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Gibbs Sampling for Double Seasonal Autoregressive Models

  • Amin, Ayman A. (Department of Mathematics, Statistics and Insurance, Munofia University) ;
  • Ismail, Mohamed A. (Department of Statistics, Faculty of Economics and Political Science, Cairo University)
  • Received : 2015.01.29
  • Accepted : 2015.09.23
  • Published : 2015.11.30

Abstract

In this paper we develop a Bayesian inference for a multiplicative double seasonal autoregressive (DSAR) model by implementing a fast, easy and accurate Gibbs sampling algorithm. We apply the Gibbs sampling to approximate empirically the marginal posterior distributions after showing that the conditional posterior distribution of the model parameters and the variance are multivariate normal and inverse gamma, respectively. The proposed Bayesian methodology is illustrated using simulated examples and real-world time series data.

Keywords

References

  1. Au, T., Ma, G. Q. and Yeung, S. N. (2011). Automatic Forecasting of Double Seasonal Time Series with Applications on Mobility Network Traffic Prediction. 2011 Joint Statistical Meetings, July 30-August4, Miami Beach, Florida, USA.
  2. Baek, M. (2010). Forecasting hourly electricity loads of South Korea: Innovations state space modeling approach, The Korean Journal of Economics, 17, 301-317.
  3. Box, G. E. P., Jenkins, G. M. and Reinsel, G. C. (1994). Time Series Analysis: Forecasting and Control, 3rd ed, Prentice-Hall, NJ.
  4. Caiado, J. (2008). Forecasting Water Consumption in Spain Using Univariate Time Series Models, MPRA Paper No. 6610.
  5. Cortez, P., Rio, M., Rocha, M. and Sousa, P. (2012). Multi-scale internet traffic forecasting using neural networks and time series methods, Expert Systems, 29, 143-155.
  6. Cruz, A., Munoz, A., Zamora, J. L. and Espinola, R. (2011). The effect of wind generation and weekday on Spanish electricity spot price forecasting, Electric Power Systems Research, 81, 1924-1935. https://doi.org/10.1016/j.epsr.2011.06.002
  7. Feinberg, E. and Genethliou, D. (2005). Load Forecasting, In F. W. J. Chow, Applied Mathematics for Restructured Electric Power Systems: Control and Computational Intelligence (269-285). Springer.
  8. Geweke, J. (1992). Evaluating the Accuracy of Sampling-Based Approaches to the Calculations of Posterior Moments. In Bayesian Statistics 4, J. M., Bernardo, J. O., Berger, A. P., Dawid, and A. F. M., Smith, (eds), 641-649. Oxford, Clarendon Press.
  9. Ismail, M. A. (2003a). Bayesian analysis of seasonal autoregressive models, Journal of Applied Statistical Science, 12, 123-136.
  10. Ismail, M. A. (2003b). Bayesian analysis of seasonal moving average model: A Gibbs sampling approach, Japanese Journal of Applied Statistics, 32, 61-75. https://doi.org/10.5023/jappstat.32.61
  11. Ismail, M. A. and Amin, A. A. (2010). Gibbs Sampling for SARMA Models, Working paper #7-2010, IDSC, Egyptian Cabinet.
  12. Ismail, M. A. and Zahran, A. R. (2014). Bayesian inference on double seasonal autoregressive models, Journal of Applied Statistical Science, 12, 123-136.
  13. Kim, M. S. (2013). Modeling special-day effects for forecasting intraday electricity demand, European Journal of Operational Research, 230, 170-180. https://doi.org/10.1016/j.ejor.2013.03.039
  14. Korisha, S. and Pukkila, T. (1990). Linear methods for estimating ARMA and regression model with serial correlation, Communications in Statistics: Simulation, 19, 71-102. https://doi.org/10.1080/03610919008812846
  15. LeSage, J. P. (1999). Applied Econometrics using MATLAB, Department of Economics, University of Toledo, available at http://www.econ.utoledo.edu.
  16. Mohamed, N., Ahmad, M. H., Ismail, Z. and Suhartono (2010). Double seasonal ARIMA model for forecasting load demand, Matematika, 26, 217-231.
  17. Mohamed, N., Ahmad, M. H. and Suhartono (2011). Forecasting short term load demand using double seasonal ARIMA model, World Applied Sciences Journal, 13, 27-35.
  18. Raftrey, A. E. and Lewis, S. (1992). One long run with diagnostics: Implementation strategies for Markov Chain Monte Carlo, Statistical Science, 7, 493-497. https://doi.org/10.1214/ss/1177011143
  19. Raftrey, A. E. and Lewis, S. (1995). The number of iterations, convergence diagnostics and generic Metropolis algorithms. In Practical Markov Chain Monte Carlo, W. R., Gilks, D. J., Spiegelhalter and S., Richardson, (eds). London, Chapman and Hall.
  20. Shaarawy, S. and Ismail, M. A. (1987). Bayesian inference for seasonal ARMA models, The Egyptian Statistical Journal, 31, 323-336.
  21. Taylor, J. W. (2003). Short-term electricity demand forecasting using double seasonal exponential smoothing, The Journal of the Operational Research Society, 54, 799-805. https://doi.org/10.1057/palgrave.jors.2601589
  22. Taylor, J. W., de Menezes, L. M. and McSharry, P. A. (2006). Comparison of univariate methods for forecasting electricity demand up to a day ahead, International Journal of Forecasting, 22, 1-6. https://doi.org/10.1016/j.ijforecast.2005.06.006
  23. 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, 645-658. https://doi.org/10.1016/j.ijforecast.2008.07.007
  24. Taylor, J.W. (2008b). A comparison of univariate time series methods for forecasting intraday arrivals at a call center, Management Science, 54, 253-265. https://doi.org/10.1287/mnsc.1070.0786
  25. Thompson, H. E. and Tiao, G. C. (1971). Analysis of telephone data, The Bell Journal of Economics and Management Science, 2, 514-541.

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  1. Bayesian inference for double SARMA models pp.1532-415X, 2018, https://doi.org/10.1080/03610926.2017.1390132
  2. Bayesian identification of double seasonal autoregressive time series models pp.1532-4141, 2018, https://doi.org/10.1080/03610918.2018.1458130