Robust detection of outliers in bilinear (P,0,1,1) time series model

Bilinear time series model is the simplest model among the nonlinear time series models. Like other time series models, parameter estimation is a crucial process to determine the precision of the model. Nonlinear least squares (NLS) method along with Newton-Raphson (NR) iterative procedure is deemed...

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Main Author:	Mohd Isfahani, Ismail
Format:	Thesis
Language:	eng eng eng
Published:	2024
Subjects:	QA154 Algebra.
Online Access:	https://etd.uum.edu.my/11195/1/depositpermission.pdf https://etd.uum.edu.my/11195/2/s900981_01.pdf https://etd.uum.edu.my/11195/3/s900981_02.pdf
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spelling	my-uum-etd.111952024-06-23T03:07:53Z Robust detection of outliers in bilinear (P,0,1,1) time series model 2024 Mohd Isfahani, Ismail Ahad, Nor Aishah Awang Had Salleh Graduate School of Arts & Sciences Awang Had Salleh Graduate School of Arts And Sciences QA154 Algebra. Bilinear time series model is the simplest model among the nonlinear time series models. Like other time series models, parameter estimation is a crucial process to determine the precision of the model. Nonlinear least squares (NLS) method along with Newton-Raphson (NR) iterative procedure is deemed as the best method to estimate parameters for bilinear Model. However, the existence of outliers will affect the accuracy of the estimated parameters. In addition, the effect of masking and swamping in outlier detection could also jeopardize the estimation. Therefore, detecting outliers and correcting its effects are vital in the construction of a good model. This study proposed two common detection procedures and two bootstrap detection procedures using robust estimators namely mommadn and momtn to improve the performance of outlier detection and to control the Type I error rate In bilinear (p,0,1,1) models, where p=1,2,3. The effectiveness of the detection procedures was evaluated based on the probability of outlier detection and the level of robustness based on Type I error rate which obtained from simulation study. This study focused on two types of outliers that are often encountered in bilinear data namely additional outlier and Innovational outlier. The findings revealed that the robust bootstrap detection procedures perform better than the other detection procedures. The parameter of bilinear (p,0,1,1) models were estimated through the robust NLS (RNLS) method. The effect of the identified outlier was removed by subtracting its estimated magnitude of outlier effect from observation and the model parameters were re-estimated on the corrected series. The Proposed four procedures and RNLS method improved the capability of outlier detection on real environmental data. 2024 Thesis https://etd.uum.edu.my/11195/ https://etd.uum.edu.my/11195/1/depositpermission.pdf text eng staffonly https://etd.uum.edu.my/11195/2/s900981_01.pdf text eng 2027-04-08 staffonly https://etd.uum.edu.my/11195/3/s900981_02.pdf text eng 2027-04-08 staffonly phd doctoral Universiti Utara Malaysia
institution	Universiti Utara Malaysia
collection	UUM ETD
language	eng eng eng
advisor	Ahad, Nor Aishah
topic	QA154 Algebra.
spellingShingle	QA154 Algebra. Mohd Isfahani, Ismail Robust detection of outliers in bilinear (P,0,1,1) time series model
description	Bilinear time series model is the simplest model among the nonlinear time series models. Like other time series models, parameter estimation is a crucial process to determine the precision of the model. Nonlinear least squares (NLS) method along with Newton-Raphson (NR) iterative procedure is deemed as the best method to estimate parameters for bilinear Model. However, the existence of outliers will affect the accuracy of the estimated parameters. In addition, the effect of masking and swamping in outlier detection could also jeopardize the estimation. Therefore, detecting outliers and correcting its effects are vital in the construction of a good model. This study proposed two common detection procedures and two bootstrap detection procedures using robust estimators namely mommadn and momtn to improve the performance of outlier detection and to control the Type I error rate In bilinear (p,0,1,1) models, where p=1,2,3. The effectiveness of the detection procedures was evaluated based on the probability of outlier detection and the level of robustness based on Type I error rate which obtained from simulation study. This study focused on two types of outliers that are often encountered in bilinear data namely additional outlier and Innovational outlier. The findings revealed that the robust bootstrap detection procedures perform better than the other detection procedures. The parameter of bilinear (p,0,1,1) models were estimated through the robust NLS (RNLS) method. The effect of the identified outlier was removed by subtracting its estimated magnitude of outlier effect from observation and the model parameters were re-estimated on the corrected series. The Proposed four procedures and RNLS method improved the capability of outlier detection on real environmental data.
format	Thesis
qualification_name	Doctor of Philosophy (PhD.)
qualification_level	Doctorate
author	Mohd Isfahani, Ismail
author_facet	Mohd Isfahani, Ismail
author_sort	Mohd Isfahani, Ismail
title	Robust detection of outliers in bilinear (P,0,1,1) time series model
title_short	Robust detection of outliers in bilinear (P,0,1,1) time series model
title_full	Robust detection of outliers in bilinear (P,0,1,1) time series model
title_fullStr	Robust detection of outliers in bilinear (P,0,1,1) time series model
title_full_unstemmed	Robust detection of outliers in bilinear (P,0,1,1) time series model
title_sort	robust detection of outliers in bilinear (p,0,1,1) time series model
granting_institution	Universiti Utara Malaysia
granting_department	Awang Had Salleh Graduate School of Arts & Sciences
publishDate	2024
url	https://etd.uum.edu.my/11195/1/depositpermission.pdf https://etd.uum.edu.my/11195/2/s900981_01.pdf https://etd.uum.edu.my/11195/3/s900981_02.pdf
_version_	1804888216572002304

Robust detection of outliers in bilinear (P,0,1,1) time series model

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