Bayesian Analysis of Double Seasonal Autoregressive Models
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In this paper we use the Gibbs sampling algorithm to present a Bayesian analysis to multiplicative double seasonal autoregressive (DSAR) models, considering both estimation and prediction problems. Assuming the model errors are normally distributed and using natural conjugate and g priors on the initial values and model parameters, we show that the conditional posterior distributions of the model parameters and variance are multivariate normal and inverse gamma respectively, and the conditional predictive distribution of the future observations is a multivariate normal. Using these closed-form conditional posterior and predictive distributions, we apply the Gibbs sampling to approximate empirically the marginal posterior and predictive distributions, enabling us easily to carry out multiple-step ahead predictions. The proposed Bayesian method is evaluated using simulation study and real-world time series dataset.
Keywords and phrasesMultiplicative seasonal autoregressive Multiple seasonality Posterior analysis Predictive analysis MCMC methods Gibbs sampler Internet traffic data
AMS (2000) subject classificationPrimary 37M10 Secondary 62F15
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- 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, Egypt.Google Scholar
- Amin, A. (2017a). Bayesian Inference for Double SARMA Models. Communications in Statistics: Theory and Methods. https://doi.org/10.1080/03610926.2017.1390132.
- Amin, A. (2017c). 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.Google Scholar
- Amin, A. (2017d). 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.Google Scholar
- Amin, A. (2018a). Bayesian Identification of Double Seasonal Autoregressive Time Series Models. Communications in Statistics: Simulation and Computation, https://doi.org/10.1080/03610918.2018.1458130.
- Amin, A. (2018b). Kullback-Leibler Divergence to Evaluate Posterior Sensitivity to Different Priors for Autoregressive Time Series Models. Communications in Statistics: Simulation and Computation, https://doi.org/10.1080/03610918.2017.1410709.
- Au, T., Ma, G. and Yeung, S. (2011). Automatic Forecasting of Double Seasonal Time Series with Applications on Mobility Network Traffic Prediction. Joint Statistical Meetings, Florida, USA.Google Scholar
- Baek, M. (2010). Forecasting hourly electricity loads of South Korea: Innovations state space modeling approach. The Korean Journal of Economics 17, 2, 301–317.Google Scholar
- Broemeling, L.D. (1985). Bayesian analysis of linear models. CRC Press.Google Scholar
- Broemeling, L.D. and Shaarawy, S. (1988). Time series: a bayesian analysis in time domain. Marcel Dekker, New York, spall, J. (ed.),.Google Scholar
- Cortez, P., Rio, M., Rocha, M. and Sousa, P. (2012). Multi-scale internet traffic forecasting using neural networks and time series methods. Expert. Syst. 29, 2, 143–155.Google Scholar
- Geweke, J. (1992). Evaluating the accuracy of sampling-based approaches to the calculations of posterior moments. Clarendon Press, Oxford, Bernardo, J. M., Berger, J. O., Dawid, A. P. and Smith, A. F. M. (eds.),.Google Scholar
- Laing, W. and Smith, D. (1987). A comparison of time series forecasting methods for predicting the CEGB demand. In: Proceedings of the Ninth Power Systems Computation Conference.Google Scholar
- Mohamed, N., Ahmad, M. and Suhartono, S. (2011). Forecasting short term demand using double seasonal ARIMA model. World Appl. Sci. J. 13, 27–35.Google Scholar
- Raftrey, A.E. and Lewis, S. (1995). The number of iterations, convergence diagnostics and generic metropolis algorithms. Chapman and Hall, London, Gilks, W. R., Spiegelhalter, D. J. and Richardson, S. (eds.),.Google Scholar