Perbandingan Metode-Metode Pendugaan Parameter Model Arfima

Irhamah, Irhamah (2001) Perbandingan Metode-Metode Pendugaan Parameter Model Arfima. Masters thesis, Institut Teknologi Sepuluh November.

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Abstract

Model Autoregressive Fractionally Integrated Moving Average (ARFIMA) dikembangkan dari model ARIMA dengan parameter pembedaan d tidak dibatasi hanya bernilai integer tetapi real. Pendugaan parameter model dapat dilakukan dengan beberapa metode. Tujuan dari penelitian ini adalah membandingkan tiga metode diantaranya yaitu metode Geweke dan Porter-Hudak (GH), metode Exact Maximum Likelihood (EML) dan metode Non-linear Least Squares (NLS) berdasarkan ukuran kebaikan penduga (goodness of estimator) yaitu bias dan MSE empiris dan akurasi peramalan. Perbandingan dilakukan terhadap model ARFIMA(0,0,0) untuk interval d = [-0.45, 0.45] melalui simulasi Monte Carlo. Studi ini menyatakan bahwa penduga GPH meminimumkan bias dan AIC tetapi memaksimumkan MSE nilai duga. Untuk d >= 0 penduga EML paling efisien dan menghasilkan ramalan paling akurat namun memberikan bias dan AIC maksimum. Sebaliknya untuk d < 0 penduga NLS paling efisien. Pada kasus ini bias penduga menunjukkan tingkat kemencengan distribusi sampling dimana untuk T = 100 bias GPH selalu positif sedangkan bias penduga EML selalu negatif serta kesalahan peramalan MSE out of sample selalu lebih besar dari MSE in sample. Prosedur pendugaan NLS menggabungkan pendekatan dua metode yang lain, hal ini mengakibatkan perilaku menarik dari bias dan MSE penduga NLS yang hampir sama dengan penduga GPH namun nilai-nilainya mendekati hasil penduga EML. Penambahan jumlah sampel berpengaruh pada peningkatan efisiensi penduga kurang lebih sebesar 50 persen dan penurunan bias sampai lebih dari 50 persen.
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Autoregressive Fractionally Integrated Moving Average (ARFIMA) Models are generalized from the well-known ARIMA models by permitting the degree of differencing d to take any real value rather than being restricted to integer values. Various methods for estimating the differencing parameter are available. The aim of the present paper is to compare three of it, Geweke and Porter-Hudak (GPH), Exact Maximum likelihood (EML) and Non-linear Least Squares (NLS), based on goodness of estimator that is empirically bias and MSE of estimators and forecasting accuracy. This is done to ARFIMA(0,0,0) model for d = [-0.45, 0.45] through the Monte Carlo simulation method. This study results that GPH estimator minimizes bias and AIC but maximizes MSE of estimator. For d >= 0, EML is the most efficient estimator and yields the most reliable forecast, nevertheless it gives maximum bias and AIC. At the contrary, for d < 0 the most efficient estimator is NLS. In this cases, bias of estimators shows the degree of sampling distribution's skewness where for T = 100 GPH always give positive bias whereas EML always give negative bias. The present study also yields out of sample forecasting error always large than in sample forecasting error. NLS estimator combines the other two estimation methods, it causes an interesting feature in bias and MSE of NLS that are almost look like the GPH but the values close to the EML. Increasing sample size effects the efficiency improvement of approximately 50% and bias decreasing up to 50% in comparison to the smaller sample size.

Item Type:	Thesis (Masters)
Additional Information:	RT 519.535 Irh p
Uncontrolled Keywords:	ARFIMA, pendugaan parameter, bias, MSE, akurasi peramalan, ARFIMA, estimation methods, bias, MSE, forecasting accuracy.
Subjects:	Q Science > QA Mathematics > QA280 Box-Jenkins forecasting
Divisions:	Faculty of Mathematics and Science > Statistics > 49101-(S2) Master Thesis
Depositing User:	magang .
Date Deposited:	02 Oct 2026 04:03
Last Modified:	02 Oct 2026 04:03
URI:	http://repository.its.ac.id/id/eprint/145183

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