Mixed Seasonal and Subset Fourier Model with Seasonal Harmonics

Iberedem Aniefiok Iwok; Murphy Dooga

doi:doi:10.11648/j.sjams.20170501.11

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Mixed Seasonal and Subset Fourier Model with Seasonal Harmonics

Iberedem Aniefiok Iwok, Murphy Dooga

Published in Science Journal of Applied Mathematics and Statistics (Volume 5, Issue 1)

Received: 30 September 2016 Accepted: 13 October 2016 Published: 14 January 2017

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Abstract

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.

Published in	Science Journal of Applied Mathematics and Statistics (Volume 5, Issue 1)
DOI	10.11648/j.sjams.20170501.11
Page(s)	1-9
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Seasonal Model, Fourier Series, Subset Fourier Series, Model Selection, Periodogram and White Noise Process

References

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[2]	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.
[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).
[4]	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.
[5]	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.
[6]	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.
[7]	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.
[8]	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.
[9]	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.
[10]	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.

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APA Style

Iberedem Aniefiok Iwok, Murphy Dooga. (2017). Mixed Seasonal and Subset Fourier Model with Seasonal Harmonics. Science Journal of Applied Mathematics and Statistics, 5(1), 1-9. https://doi.org/10.11648/j.sjams.20170501.11

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ACS Style

Iberedem Aniefiok Iwok; Murphy Dooga. Mixed Seasonal and Subset Fourier Model with Seasonal Harmonics. Sci. J. Appl. Math. Stat. 2017, 5(1), 1-9. doi: 10.11648/j.sjams.20170501.11

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AMA Style

Iberedem Aniefiok Iwok, Murphy Dooga. Mixed Seasonal and Subset Fourier Model with Seasonal Harmonics. Sci J Appl Math Stat. 2017;5(1):1-9. doi: 10.11648/j.sjams.20170501.11

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@article{10.11648/j.sjams.20170501.11,
  author = {Iberedem Aniefiok Iwok and Murphy Dooga},
  title = {Mixed Seasonal and Subset Fourier Model with Seasonal Harmonics},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {5},
  number = {1},
  pages = {1-9},
  doi = {10.11648/j.sjams.20170501.11},
  url = {https://doi.org/10.11648/j.sjams.20170501.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20170501.11},
  abstract = {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.},
 year = {2017}
}

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TY  - JOUR
T1  - Mixed Seasonal and Subset Fourier Model with Seasonal Harmonics
AU  - Iberedem Aniefiok Iwok
AU  - Murphy Dooga
Y1  - 2017/01/14
PY  - 2017
N1  - https://doi.org/10.11648/j.sjams.20170501.11
DO  - 10.11648/j.sjams.20170501.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 1
EP  - 9
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20170501.11
AB  - 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.
VL  - 5
IS  - 1
ER  -

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Author Information

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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APA Style

Iberedem Aniefiok Iwok, Murphy Dooga. (2017). Mixed Seasonal and Subset Fourier Model with Seasonal Harmonics. Science Journal of Applied Mathematics and Statistics, 5(1), 1-9. https://doi.org/10.11648/j.sjams.20170501.11

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ACS Style

Iberedem Aniefiok Iwok; Murphy Dooga. Mixed Seasonal and Subset Fourier Model with Seasonal Harmonics. Sci. J. Appl. Math. Stat. 2017, 5(1), 1-9. doi: 10.11648/j.sjams.20170501.11

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AMA Style

Iberedem Aniefiok Iwok, Murphy Dooga. Mixed Seasonal and Subset Fourier Model with Seasonal Harmonics. Sci J Appl Math Stat. 2017;5(1):1-9. doi: 10.11648/j.sjams.20170501.11

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@article{10.11648/j.sjams.20170501.11,
  author = {Iberedem Aniefiok Iwok and Murphy Dooga},
  title = {Mixed Seasonal and Subset Fourier Model with Seasonal Harmonics},
  journal = {Science Journal of Applied Mathematics and Statistics},
  volume = {5},
  number = {1},
  pages = {1-9},
  doi = {10.11648/j.sjams.20170501.11},
  url = {https://doi.org/10.11648/j.sjams.20170501.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.sjams.20170501.11},
  abstract = {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.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Mixed Seasonal and Subset Fourier Model with Seasonal Harmonics
AU  - Iberedem Aniefiok Iwok
AU  - Murphy Dooga
Y1  - 2017/01/14
PY  - 2017
N1  - https://doi.org/10.11648/j.sjams.20170501.11
DO  - 10.11648/j.sjams.20170501.11
T2  - Science Journal of Applied Mathematics and Statistics
JF  - Science Journal of Applied Mathematics and Statistics
JO  - Science Journal of Applied Mathematics and Statistics
SP  - 1
EP  - 9
PB  - Science Publishing Group
SN  - 2376-9513
UR  - https://doi.org/10.11648/j.sjams.20170501.11
AB  - 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.
VL  - 5
IS  - 1
ER  -

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