Numerical Integral Equation Method for ARL of CUSUM Chart for Long-Memory Process with Non-Seasonal and Seasonal ARFIMA Models

Authors

  • Wilasinee Peerajit Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
  • Yupaporn Areepong Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand
  • Saowanit Sukparungsee Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand

Keywords:

Average Run Length (ARL), cumulative sum (CUSUM) chart, exponential white noise, Numerical Integral Equation (NIE) method, ARFIMA(p,d,q) process, SARFIMA(P,D,Q)S process

Abstract

This paper presents an approximate average run length (ARL) of CUSUM chart for long-memory process by using numerical integral equation (NIE) method based on Gauss-Legendre quadrature rule. Measurement was a performance with the ARL between NIE method and explicit formulas in terms of percentage error when observations are non-seasonal and seasonal ARFIMA models with exponential white noise. Results indicated that ARL values by using both methods were similar and excellent agreement with the percentage error. Apparently, the NIE method is an alternative to explicit formulas for two models.

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Published

2018-01-25

How to Cite

Peerajit, W., Areepong, Y., & Sukparungsee, S. (2018). Numerical Integral Equation Method for ARL of CUSUM Chart for Long-Memory Process with Non-Seasonal and Seasonal ARFIMA Models. Thailand Statistician, 16(1), 26–37. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/110205

Issue

Vol. 16 No. 1 (2018): January

Section

Articles