A Bayesian ARMA-GARCH EWMA monitoring scheme for long run: A case study on monitoring the USD/ZAR exchange rate

Abstract

Statistical process monitoring (SPM) offers an important toolkit used to monitor the stability of a process to improve the quality of outputs and/or services. More often, the design of control charts requires the estimation of the probability density function that involves selecting a common distribution that facilitates the estimation of the process parameters. The Bayesian approach is one of the most efficient techniques used in such instances. It incorporates informative and non-informative priors, i.e., uses information on past data and charting structures, to estimate parameters more efficiently than classical approaches. Bayesian approaches reduce the total expected cost over a finite horizon or the long-run expected average cost. This paper introduces a new Bayesian exponentially weighted moving average (EWMA) monitoring scheme for long runs based on an ARMA-GARCH model. The properties of the new monitoring scheme are investigated in terms of the run-length distribution. A case study on monitoring the USD to ZAR exchange rate is provided using the proposed Bayesian ARMA-GARCH EWMA monitoring scheme.

Keywords:

• ARMA
• ARMA-GARCH
• Bayesian approach
• control chart
• EWMA
• GARCH
• financial data
• prior distribution
• posterior distribution
• statistical process monitoring

Notes

1 Federal Reserve Economic Data (FRED); Link: https://fred.stlouisfed.org

Additional information

Funding

The second author thanks the South African National Research Foundation (NRF) for their support under the grant (RA210125583099) and the Research Development Programme at the University of Pretoria, Department of Research and Innovation (DRI). The second author also thanks the UCDP for their support under the grant (UCDP-732).

Notes on contributors

Mxengeni Shingwenyana

Mxengeni Shingwenyana graduated from the University of Pretoria with BCom (Honours) in Statistics and Data Science. His research interests include Statistical Process Control, Artificial Intelligence and Machine Learning.

Jean-Claude Malela-Majika

Jean‐Claude Malela‐Majika obtained his BSc (Honours) degree in Mathematical Statistics from the High Institute of Statistics from the D.R. Congo (Known as ISS), Honours and Master's degrees in Statistics from the University of Pretoria, and a PhD in Statistics from the University of South Africa. He is currently working as a Senior lecturer at the University of Pretoria in the Department of Statistics and he is a member of the South African Statistical Association, the International Statistical Institute (ISI), and the Institute of Certificated and Chartered Statisticians of South Africa (ICCSSA). His principal research interests include statistical process/quality control, distribution theory and Statistical inference.

Philippe Castagliola

Schalk W Human is an extra-ordinary lecturer in Statistics at the University of Pretoria. His research mainly focuses on the characteristics of the run-length distribution of control charts in case the parameters of the distribution are estimated. His favourite hobbies are cycling and playing online chess.

Schalk W. Human

Philippe Castagliola graduated (PhD 1991) from the UTC (Université de Technologie de CompiÃgne, France). He is currently full professor at the Université de Nantes, Nantes, France, and he is also a member of the LS2N (Laboratoire des Sciences du Numérique de Nantes), UMR CNRS 6004. He is an associate editor for Quality Engineering, Communications in Statistics (LSTA, LSSP, and UCAS), and Quality Technology & Quantitative Management. His research activity includes developments of new statistical process monitoring techniques.