with respective weights of 18.83%, 77.12%, and 4.05%. This portfolio yields a return of 1.22% with a risk level of 4.93%. The VaR calculation at a 95% confidence level indicates a maximum potential loss of 8.11% of the initial investment value.
Spatio-Temporal Forecasting and Continuous Spatial Reconstruction of Fire Radiative Power Using Sequential GSTARX-IDW and Ordinary Kriging Nurfitri Imro'ah; Nur'ainul Miftahul Huda; Yundari Yundari; Gita Fitriyana
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 11, No 2 (2026): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/cauchy.v11i2.44480

Abstract

This study presents a sequential hybrid spatio-temporal forecasting framework combining the Generalized Space-Time Autoregressive with Exogenous Variables (GSTARX-IDW) model and Ordinary Kriging (OK) to model and map weekly Fire Radiative Power (FRP) dynamics in West Kalimantan from January 2021 to October 2025. A strong dominance of spatial contagion was observed, with the spatial autoregressive parameter (p1) being statistically significant across 95.56% of operational grid centroids, providing empirical validation of Tobler's First Law of Geography. Locally, Land Surface Temperature (LST) serves as a key exogenous forcing variable, exhibiting geographical dichotomies driven by localized microclimatic conditions and peatland hydrology. To overcome the limitation of discrete point forecasts at grid centroids, Ordinary Kriging was applied directly to the k-step ahead GSTARX-IDW point forecasts, successfully reconstructing continuous spatial risk surfaces for October 2025. Evaluated through robust out-of-sample metrics, the framework achieved a Root Mean Squared Error (RMSE) of 1.1380, a Mean Absolute Error (MAE) of 0.8736, and a Mean Absolute Scaled Error (MASE) of 1.0008, demonstrating competitive temporal point forecasting on par with baseline dynamics while offering superior spatial continuous risk mapping. This sequential framework provides a mathematically grounded baseline for short-term spatio-temporal risk assessment in highly fragmented tropical landscapes.
Co-Authors Evy Sulistianingsih Gita Fitriyana Hesty Pratiwi Kartika Sari Mely Amara Putri Muhammad Yahya Ayyash NUR’AINUL MIFTAHUL HUDA Rahmi Hidayati Yundari, Yundari