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Hybrid ARIMA-Spatial Autocorrelation (Moran Index and LISA) for Covid-19 Vaccination in All Indonesian Provinces Huda, Nur'ainul Miftahul; Imro'ah, Nurfitri
Jambura Journal of Biomathematics (JJBM) Volume 4, Issue 2: December 2023
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v4i2.20915

Numerous issues arise from stochastic processes with temporal and spatial index parameters. From 2020, Covid-19 has occurred worldwide. Combining time series with geographical analysis is crucial. ARIMA and spatial autocorrelation analysis using Moran's Index and LISA are prominent models for the two analyses. ARIMA predicts future values. The ARIMA model is applied to all recorded locations since it involves a stochastic process with a time and location parameter index. Then the prediction results at each location were examined using spatial autocorrelation, starting with the Moran index to see global relationships, then LISA (to look at the relationship between locations locally, to see which locations have a significant effect). The Queen Contiguity weight matrix calculates spatial autocorrelation (assuming that locations that are directly adjacent to each other have a spatial effect). Spatial autocorrelation will divide each place into four quadrants: High-High (HH), High-Low (HL), Low-High (LH), and Low-Low (LL). This approach was applied to 2021 Indonesian vaccination rates in all 34 provinces (354 days). Hence, the ARIMA model was applied to the 34 provinces, and each location received three forecasting. Moran's Index revealed spatial autocorrelation in the 354th and 355th time forecasts. LISA shows that Aceh (LL), West Sumatra (LH), South Sumatra (HH), Lampung (LH), and North Maluku (LL) influence other provinces (LH).

PEMODELAN GEOGRAPHICALLY WEIGTED REGRESSION PADA ANGKA PARTISIPASI SEKOLAH DI KALIMANTAN BARAT TAHUN 2022 Mujiarti, Eka May; Yundari, Yundari; Huda, Nur'ainul Miftahul
Jurnal Gaussian Vol 13, No 1 (2024): Jurnal Gaussian
Publisher : Department of Statistics, Faculty of Science and Mathematics, Universitas Diponegoro

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.14710/j.gauss.13.1.36-47

Angka Partisipasi Sekolah" (APS) indicates educational quality in a region, with higher APS reflecting better education. In 2022, APS for SMA/SMK/MA/Paket C in West Kalimantan was 68.72%, a decrease from the previous year. A Geographically Weighted Regression (GWR) approach which considers geographic characteristics in modeling the relationship between response and predictor variables, is used to analyze factors influencing APS in West Kalimantan. This study aims to model APS and identify influencing factors. Initial steps include detecting multicollinearity and spatial heterogeneity, and determining the Euclidean distance and bandwidth value of the weighting function. The study uses fixed and adaptive Gaussian, bisquare, and tricube kernels. GWR model parameters are then estimated, and the best model is chosen based on the smallest Akaike Criterion Information (AIC) value. Results show that the best weight is the adaptive bisquare kernel with the smallest AIC. Key factors influencing APS, with a 99.07% coefficient of determination, include the number of schools, teachers, student-teacher ratio, poverty rate, and PDRB per capita, with the remaining 0.93% influenced by unstudied factors.

ANALISIS CLUSTER MENGGUNAKAN METODE K-MEANS DAN FUZZY C-MEANS PADA FAKTOR SOSIAL EKONOMI DI KALIMANTAN BARAT Rachmawati, Febby; Yundari, Yundari; Huda, Nur'ainul Miftahul
BIMASTER : Buletin Ilmiah Matematika, Statistika dan Terapannya Vol 13, No 5 (2024): Bimaster : Buletin Ilmiah Matematika, Statistika dan Terapannya
Publisher : FMIPA Universitas Tanjungpura

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26418/bbimst.v13i5.81858

Peningkatan kesejahteraan masyarakat merupakan tujuan pembangunan nasional yang mencakup pertumbuhan ekonomi. Baik itu kemajuan di bidang pendidikan, perekonomian, maupun infrastruktur. Indeks Pembangunan Manusia (IPM) dan indikator sosial ekonomi lainnya seperti Produk Domestik Regional Bruto (PDRB), Tingkat Pengangguran Terbuka (TPT), dan Jumlah Penduduk Miskin (JPM) digunakan untuk memastikan pencapaian pembangunan. Pengelompokan diperlukan untuk menentukan kualifikasi setiap indikasi; dengan melakukan hal ini, Anda dapat melihat indikator dari yang paling memenuhi syarat hingga yang paling tidak memenuhi syarat. Penelitian ini bertujuan untuk mengklasifikasikan kabupaten dan kota di Kalimantan Barat menurut karakteristik sosial ekonomi dengan menggunakan metodologi K-Means dan Fuzzy C-Means. Fuzzy C-Means mengurutkan informasi berdasarkan tingkat keanggotaan, sedangkan K-Means mengurutkannya berdasarkan kemiripan atau kedekatannya dengan pusat massa. Pendekatan K-Means mencapai hasilnya pada iterasi ketiga sedangkan metode Fuzzy C-Means mencapai hasilnya pada iterasi kedua, dengan nilai centroid tetap konstan. Algoritma K-Means dan Fuzzy C-Means menggunakan tiga struktur pengelompokan yang berbeda. Terdapat tiga kelompok kabupaten/kota berdasarkan status sosial ekonominya: satu dengan delapan kelompok masyarakat berpendapatan rendah, satu dengan empat kelompok masyarakat berpendapatan tinggi, dan satu dengan dua kelompok masyarakat berpendapatan menengah. Kata Kunci : sosial ekonomi, clustering, analisis faktor

Analisis Portofolio Optimal dengan Metode Liquidity Adjusted Capital Asset Pricing Model Pada Indeks Saham LQ-45 Safira, Shafa Alya; Satyahadewi, Neva; Huda, Nur'ainul Miftahul
Journal of Mathematics Education and Science Vol. 7 No. 2 (2024): Journal of Mathematics Education and Science
Publisher : Universitas Nahdlatul Ulama Sunan Giri Bojonegoro

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.32665/james.v7i2.2282

Investor wajib mempunyai kemampuan analisis terhadap hubungan diantara return yang diharapkan dan risiko. Salah satu model yang dikembangkan dalam pembentukan portofolio optimal adalah Liquidity Adjusted Capital Asset Pricing Model (LCAPM). LCAPM adalah model CAPM yang dipengaruhi oleh risiko likuiditas. Dalam penelitian, dilakukan pembentukan bobot optimal menggunakan LCAPM untuk indeks saham LQ-45 periode Februari 2019-Januari 2022. Penelitian ini bertujuan membentuk portofolio optimal indeks saham LQ-45 dan menerapkan LCAPM pada pengambilan keputusan investasi saham. Teknik pengambilan sampel pada penelitian ini menggunakan purposive sampling. Langkah penelitian setelah data terkumpul yaitu menghitung return harga penutupan indeks saham LQ-45, return pasar (IHSG), uji signifikan parameter, menghitung likuiditas saham serta likuiditas pasar, return bebas risiko, nilai beta saham, serta expected return dan memilih saham yang memiliki expected return yang bernilai positif untuk dibentuk portofolio. Kemudian dilakukan penyusunan kombinasi, pembobotan serta pengukuran kinerja portofolio. Hasil penelitian menunjukkan dari ketiga portofolio yang terbentuk memiliki nilai indeks sharpe yang bernilai negatif.. Investor lebih baik berinvestasi di bank yang menghasilkan expected return lebih tinggi dibanding portofolio saham yang dibentuk.

The GSTAR (1;1) Modelling with Three Combination of the Grid Sizes and Spatial Weight Matrix in Forest Fires Cases Ayyash, Muhammad Yahya; Huda, Nur'ainul Miftahul; Imro'ah, Nurfitri
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.27543

One of the models that is utilized in spatio-temporal analysis is known as the Generalized Space-Time Autoregressive (GSTAR). This model incorporates two dimensions, namely the geographical and temporal aspects of the situation. This approach assists in the identification of patterns and correlations between data by taking into account both spatial and temporal elements. From modeling the confidence level of forest fire hotspot cases in Kubu Raya and its surrounds using the GSTAR (1;1) model with three different combinations of grids and special weight matrices, the purpose of this study is to discover which combination of grids and spatial weight matrices is the most effective. The results of diagnostic tests and the degrees of MAPE accuracy are used to determine which model is the most suitable. The data was obtained from the FIRMS-NASA platform, ranging from January 2014 to August 2024. A grid with a dimension of 1.25 x 1.25 degrees and a rook contiguity weight matrix is a combination of grids and spatial weight matrices that meet the white noise assumption, according to the findings of the study. This conclusion is based on the diagnostic test. As a result, the combination of a grid with a size of 1.25 x 1.25 and a rook contiguity weight matrix is the best in this modeling. This combination has a MAPE of 11.797%, which indicates that this model has a good level of accuracy.

COMPARISON OF WEIGHT MATRIX IN HOTSPOT MODELING IN WEST KALIMANTAN USING THE GSTAR METHOD Pratiwi, Hesty; Imro'ah, Nurfitri; Huda, Nur'ainul Miftahul; Ayyash, Muhammad Yahya
Jurnal Matematika UNAND Vol 14, No 1 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.1.31-45.2025

This research aims to investigate the usefulness of the Generalized Space- Time Autoregressive (GSTAR) approach in predicting the number of fire hotspots in West Kalimantan Province. Specifically, the study compares the performance of the Queen contiguity method and the uniform weight matrix. Fires in the forests and on the land in West Kalimantan are severe problems that cause harm to the environment and other adverse effects. Data on fire hotspots were collected from four different regencies in West Kalimantan between January 2018 and March 2023 to provide the information used in this study. Compared to the uniform weight matrix, the study results reveal that the Queen contiguity weight matrix produces more accurate results. This is evidenced by the fact that the Root Mean Squared Error (RMSE) and Mean Absolute Deviation (MAD) values are lower in the Queen contiguity weight matrix. Based on these findings, more effective techniques for preventing forest and land fires are anticipated to be considered for planning purposes.

Peramalan Inflasi Kota Pontianak dengan Metode Seasonal Autoregressive Integrated Moving Average Aulia, Alwa; Huda, Nur'ainul Miftahul; Rofatunnisa, Sifa
Jurnal Forum Analisis Statistik Vol. 4 No. 2 (2024): Jurnal Forum Analisis Statistik (FORMASI)
Publisher : Badan Pusat Statistik Provinsi Kalimantan Barat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.57059/formasi.v4i2.99

One measure of regional economic stability that is always interesting to discuss is inflation, as it has a major impact on economic growth, external balance, competitiveness, interest rates, and even income distribution. Inflation is a term that refers to a consistent rise in the prices of goods and services over a period of time. This rise in prices can lead to a decrease in the purchasing power of money. To solve this problem, it is necessary to make predictions to forecast the value of inflation in the future. This research uses the Seasonal Autoregressive Moving Average method to forecast Pontianak City inflation from January 2025 to December 2025. The data used in this research comes from BPS Pontianak City. The best model is determined from the accuracy test with MAPE value. Based on the results of the analysis conducted, the ???????????????????????? (6,0,4)(2,1,1)6 model is the best model for forecasting inflation in Pontianak City with a MAPE value of 2.02%.

Double Intervention Analysis on The Arima Model of Covid-19 Cases in Bali Imro'ah, Nurfitri; Huda, Nur'ainul Miftahul
Journal of the Indonesian Mathematical Society Vol. 31 No. 1 (2025): MARCH
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.v31i1.1347

The time series process is not only influenced by previous observations, but some phenomena result in drastic changes to observations in the time series process so that there is a change in the average or only a temporary change in observations. For example, there is a policy from the government towards handling a case. This is referred to as an intervention. Therefore, it is necessary to do time series modeling with intervention factors. One form of intervention in the current pandemic era is a policy issued by the government. In this study, the time series model used is ARIMA. This study aimed to analyze the effect of an intervention on the ARIMA model on Covid-19 cases in Bali. This study uses data on the number of new Covid-19 cases in Bali from 24 April 2020 to 31 May 2021. There are two interventions used in this study, namely restrictions on activities for the Panca Yadnya ceremony and crowds in Bali and restrictions on traveling outside the area and/or going home and/or leaving for employees of the State Civil Apparatus during the Covid-19 pandemic. The results of this study show that two policies issued by the Bali provincial government can handle the addition of new cases of Covid-19. It can be seen from the decline in the number of new Covid-19 cases in Bali until the end of May 2021.

COMPARISON OF WEIGHT MATRIX IN HOTSPOT MODELING IN WEST KALIMANTAN USING THE GSTAR METHOD Pratiwi, Hesty; Imro'ah, Nurfitri; Huda, Nur'ainul Miftahul; Ayyash, Muhammad Yahya
Jurnal Matematika UNAND Vol. 14 No. 1 (2025)
Publisher : Departemen Matematika dan Sains Data FMIPA Universitas Andalas Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.25077/jmua.14.1.31-45.2025

This research aims to investigate the usefulness of the Generalized Space- Time Autoregressive (GSTAR) approach in predicting the number of fire hotspots in West Kalimantan Province. Specifically, the study compares the performance of the Queen contiguity method and the uniform weight matrix. Fires in the forests and on the land in West Kalimantan are severe problems that cause harm to the environment and other adverse effects. Data on fire hotspots were collected from four different regencies in West Kalimantan between January 2018 and March 2023 to provide the information used in this study. Compared to the uniform weight matrix, the study results reveal that the Queen contiguity weight matrix produces more accurate results. This is evidenced by the fact that the Root Mean Squared Error (RMSE) and Mean Absolute Deviation (MAD) values are lower in the Queen contiguity weight matrix. Based on these findings, more effective techniques for preventing forest and land fires are anticipated to be considered for planning purposes.

FOREST FIRE ANALYSIS FROM PERSPECTIVE OF SPATIAL-TEMPORAL USING GSTAR (p;λ_1,λ_2,…,λ_p) MODEL Pratiwi, Hesty; Imro'ah, Nurfitri; Huda, Nur'ainul Miftahul
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 19 No 2 (2025): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol19iss2pp1379-1392

West Kalimantan is particularly susceptible to the devastating effects of forest fires, among the natural disasters that have a significant impact. One of the indicators that can be used to identify forest fires is the presence of hotspots. The term "hotspot" refers to data that has both spatial and temporal characteristics. Using the Generalized Space-Time Autoregressive (GSTAR) model combined with the Queen Contiguity weight matrix, this research aims to model and forecast the confidence level of hotspots in Kubu Raya Regency and its surrounding areas. We chose the GSTAR model because of its ability to model spatial interactions between locations and temporal change patterns over time. According to NASA FIRMS, the data used in this study were confidence level hotspot data, covering the period from January 2014 to August 2024. To define locations for modeling, the study area was divided into grids measuring degrees. The maximum confidence level value in each grid was used to represent the highest potential fire risk. The research process consists of the following stages: data preparation, stationarity testing, calculation of the Queen Contiguity spatial weight matrix, identification of model orders based on STACF and STPACF plots, and estimation of model parameters to predict hotspot confidence levels. The GSTAR (3;1) model was selected as the best model because it satisfies the white-noise assumption and has a MAPE value of 14.78%. Based on the MAPE, the GSTAR (3;1) model can provide reasonably accurate predictions for the confidence level of fire points over the following three periods. The prediction results indicate a decline in the fire point confidence level across all locations during the following three periods. The findings of this study can support the optimization of resource allocation in the prevention of forest fires.

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