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Articles

Gibbs sampling for Bayesian estimation of triple seasonal autoregressive models

Pages 7303-7322 | Received 21 Sep 2021, Accepted 12 Feb 2022, Published online: 25 Feb 2022

References

  • Amin, A. 2009. Bayesian inference for seasonal ARMA models: A Gibbs sampling approach. Master’s thesis, Statistics Department, Faculty of Economics and Political Science, Cairo University.
  • Amin, A. 2017a. Gibbs sampling for double seasonal ARMA models. In Proceedings of of the 29th Annual International Conference on Statistics and Computer Modeling in Human and Social Sciences, Egypt.
  • Amin, A. 2017c. Identification of double seasonal autoregressive models: A Bayesian approach. In Proceedings of the 52nd Annual International Conference of Statistics, Computer Science and Operations Research, Egypt.
  • Amin, A., and M. Ismail. 2015b. Gibbs sampling for double seasonal moving average models. In Proceedings of of the 60th ISI World Statistics Congress (WSC), Rio de Janeiro, Brazil.
  • Amin, A. 2017b. Bayesian inference for double seasonal moving average models: A Gibbs sampling approach. Pakistan Journal of Statistics and Operation Research 13 (3):483–99. doi:10.18187/pjsor.v13i3.1647.
  • Amin, A. 2017d. Sensitivity to prior specification in Bayesian identification of autoregressive time series models. Pakistan Journal of Statistics and Operation Research 13 (4):699–713. doi:10.18187/pjsor.v13i4.1498.
  • Amin, A. 2018a. Bayesian identification of double seasonal autoregressive time series models. Communications in Statistics: Simulation and Computation 48 (8):2501–11. doi:10.1080/03610918.2018.1458130.
  • Amin, A. 2018b. Bayesian inference for double SARMA models. Communications in Statistics - Theory and Methods 47 (21):5333–45. doi:10.1080/03610926.2017.1390132.
  • Amin, A. 2019a. Gibbs sampling for Bayesian prediction of SARMA processes. Pakistan Journal of Statistics and Operation Research 15 (2):397–418. doi:10.18187/pjsor.v15i2.2174.
  • Amin, A. A. 2019b. Kullback-Leibler divergence to evaluate posterior sensitivity to different priors for autoregressive time series models. Communications in Statistics - Simulation and Computation 48 (5):1277–91. doi:10.1080/03610918.2017.1410709.
  • Amin, A. A. 2020. Bayesian analysis of double seasonal autoregressive models. Sankhya B 82 (2):328–52. doi:10.1007/s13571-019-00192-z.
  • Amin, A., and M. Ismail. 2015a. Gibbs sampling for double seasonal autoregressive models. Communications for Statistical Applications and Methods 22 (6):557–73. doi:10.5351/CSAM.2015.22.6.557.
  • Barnett, G., R. Kohn, and S. Sheather. 1996. Bayesian estimation of an autoregressive model using Markov Chain Monte Carlo. Journal of Econometrics 74 (2):237–54. doi:10.1016/0304-4076(95)01744-5.
  • Box, G., G. Jenkins, G. Reinsel, and G. Ljung. 2016. Time series analysis, Forecasting and control. Hoboken, New Jersey: John Wiley & Sons.
  • Broemeling, L. D. 1985. Bayesian analysis of linear models. New York: CRC Press.
  • Broemeling, L. D., and S. Shaarawy. 1984. Bayesian inferences and forecasts with moving average processes. Communications in Statistics: Theory and Methods 13:1871–88.
  • De Livera, A. M., R. J. Hyndman, and R. D. Snyder. 2011. Forecasting time series with complex seasonal patterns using exponential smoothing. Journal of the American Statistical Association 106 (496):1513–27. doi:10.1198/jasa.2011.tm09771.
  • Deb, C., F. Zhang, J. Yang, S. E. Lee, and K. W. Shah. 2017. A review on time series forecasting techniques for building energy consumption. Renewable and Sustainable Energy Reviews 74:902–24. doi:10.1016/j.rser.2017.02.085.
  • Dumas, J., and B. Cornélusse. 2018. Classification of load forecasting studies by forecasting problem to select load forecasting techniques and methodologies. arXiv Preprint arXiv:1901.05052
  • Geweke, J. 1992. Evaluating the accuracy of sampling-based approaches to the calculations of posterior moments. In Bayesian statistics, Vol. 4, ed. J. M., Bernardo, J. O. Berger, A. P. Dawid, and A. F. M. Smith, 641–9. Oxford: Clarendon Press.
  • Hoff, P. D. 2009. A first course in Bayesian statistical methods. New York: Springer.
  • Hyndman, R. J., and G. Athanasopoulos. 2018. Forecasting: Principles and practice. Melbourne, Australia: OTexts.
  • Ismail, M. A., and A. A. Amin. 2014. Gibbs sampling for SARMA models. Pakistan Journal of Statistics 30 (2):153–68.
  • Lago, J., F. De Ridder, and B. De Schutter. 2018. Forecasting spot electricity prices: Deep learning approaches and empirical comparison of traditional algorithms. Applied Energy 221:386–405. doi:10.1016/j.apenergy.2018.02.069.
  • Raftrey, A. E., and S. Lewis. 1995. The number of iterations, convergence diagnostics and generic Metropolis algorithms. In Practical Markov Chain Monte Carlo, ed. W. R. Gilks, D. J. Spiegelhalter, and S. Richardson. London: Chapman and Hall.
  • Ryu, S., J. Noh, and H. Kim. 2016. Deep neural network based demand side short term load forecasting. Energies 10 (1):3–20. doi:10.3390/en10010003.
  • Shaarawy, S., and S. Ali. 2003. Bayesian identification of seasonal autoregressive models. Communications in Statistics - Theory and Methods 32 (5):1067–84. doi:10.1081/STA-120019963.
  • Taylor, J. W. 2008a. An evaluation of methods for very short-term load forecasting using minute-by-minute British data. International Journal of Forecasting 24 (4):645–58. doi:10.1016/j.ijforecast.2008.07.007.
  • Taylor, J. W. 2008b. A comparison of univariate time series methods for forecasting intraday arrivals at a call center. Management Science 54 (2):253–65. doi:10.1287/mnsc.1070.0786.
  • Taylor, J. W. 2010a. Triple seasonal methods for short-term electricity demand forecasting. European Journal of Operational Research 204 (1):139–52. doi:10.1016/j.ejor.2009.10.003.
  • Taylor, J. W. 2010b. Exponentially weighted methods for forecasting intraday time series with multiple seasonal cycles. International Journal of Forecasting 26 (4):627–46. doi:10.1016/j.ijforecast.2010.02.009.
  • Taylor, J. W., and R. D. Snyder. 2012. Forecasting intraday time series with multiple seasonal cycles using parsimonious seasonal exponential smoothing. Omega 40 (6):748–57. doi:10.1016/j.omega.2010.03.004.
  • Taylor, J. W., P. E. McSharry, and M. E. El-Hawary. 2017. Univariate methods for short-term load forecasting. In Advances in electric power and energy systems: Load and price forecasting, ed. M. E. El-Hawary. 17–39. Hoboken, New Jersey: John Wiley & Sons.
  • Vermaak, J., M. Niranjan, and S. J. Godsill. 1998. Markov chain Monte Carlo estimation for the seasonal autoregressive process with application to pitch modelling. Cambridge: Department of Engineering, University of Cambridge.

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