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

Diserahkan: 29 Disember 2009 / Diterima: 4 Ogos 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

RUJUKAN

Chang, I., Tiao, G.C. & Chen, C. 1988. Estimation of time series parameters in the presence of outliers. Technometrics 30: 193-204.

Chen, C. & Liu, L.-M. 1993. Joint estimation of model parameters and outlier effects in time series. Journal of American Statistical Society 88: 284-297.

Chen, C.W.S. 1997. Detection of additive outliers in bilinear time series. Computational Statistics and Data Analysis 24: 283-294.

Fox, A.J. 1972. Outliers in time series. Journal of the Royal Statistical Society B 34: 350-363.

Granger, C.W.J. & Andersen, A.P. 1978. Introduction to Bilinear Time Series Models. Gottinge: Vandenhoeck and Ruprecht.

Hampel, F.R., Ronchetti, E.O., Rousseeuw, P.J. & Stahel, W.A. 1986. Robust Statistics: The Approach Based on Influence Functions. Toronto: John Wiley Inc.

Ismail, M.I, Mohamed, I.B. & Yahya, M.S. 2008. Improvement on additive outlier detection procedure in bilinear model. Malaysian Journal of Science 27(2): 107-114.

Keenan, D.M. 1985. ATukey non-additivity type test for time series nonlinearity. Biometrika 72: 39-44.

Priestley, M.B. 1991. Non-linear and Non-stationary Time Series Analysis. San Diego: Academic Press.

Tsay, R. S. 1986a. Nonlinearity test for time series. Biometrika 73: 461-466.

Tsay, R.S. 1986b. Time series model specification in the presence of outliers. Journal of the American Statistical Association 81: 132-141.

Zaharim, A., Mohamed, I. B., Ahmad, I., Abdullah, S. & Omar, M.Z. 2006. Performances Test statistics for single outlier detection in bilinear (1,1,1,1) models, WSEAS Transactions on Mathematics 5(12): 1359-1364.

*Pengarang untuk surat-menyurat; email: imohamed@um.edu.my