Sains Malaysiana
40(2)(2011): 191–196
Improvement on the
Innovational Outlier Detection Procedure in a Bilinear Model
(Pembaikan Prosedur Pengesanan Nilai Sisihan Inovasi dalam Model
Bilinear)
Ibrahim Mohamed* & M.I. Ismail
Institute of Mathematical Sciences, University
of Malaya, 50603 Kuala Lumpur, Malaysia
M.S. Yahya & A.G. Hussin
& N. Mohamed
Centre for Foundation of Studies in
Sciences, University of Malaya
50603 Kuala Lumpur, Malaysia
A. Zaharim
Faculty of Engineering
and Built Environment, 43600 UKM Bangi, Selangor D.E., Malaysia
M.S. Zainol
Fakulti Teknologi Maklumat dan Sains
Kuantitatif, Universiti Teknologi MARA
47000 Shah Alam,
Selangor D.E., Malaysia
Received: 29 December 2009 / Accepted: 4 August 2010
ABSTRACT
This paper considers the
problem of outlier detection in bilinear time series data with special focus on
BL(1,0,1,1) and BL(1,1,1,1) models. In the previous study, the formulations of
effect of innovational outlier on the observations and residuals from the
process had been developed and the corresponding least squares estimator of
outlier effect had been derived. Consequently, an outlier detection procedure
employing bootstrap-based procedure to estimate the variance of the estimator
had been proposed. In this paper, we proposed to use the mean absolute deviance
and trimmed mean formula to estimate the variance to improve the performances
of the procedure. Via simulation, we showed that the procedure based on the
trimmed mean formula has successfully improved the performance of the
procedure.
Keywords: Bootstrap;
bilinear; innovational outlier; least squares method
ABSTRAK
Kertas kerja ini
mempertimbangkan masalah pengesanan nilai terpencil dalam data siri masa
bilinear dengan fokus khas kepada model BL(1,0,1,1) dan BL(1,1,1,1). Dalam
kajian terdahulu, formulasi kesan nilai terpencil inovasi ke atas cerapan dan
ralat daripada proses di atas telah dibina dan penganggar kuasa dua terkecil
kesan outlier telah diterbitkan. Justeru, prosedur pengesanan nilai terpencil
menggunakan prosedur bootstrap untuk menganggar varians penganggar telah
dicadangkan. Dalam kertas kerja ini, kami mencadangkan untuk menggunakan “min
sisihan mutlak” dan formula “min terkemas” bagi menganggar varians untuk
memperbaiki keupayaan prosedur. Melalui simulasi, kami menunjukkan bahawa
prosedur berdasarkan formula “min terkemas” telah berjaya memperbaiki keupayaan
prosedur.
Kata kunci:
Bilinear; bootstrap; kaedah kuasa dua terkecil; nilai tersisih inovasi
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*Corresponding
author; email: imohamed@um.edu.my