Detecting additive and innovational outliers in BL(p,0,1,1) process

Ismail, Mohd Isfahani (2009) Detecting additive and innovational outliers in BL(p,0,1,1) process. Masters thesis, University of Malaya.

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Official URL: http://dspace.fsktm.um.edu.my/handle/1812/517

Abstract

This study proposed an outlier detection rocedure for the BL(p,0,1,1) models, where p = 1,2,3. In this process, a time series was first fitted by the models using the Box-Jenkins approach. In the estimation stage, the parameter estimates for the model were found using the nonlinear least squares method. The existence of additive outlier (AO) and innovational outlier (IO) in data from the BL(p,0,1,1) models, p = 1,2,3, were considered in this study. Their features were studied so that the different patterns caused by both type of outliers were distinguishable. Further, the measure of outlier effect for AO and IO were derived using the least square method. Due to the complexity of the statistics, bootstrapping is used to find the variance of the statistics. Based on the bootstrap samples, three different formulae were used to calculate the variance. These formulas are the standard formula, trimmed mean (TM) and MAD. The appropriate test criteria and test statistics to identify the occurrence of outliers were found by standardizing the observed ω giving three different bootstrap-based procedures. These procedures are then compared to the model-based (MB) procedure. The detection of outliers was carried out by examining the maximum value of the standardized statistics of the outlier effects. The outlier detection procedure for identifying the type of outlier at time point t was proposed. Simulation study was carried out to study the performance of the procedure in BL(p,0,1,1) models, p = 1,2,3. It was found out, in general, the proposed procedure performed well in detecting outliers. As for illustration, the proposed procedure was applied on rainfall data and air quality index data.

Item Type: Thesis (Masters)
Subjects: Q Science > Q Science (General)
Depositing User: MS SITI NUR ATIKAH MOHAMAD RUSDI
Date Deposited: 31 Jul 2013 03:11
Last Modified: 31 Jul 2013 03:11
URI: http://repository.um.edu.my/id/eprint/1165

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