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

References

• Abbas, T., F. Rafique, T. Mahmood, and M. Riaz. 2019b. Efficient phase II monitoring methods for linear profiles under the random effect model. IEEE Access 7:148278–96. doi: 10.1109/ACCESS.2019.2946211.
   Web of Science ®Google Scholar
• Abbas, T., S. A. Abbasi, M. Riaz, and Z. Qian. 2019a. Phase II monitoring of linear profiles with random explanatory variable under Bayesian framework. Computers & Industrial Engineering 127:1115–29. doi: 10.1016/j.cie.2018.12.001.
   Web of Science ®Google Scholar
• Abbasi, S. A., T. Abbas, M. Riaz, and A.-S. Gomaa. 2018. Bayesian monitoring of linear profiles using DEWMA control structures with random X. IEEE Access. 6:78370–85. doi: 10.1109/ACCESS.2018.2885014.
   Web of Science ®Google Scholar
• Al‐Osh, M. A., and A. A. Alzaid. 1987. First‐order integer‐valued autoregressive (InAR(1)) process. Journal of Time Series Analysis 8 (3):261–75. doi: 10.1111/j.1467-9892.1987.tb00438.x.
   Google Scholar
• Alwan, L. C. 1992. Effects of autocorrelation on control chart performance. Communications in Statistics - Theory and Methods 21 (4):1025–49. doi: 10.1080/03610929208830829.
   Web of Science ®Google Scholar
• Alwan, L. C., and H. V. Roberts. 1988. Time series modelling for statistical process control. Journal of Business & Economic Statistics 6 (1):87–95. doi: 10.2307/1391421.
   Web of Science ®Google Scholar
• Aunali, A. S., and D. Venkatesan. 2019. Bayesian approach in control charts techniques. International Journal of Scientific Research. in Mathematical and Statistical Sciences 6 (2):217–21.
   Google Scholar
• Biswas, A., and P. X.-K. Song. 2009. Discrete-valued ARMA processes. Statistics & Probability Letters 79 (17):1884–9. doi: 10.1016/j.spl.2009.05.025.
   Web of Science ®Google Scholar
• Brooks, S. 1998. Markov chain Monte Carlo method and its application. Journal of the Royal Statistical Society: Series D (the Statistician) 47 (1):69–100. doi: 10.1111/1467-9884.00117.
   Google Scholar
• Celano, G., and S. A. Chakraborti. 2021. distribution-free Shewhart-type Mann–Whitney control chart for monitoring finite horizon productions. International Journal of Production Research 59 (20):6069–86. doi: 10.1080/00207543.2020.1802079.
   Web of Science ®Google Scholar
• Ferland, R., A. Latour, and D. Oraichi. 2006. Integer‐valued GARCH processes. Journal of Time Series Analysis 27 (6):923–42. doi: 10.1111/j.1467-9892.2006.00496.x.
   Web of Science ®Google Scholar
• Gadde, S. R., A. K. Fulment, and P. K. Josephat. 2019. Attribute control charts for the Dagum distribution under truncated life tests. Life Cycle Reliability and Safety Engineering 8 (4):329–35. doi: 10.1007/s41872-019-00090-3.
   Google Scholar
• Ibazizen, M., and H. Fellag. 2003. Bayesian estimation of an AR (1) process with exponential white noise. Statistics 37 (5):365–72. doi: 10.1080/0233188031000078042.
   Web of Science ®Google Scholar
• Imran, M., J. Sun, F. S. Zaidi, Z. Abbas, and H. Z. Nazir. 2022. Multivariate cumulative sum control chart for compositional data with known and estimated process parameters. Quality and Reliability Engineering International 38 (5):2691–714. doi: 10.1002/qre.3099.
   Web of Science ®Google Scholar
• Jiang, W., K.-L. Tsui, and W. H. Woodall. 2000. A new SPC monitoring method: The ARMA chart. Technometrics 42 (4):399–410. doi: 10.1080/00401706.2000.10485713.
   Web of Science ®Google Scholar
• Jones, C. L., A. S. G. Abdel‐Salam, and D. A. Mays. 2023. Novel Bayesian CUSUM and EWMA control charts via various loss functions for monitoring processes. Quality and Reliability Engineering International 39 (1):164–89. doi: 10.1002/qre.3229.
   Web of Science ®Google Scholar
• Kim, M. 2015. Cost-sensitive estimation of ARMA models for financial asset return data. Mathematical Problems in Engineering 2015:1–8. doi: 10.1155/2015/232184.
   Web of Science ®Google Scholar
• Knoth, S., and W. Schmid. 2004. Control charts for time series: A review. In Frontiers in statistical quality control, vol. 7, ed. H. J. Lenz and P. T. Wilrich, 210–36. Heidelberg: Physica. doi: 10.1007/978-3-7908-2674-6_14.
   Google Scholar
• Kwiatkowski, D., P. C. B. Phillips, P. Schmidt, and Y. Shin. 1992. Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? Journal of Econometrics 54 (1–3):159–78. doi: 10.1016/0304-4076(92)90104-Y.
   Web of Science ®Google Scholar
• Lange, T. 2011. Tail behavior and OLS estimating in AR-GARCH models. Statistica Sinica 21 (3):1191–200. doi: 10.5705/ss.2009.066.
   Web of Science ®Google Scholar
• Lawrance, A. J. 2013. Exploration graphics for financial time series volatility. Journal of the Royal Statistical Society Series C: Applied Statistics 62 (5):669–86. doi: 10.1111/rssc.12016.
   Web of Science ®Google Scholar
• Lopez, J. H. 1997. The power of the ADF test. Economics Letters 57 (1):5–10. doi: 10.1016/S0165-1765(97)81872-1.
   Web of Science ®Google Scholar
• Luengo, D., L. Martino, M. Bugallo, V. Elvira, and S. Särkkä. 2020. A survey of Monte Carlo methods for parameter estimation. EURASIP Journal on Advances in Signal Processing 2020 (1):1–62. doi: 10.1186/s13634-020-00675-6.
   Web of Science ®Google Scholar
• Mabude, K., J.-C. Malela-Majika, P. Castagliola, and S. C. Shongwe. 2020. Distribution-free mixed GWMA-CUSUM and CUSUM-GWMA Mann-Whitney charts to monitor unknown shifts in the process location. Communication in Statistics- Simulation and Computation 51 (11):6667–90. doi: 10.1080/03610918.2020.1811331.
   Web of Science ®Google Scholar
• Malela-Majika, J.-C., K. Chatterjee, and C. Koukouvinos. 2022b. Univariate and multivariate linear profiles using max-type extended exponentially weighted moving average schemes. IEEE Access. 10:6126–46. doi: 10.1109/ACCESS.2022.3142245.
   Web of Science ®Google Scholar
• Malela-Majika, J.-C., S. Shongwe, K. Chatterjee, and C. Koukouvinos. 2022a. Monitoring univariate and multivariate proles using the triple exponentially weighted moving average scheme with fixed and random explanatory variables. Computers & Industrial Engineering 163:107846. doi: 10.1016/j.cie.2021.107846.
   Web of Science ®Google Scholar
• Maravelakis, P., J. Panaretos, and S. Psarakis. 2002. Effect of estimation of the process parameters on the control limits of the univariate control charts for process dispersion. Communications in Statistics - Simulation and Computation 31 (3):443–61. doi: 10.1081/SAC-120003851.
   Web of Science ®Google Scholar
• McKenzie, E. 1988. Some ARMA models for dependent sequences of Poisson counts. Advances in Applied Probability 20 (4):822–35. doi: 10.2307/1427362.
   Web of Science ®Google Scholar
• Montgomery, D. 2020. Introduction to statistical quality control. 8th ed. Hoboken, NJ: John Wiley & Sons, Inc.
   Google Scholar
• Owlia, M. S., M. H. Doroudyan, A. Amiri, and H. Sadeghi. 2017. The effect of parameter estimation on phase II control chart performance in monitoring financial GARCH processes with contaminated data. Journal of Industrial and Systems Engineering 10:93–108.
   Google Scholar
• Paparoditis, E., and D. N. Politis. 2018. The asymptotic size and power of the augmented Dickey–Fuller test for a unit root. Econometric Reviews 37 (9):955–73. doi: 10.1080/00927872.2016.1178887.
   Web of Science ®Google Scholar
• Sheu, S.-H., and T.-C. Lin. 2003. The generally weighted moving average control chart for detecting small shifts in the process mean. Quality Engineering 16 (2):209–31. doi: 10.1081/QEN-120024009.
   Google Scholar
• Stone, R., and M. Taylor. 1995. Time series models in statistical process control: considerations of applicability. Journal of the Royal Statistical Society Series D: The Statistician, 44 (2):227–34. doi: 10.2307/2348446.
   Google Scholar
• Tan, Z. M., V. H. Wong, and W. Y. Pan. 2022. Control chart for monitoring stock price and trading volume in Malaysia stock market. In Proceedings of the International Conference on Mathematical Sciences and Statistics 2022 (ICMSS 2022). doi: 10.2991/978-94-6463-014-5_27.
   Google Scholar
• Vanli, O. A., R. Giroux, E. E. Ozguven, and J. J. Pignatiello, Jr. 2019. Monitoring of count data time series: Cumulative sum change detection in Poisson integer valued GARCH models. Quality Engineering 31 (3):439–52. doi: 10.1080/08982112.2018.1508696.
   Web of Science ®Google Scholar
• Weiß, C. H., and M. C. Testik. 2012. Detection of abrupt changes in count data time series: Cumulative sum derivations for INARCH (1) models. Journal of Quality Technology 44 (3):249–64. doi: 10.1080/00224065.2012.11917898.
   Web of Science ®Google Scholar
• Woodall, W. H. 1997. Control charts based on attribute data: Bibliography and review. Journal of Quality Technology 29 (2):172–83. doi: 10.1080/00224065.1997.11979748.
   Web of Science ®Google Scholar
• Xu, Y., Q. Li, and F. A. Zhu. 2023. Modified multiplicative thinning-based INARCH model: Properties, saddlepoint maximum likelihood estimation, and application. Entropy 25 (2):207. doi: 10.3390/e25020207.
   PubMed Web of Science ®Google Scholar
• Zhou, Q., and P. Qiu. 2022. Phase I monitoring of serially correlated nonparametric profiles by mixed‐effects modeling. Quality and Reliability Engineering International 38 (1):134–52. doi: 10.1002/qre.2961.
   Web of Science ®Google Scholar