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ITS » Master Theses » Statistika - S2
Posted by davi at 08/01/2007 14:44:26  •  34093 Views


PERBANDINGAN METODE - METODE PENDUGAAN PARAMETER MODEL ARFIMA

The Comparison of Estimation Methods on ARFIMA Models

Author :
IRHAMAH 




ABSTRAK

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 GPH 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 ARFIMA0t0 untuk interval d -0.450.45 melalui simulasi Monte Carlo. Hasil dari 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.


ABSTRACT

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 inetods 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 ARFIMA0d0 model for d -0.450.45 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 distributions 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.



KeywordsARFIMA; estimation methods; bias; MSE; forecasting accuracy
 
Subject:  Model matematika
Contributor
  1. Drs. Slamet Mulyono, MSc, PhD.
    Ir. Dwi Atmono Agus Widodo, Mlkom
Date Create: 08/01/2007
Type: Text
Format: pdf ; 84 pages
Language: Indonesian
Identifier: ITS-Master-3100002014547
Collection ID: 3100002014547
Call Number: 519.535 Irh p


Source
Theses Statistics RT 519.535 Irh p, 2001

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