Rahmalia, Karina (2024) Perbandingan Penetapan Ambang Batas (Threshold) Menggunakan Metode Mean Residual Life Plot, Threshold Choice, dan Measure of Surprise. Other thesis, Instiut Teknologi Sepuluh Nopember.
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Abstract
Extreme Value Therory (EVT) merupakan salah satu metode statistika yang dikembangkan untuk menganalisis kejadian ekstrem. Pendekatan yang sering digunakan adalah Block Maxima (BM) dan Peaks Over Threshold (POT). Metode Block Maxima dan Peaks Over Threshold akan memberikan distribusi yang berbeda yaitu BM akan menghasilkan distribusi Generalized Extreme Value (GEV) sedangkan metode POT akan menghasilkan Generalized Pareto Distribution (GPD), sehingga penerapan identifikasinya akan berbeda. Pengambilan nilai ekstrem pada kedua metode tersebut berbeda, Block Maxima mengambil nilai-nilai maksimum dari setiap periode waktu atau blok. Sedangkan Peaks Over Threshold mengambil nilai ekstrem melalui nilai-nilai yang melebihi ambang batas (threshold) yang telah ditentukan. Penentuan ambang batas dalam Metode POT adalah aspek kritis dalam analisis data yang memainkan peran penting dalam berbagai konteks, termasuk analisis data keuangan dan analisis data bencana. Nilai ambang batas harus ditentukan secara cermat, jika terjadi ketidak akuratan nilai ambang batas dapat menyebabkan ragam yang besar dan penduga yang bias. Penelitian ini menggunakan tiga metode yang berbeda untuk membandingkan kinerja mereka dalam menentukan ambang batas. Berdasarkan hasil penelitian, dari analisis statistika deskriptif, data keuangan seperti return saham harian dan data curah hujan menunjukkan perbedaan signifikan dalam karakteristik, terutama pada rentang nilai keduanya. Metode penetapan ambang batas seperti Mean Residual Life Plot, Threshold Choice, dan Measure of Surprise mengalami variasi penting dalam penerapannya pada kedua jenis data tersebut, memerlukan modifikasi khusus dalam penanganan nilai ekstrem. Secara khusus, dalam metode Measure of Surprise, nilai return saham harus diubah dengan mengalikan dengan faktor tertentu agar iterasi berjalan dengan baik. Hasil perbandingan metode tersebut menunjukkan bahwa, berdasarkan nilai Akaike Information Criterion (AIC) untuk data return BBCA, metode Mean Residual Life Plot dan Threshold Choice terbukti lebih optimal dalam menetapkan ambang batas untuk nilai ekstrem. Data return BBRI nilai AIC terbaik didapatkan pada metode Threshold Choice. Data curah hujan harian nilai AIC terbaik didapatkan pada metode Mean Residual Life Plot
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Extreme Value Theory (EVT) is a statistical method developed to analyze extreme events, commonly employing approaches such as Block Maxima (BM) and Peaks Over Threshold (POT). The Block Maxima method yields a Generalized Extreme Value (GEV) distribution, while the Peaks Over Threshold method results in a Generalized Pareto Distribution (GPD), leading to distinct identification applications. The extraction of extreme values differs between the two methods; Block Maxima captures maximum values within each time period or block, whereas Peaks Over Threshold identifies extremes by values exceeding a pre-determined threshold. In POT, the critical determination of the threshold is an essential aspect influencing data analysis, playing a pivotal role in various contexts, including financial and disaster data analysis. Precise threshold determination is crucial, as inaccuracies can lead to substantial variability and biased estimates. This research employs three different methods to compare their performance in threshold determination. Based on the research findings, descriptive statistical analysis reveals significant differences in the characteristics of financial data, such as daily stock returns, and rainfall data, especially in their value ranges. Threshold determination methods, such as Mean Residual Life Plot, Threshold Choice, and Measure of Surprise, undergo notable variations in their application to both types of data, requiring specific modifications in handling extreme values. Particularly in the Measure of Surprise method, stock return values must be adjusted by multiplying with a specific factor to ensure proper iteration. The results of the comparison of these methods indicate that, based on the Akaike Information Criterion (AIC) values for BBCA return data, the Mean Residual Life Plot and Threshold Choice methods are proven to be more optimal in determining the threshold for extreme values. The best AIC value for BBRI return data is obtained using the Threshold Choice method. For daily rainfall data, the best AIC value is obtained using the Mean Residual Life Plot method.
| Item Type: | Thesis (Other) |
|---|---|
| Uncontrolled Keywords: | EVT, Ukuran Kejutan, Rata-Rata Sisa Plot Kehidupan, Puncak Di Atas Ambang Batas, Pilihan Ambang Batas, Measure of Surprise, Mean Residual Life Plot, Peaks Over Threshold, Threshold Choice |
| Subjects: | Q Science Q Science > QA Mathematics > QA279.5 Bayesian statistical decision theory. Q Science > QA Mathematics > QA76 Computer software |
| Divisions: | Faculty of Science and Data Analytics (SCIENTICS) > Actuaria > 94203-(S1) Undergraduate Thesis |
| Depositing User: | Karina Rahmalia |
| Date Deposited: | 31 Jan 2024 00:54 |
| Last Modified: | 31 Jan 2024 00:54 |
| URI: | http://repository.its.ac.id/id/eprint/105601 |
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