Detecting level change outliers (LC) in GARCH (1, 1) processes

  • Authors:

  • Mohammad Said Zainol;Siti Meriam Zahari;Kamaruzaman Ibrahim;Azami Zaharim;Kamaruzaman Sopian

  • Affiliations:

  • Center of Studies for Decision Sciences, Faculty Computer Science and Mathematics, Universiti Teknologi MARA, Shah Alam, Malaysia;Center of Studies for Decision Sciences, Faculty Computer Science and Mathematics, Universiti Teknologi MARA, Shah Alam, Malaysia;Solar Energy Research Institute, Faculty of Engineering and Built Environment, UKM, Bangi, Malaysia;Centre for Engineering Education Research, Faculty of Engineering and Built Environment, UKM, Bangi, Malaysia;Solar Energy Research Institute, Faculty of Engineering and Built Environment, UKM, Bangi, Malaysia

  • Venue:
  • AMERICAN-MATH'10 Proceedings of the 2010 American conference on Applied mathematics
  • Year:
  • 2010

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Abstract

This paper reports the results of a study of outlier detection in time series data for the outlier of level change (LC) type. The main objective is to derive a test statistic for detecting LC in GARCH (1,1) processes. Subsequently a procedure for testing the presence of outliers using the statistics was developed. In the derivation of the statistics, the method applied was based on an analogy of GARCH (1,1) as being equivalent to ARMA(1,1) for the residuals εt2. Because of the difficulty in determining the sampling distributions of the outlier detection statistics, critical regions were estimated through simulations. The developed outlier detection procedure was applied for testing the presence of LC outliers in the daily observations of the Index of Consumer Product Price (ICP) for the period 1990 to 2005. Over the period, the results indicate that LC outlier occurred in year 1998.