Mixed Seasonal and Subset Fourier Model with Seasonal Harmonics
Science Journal of Applied Mathematics and Statistics
Volume 5, Issue 1, February 2017, Pages: 1-9
Received: Sep. 30, 2016;
Accepted: Oct. 13, 2016;
Published: Jan. 14, 2017
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Iberedem Aniefiok Iwok, Department of Mathematics/Statistics, University of Port-Harcourt, Port Harcourt, Nigeria
Murphy Dooga, Department of Mathematics/Statistics, University of Port-Harcourt, Port Harcourt, Nigeria
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In this work, Box-Jenkins seasonal model was fitted to a temperature series and the assumption of model adequacy was found to be violated. Subset Fourier series with seasonal harmonics was introduced and added to the pure seasonal component that was found to be inadequate. This combination resulted in a mixed seasonal and subset Fourier model with seasonal harmonics. The mixed model was fitted to the data and was subjected to diagnostic checks. The tests revealed that the model was adequate. Comparative study was also carried out and the results showed that the mixed model performed better than the pure seasonal and the subset Fourier model.
Seasonal Model, Fourier Series, Subset Fourier Series, Model Selection, Periodogram and White Noise Process
To cite this article
Iberedem Aniefiok Iwok,
Mixed Seasonal and Subset Fourier Model with Seasonal Harmonics, Science Journal of Applied Mathematics and Statistics.
Vol. 5, No. 1,
2017, pp. 1-9.
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/
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Abdul-Aziz, E., John, P. and Keneth, T. (2013). Modelling and Forecasting Rainfall Pattern in GhanaAs a Seasonal ARIMA Process: The Case of Ashanti Region. International Journal of Humanities and Social Science.Vol 3.No. 3.
Beldjilali, E. P; Bello, K., Ahis, E. and Oge, H. (2016); Prediction of Ozone Concentrations According to the Box-Jenkins Methodology for Assekrem Area. Applied Ecology and Environmental Sciences. Vol. 4, No. 2, 2016 pp48-52. http://pubs.scie.com/aees/4/2/3.
Ekpenyong, E. J; Omekara, C. O. and Akpan, S. J. (2014). Modeling the Nigerian Inflation Rates Using Periodogram and Fourier Series Analysis Methods. The Nigerian case. International journal of African and Asian studies-(vol. 4 2014).
Ekpenyong, E. J and Omekara, C. O (2008). Application of Fourier Series Analysis to Modelling Temperature Data of Uyo Metropolis. Global Journal of Mathematical Sciences, Vol. 7(1), 5-13. ISSN: 1596-6208.
Gurudeo, A. T. and Mahbub, I. (2010). Time series analysis of rainfall and temperature interaction in coastal catchments. Journal of Mathematics and Statistics 6 (3): 372-380, 2010. ISSN: 1549-3644.
Ibrahim, K., Teddy, S. and Yakubu, H. (2011). Modelling of Sokoto Daily Average Temperature: A Fractional Integration Approach. http://www.ajol.info/index.php/njbas/index Nigerian Journal of Basic and Applied Science (2011), 19(1):21- 30 ISSN 0794-5698.
Liu L. M, Hudak, G., Box G. E. P., Muller M. E. and Tiao, G. C. (2014). Short-Term Forecasting of Temperature Driven Electricity Load Using Time Series and Neural Network Model. Journal of Clean Energy Technologies, vol 2, No. 4, pp 327-37, October 2014.
Peter, R. (2005). Time series modelling of global mean temperature for managerial decision-making. Journal of environmental management impact factor: 2.72. DOI: 10.1016/j.jenvman.2005. 01.008. source: pubmed.
Song, T. S., Petre, S. and Randolph, L. M. (2014). Introduction to Spectral Analysis. ISBN: 0-13-258419-0. Prentice Hall Upper saddle River, New Jersey 07458.
Wakaura M. and Ogata Y. (2007); A Time Series Analysis on the seasonality of air temperature anomalies. Meteorol.Appl.14: 425-434(2007). www.interscience.wiley.com. DOI: 10.1002/met.41.