Open Access

ARTICLE

Wavelet Based Detection of Outliers in Volatility Time Series Models

Khudhayr A. Rashedi^1,2,*, Mohd Tahir Ismail¹, Abdeslam Serroukh³, S. Al wadi⁴

1 School of Mathematical Sciences, University Sains Malaysia, Minden, Penang, 11800, Malaysia
2 Faculty of Science, University of Ha’il, Hail, 81451, Kingdom of Saudi Arabia
3 Polydisciplinary Faculty of Larache, University Abdelmalek Essaadi, Tetouan, Morocco
4 Department of Risk Management and Insurance, Faculty of Business, The University of Jordan, Aqaba, Jordan

* Corresponding Author: Khudhayr A. Rashedi. Email:

Computers, Materials & Continua 2022, 72(2), 3835-3847. https://doi.org/10.32604/cmc.2022.026476

Received 28 December 2021; Accepted 02 March 2022; Issue published 29 March 2022

Abstract

We introduce a new wavelet based procedure for detecting outliers in financial discrete time series. The procedure focuses on the analysis of residuals obtained from a model fit, and applied to the Generalized Autoregressive Conditional Heteroskedasticity (GARCH) like model, but not limited to these models. We apply the Maximal-Overlap Discrete Wavelet Transform (MODWT) to the residuals and compare their wavelet coefficients against quantile thresholds to detect outliers. Our methodology has several advantages over existing methods that make use of the standard Discrete Wavelet Transform (DWT). The series sample size does not need to be a power of 2 and the transform can explore any wavelet filter and be run up to the desired level. Simulated wavelet quantiles from a Normal and Student t-distribution are used as threshold for the maximum of the absolute value of wavelet coefficients. The performance of the procedure is illustrated and applied to two real series: the closed price of the Saudi Stock market and the S&P 500 index respectively. The efficiency of the proposed method is demonstrated and can be considered as a distinct important addition to the existing methods

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Keywords

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