### Abstract

Abnormal observation due to an isolated incident such as a recording error is known as additive outlier and it is often found in time series. Since extreme value of additive outliers may contribute to the inaccuracy of model specification, proper detection procedure is significant to avoid such error. Equations that explain the nature of an additive outlier and the test statistics pertaining to it are discussed in this article. This is followed by two separate simulation studies that are conducted to investigate the sampling behavior and detection performance of the test statistics in ARMA (1, 1) models. Results for the first simulation study show that the test statistics is an increasing function of sample size. Whilst in the other simulation study we see that the performance of the test statistics improves as large magnitudes of outlier effect are used.

Original language | English |
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Pages (from-to) | 162-169 |

Number of pages | 8 |

Journal | International Journal of Mathematical Models and Methods in Applied Sciences |

Volume | 3 |

Issue number | 2 |

Publication status | Published - 2009 |

### Fingerprint

### Keywords

- Additive outlier
- Detection performance of test statistics
- Sampling behavior of test statistics
- Simulation

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Mathematical Physics
- Modelling and Simulation

### Cite this

*International Journal of Mathematical Models and Methods in Applied Sciences*,

*3*(2), 162-169.

**A simulation study of additive outlier in ARMA (1, 1) model.** / Zaharim, Azami; Rajali, Rafizah; Atok, Raden Mohamad; Mohamed, Ibrahim; Jafar, Khamisah.

Research output: Contribution to journal › Article

*International Journal of Mathematical Models and Methods in Applied Sciences*, vol. 3, no. 2, pp. 162-169.

}

TY - JOUR

T1 - A simulation study of additive outlier in ARMA (1, 1) model

AU - Zaharim, Azami

AU - Rajali, Rafizah

AU - Atok, Raden Mohamad

AU - Mohamed, Ibrahim

AU - Jafar, Khamisah

PY - 2009

Y1 - 2009

N2 - Abnormal observation due to an isolated incident such as a recording error is known as additive outlier and it is often found in time series. Since extreme value of additive outliers may contribute to the inaccuracy of model specification, proper detection procedure is significant to avoid such error. Equations that explain the nature of an additive outlier and the test statistics pertaining to it are discussed in this article. This is followed by two separate simulation studies that are conducted to investigate the sampling behavior and detection performance of the test statistics in ARMA (1, 1) models. Results for the first simulation study show that the test statistics is an increasing function of sample size. Whilst in the other simulation study we see that the performance of the test statistics improves as large magnitudes of outlier effect are used.

AB - Abnormal observation due to an isolated incident such as a recording error is known as additive outlier and it is often found in time series. Since extreme value of additive outliers may contribute to the inaccuracy of model specification, proper detection procedure is significant to avoid such error. Equations that explain the nature of an additive outlier and the test statistics pertaining to it are discussed in this article. This is followed by two separate simulation studies that are conducted to investigate the sampling behavior and detection performance of the test statistics in ARMA (1, 1) models. Results for the first simulation study show that the test statistics is an increasing function of sample size. Whilst in the other simulation study we see that the performance of the test statistics improves as large magnitudes of outlier effect are used.

KW - Additive outlier

KW - Detection performance of test statistics

KW - Sampling behavior of test statistics

KW - Simulation

UR - http://www.scopus.com/inward/record.url?scp=68049124920&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=68049124920&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:68049124920

VL - 3

SP - 162

EP - 169

JO - International Journal of Mathematical Models and Methods in Applied Sciences

JF - International Journal of Mathematical Models and Methods in Applied Sciences

SN - 1998-0140

IS - 2

ER -