Penaksiran Parameter Mixtures of Gaussian Process Functional Regressions Berdasarkan Pendekatan Hidden Markov Model untuk Peramalan Deret Waktu Musiman dengan Struktur Multimodal (Studi Kasus: Peramalan Suhu Permukaan Tanah Kota Surabaya)

Rahmayanti, Ilma Amira (2025) Penaksiran Parameter Mixtures of Gaussian Process Functional Regressions Berdasarkan Pendekatan Hidden Markov Model untuk Peramalan Deret Waktu Musiman dengan Struktur Multimodal (Studi Kasus: Peramalan Suhu Permukaan Tanah Kota Surabaya). Masters thesis, Institut Teknologi Sepuluh Nopember.

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Abstract

Deret waktu musiman merupakan salah satu bentuk deret waktu yang menunjukkan adanya pengulangan fluktuasi di periode yang tetap. Meskipun mempunyai pengulangan fluktuasi, tidak menutup kemungkinan bahwa data tersebut memiliki struktur multimodal, dimana terdapat heterogenitas pada pola kurva musimannya. Struktur multimodal dalam deret waktu musiman ditandai dengan adanya beberapa subpopulasi yang memiliki pola tertentu. Cara menangkap heterogenitas ini adalah dengan diterapkannya suatu model campuran seperti pada Mixtures of Gaussian Process Functional Regressions (Mix-GPFR). Mix-GPFR mengasumsikan bahwa suatu deret waktu disusun oleh K proses random dengan struktur pola berbeda-beda, dimana setiap kurva musiman akan dimodelkan dengan K model GPFR secara bersamaan dan menggunakan probabilitas tertentu untuk masing-masing komponen pembentuknya. Kendati demikian, metode Mix-GPFR masih memiliki kekurangan karena setiap kurva musiman dianggap sebagai observasi saling bebas. Tentunya hal ini sangat berlawanan dengan sifat deret waktu yang memiliki dependensi temporal. Oleh karena itu, dikembangkan metode Hidden Markov-Based Mixtures of Gaussian Process Functional Regressions (HM-GPFR), yaitu metode ekstensi dari Mix-GPFR yang menerapkan konsep Hidden Markov Model. Metode HM-GPFR mampu menangkap setiap pola pada kurva musiman menggunakan suatu hidden state yang bisa ditelaah transisinya antar periode waktu. Metode HM-GPFR selanjutnya juga dicoba dikembangkan ke pendekatan Bayesian dalam rangka mengurangi kemungkinan terjadinya overfitting, yang kemudian disebut sebagai Bayesian Hidden Markov-Based Mixtures of Gaussian Process Functional Regressions (BHM-GPFR). Penelitian ini bertujuan guna mendapatkan penaksir parameter model HM-GPFR dan BHM-GPFR, sekaligus mengetahui performansi peramalan dari kedua metode jika diaplikasikan pada data suhu permukaan tanah Kota Surabaya. Data suhu permukaan tanah yang digunakan dalam penelitian ini merupakan data per-jam dengan efek musiman berperiodisitas harian, yang mana nilai tertinggi umumnya dicapai saat siang dan nilai terendah dicapai saat pagi, dengan pola tersebut berulang setiap hari. Dalam realitanya, walau memiliki efek musiman, kurva harian dari suhu permukaan tanah sangat mungkin mengandung keanekaragaman. Hal ini bisa disebabkan karena adanya pergantian musim ataupun fenomena-fenomena alam lain. Hasil penelitian menunjukkan bahwa performansi HM-GPFR dan BHM-GPFR dalam meramalkan suhu permukaan tanah Kota Surabaya sudah sangat baik, bahkan untuk jangka panjang, dengan nilai MAPE yang berada di sekitar angka 5%.
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Seasonal time series is a time series that shows repeated fluctuations over a fixed period. Even though it has repeated fluctuations, it does not rule out the possibility that the data have multimodal structure, which indicated from the heterogeneity in shape of seasonal curves. This multimodal structure can be characterized through the existence of several subpopulations, each of which has specific seasonal pattern. The way to capture the heterogeneity is by applying a mixture model such in Mixtures of Gaussian Process Functional Regressions (Mix-GPFR). Mix-GPFR assumes that a time series is made up of K random processes with different pattern structures, while each seasonal curve would be modeled with K GPFR models simultaneously and used certain probability for every component. However, Mix-GPFR still has drawback as the seasonal curves were deemed to be independent observations. Of course, this is in direct contrast to the nature of time series which has temporal dependencies. Therefore, an extension method of Mix-GPFR that applies the Hidden Markov Model concept, which is called as Hidden Markov-Based Mixtures of Gaussian Process Functional Regressions (HM-GPFR), is developed. The HM-GPFR is able to capture every pattern of seasonal curve using a hidden state, whose transitions between each period can be studied well. This HM-GPFR is then being further developed into a Bayesian approach to reduce the risk of overfitting, which is hereinafter referred as Bayesian Hidden Markov-Based Mixtures of Gaussian Process Functional Regressions (BHM-GPFR). This research aims to obtain parameter estimates for the HM-GPFR and BHM-GPFR models, as well as to know the forecasting performance of those two methods when applied to Surabaya city’s land surface temperature (LST). The land surface temperatures analyzed in this study consist of hourly measurements influenced by seasonal patterns that follow a daily cycle. Temperature data typically reach their peak in the afternoon and drop to their lowest in the morning, with this pattern repeating each day. Despite these seasonal effects, daily curves may vary slightly due to changes in season or other natural phenomena. The results of this study indicate that both HM-GPFR and BHM-GPFR perform exceptionally well in predicting LST in Surabaya, even for long-term forecasts, with MAPEs of approximately 5%.

Item Type:	Thesis (Masters)
Uncontrolled Keywords:	Algoritma Expectation-Maximization, Expectation-Maximization Algorithm, Gaussian Process, Hidden Markov Model, Mixtures of Gaussian Process Functional Regressions, Proses Gaussian
Subjects:	H Social Sciences > HA Statistics H Social Sciences > HA Statistics > HA30.3 Time-series analysis H Social Sciences > HA Statistics > HA31.3 Regression. Correlation. Logistic regression analysis. H Social Sciences > HA Statistics > HA31.7 Estimation Q Science > QA Mathematics Q Science > QA Mathematics > QA274.7 Markov processes--Mathematical models.
Divisions:	Faculty of Science and Data Analytics (SCIENTICS) > Statistics > 49101-(S2) Master Thesis
Depositing User:	Ilma Amira Rahmayanti
Date Deposited:	05 Feb 2025 08:38
Last Modified:	05 Feb 2025 08:38
URI:	http://repository.its.ac.id/id/eprint/118350

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