Average Power Function of Noise and Its Applications in Seasonal Time Series Modeling and Forecasting

DOI: 10.4236/ajor.2011.14034   PDF   HTML     6,230 Downloads   9,432 Views   Citations


This paper presents a new method of detecting multi-periodicities in a seasonal time series. Conventional methods such as the average power spectrum or the autocorrelation function plot have been used in detecting multiple periodicities. However, there are numerous cases where those methods either fail, or lead to incorrectly detected periods. This, in turn in applications, produces improper models and results in larger forecasting errors. There is a strong need for a new approach to detecting multi-periodicities. This paper tends to fill this gap by proposing a new method which relies on a mathematical instrument, called the Average Power Function of Noise (APFN) of a time series. APFN has a prominent property that it has a strict local minimum at each period of the time series. This characteristic helps one in detecting periods in time series. Unlike the power spectrum method where it is assumed that the time series is composed of sinusoidal functions of different frequencies, in APFN it is assumed that the time series is periodic, the unique and a much weaker assumption. Therefore, this new instrument is expected to be more powerful in multi-periodicity detection than both the autocorrelation function plot and the average power spectrum. Properties of APFN and applications of the new method in periodicity detection and in forecasting are presented.

Share and Cite:

Q. Song, "Average Power Function of Noise and Its Applications in Seasonal Time Series Modeling and Forecasting," American Journal of Operations Research, Vol. 1 No. 4, 2011, pp. 293-304. doi: 10.4236/ajor.2011.14034.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] P. Cortez, M. Rio, M. Rocha and P. Sousa, “Internet Traffic Forecasting Using Neural Networks,” 2006 International Joint Conference on Neural Networks, Vancouver, 16-21 July 2006, pp. 2635-2642.
[2] A. M. De Livera and R. J. Hyndman, “Forecasting Time Series with Complex Seasonal Patterns Using Exponential Smoothing,” Working Paper, Department of Econometrics and Business Statistics, Monash University, 2009.
[3] P. G. Gould, A. B. Koehler, J. K. Ord, R. D. Snyder, R. J. Hyndman and F. Vahid-Araghi, “Forecasting Time Series with Multiple Seasonal Patterns,” European Journal of Operational Research, Vol. 191, No. 1, 2008, pp. 207- 222. doi:10.1016/j.ejor.2007.08.024
[4] B. J. Morzuch and P. G. Allen, “Forecasting Hospital Emergency Department Arrivals,” 26th Annual Symposium on Forecasting, Santander, June 11-14 2006.
[5] J. W. Taylor, “A Comparison of Univariate Time Series Methods for Forecasting Intraday Arrivals at a Call Center,” Management Science, Vol. 54, No. 2, 2008, pp. 253- 265. doi:10.1287/mnsc.1070.0786
[6] J. W. Taylor, L. M. de Menezes and P. E. McSharry, “A Comparison of Univariate Methods for Forecasting Electricity Demand up to a Day Ahead,” International Journal of Forecasting, Vol. 22, No. 1, 2006, pp. 1-16. doi:10.1016/j.ijforecast.2005.06.006
[7] J. W. Taylor, “Short-Term Electricity Demand Forecasting Using Double Seasonal Exponential Smoothing,” Journal of Operational Research Society, Vol. 54, No. 8, 2003, pp. 799-805. doi:10.1057/palgrave.jors.2601589
[8] J. W. Taylor, “Triple Seasonal Methods for Short-Term Electricity Demand Forecasting,” European Journal of Operational Research, Vol. 204, No. 1, 2010, pp. 139- 152. doi:10.1016/j.ejor.2009.10.003
[9] G. E. P. Box, G. M. Jenkins, and G. C. Reinsel, “Time Series Analysis,” 3rd Edition, Prentice Hall, New Jersey, 1994.
[10] D. Pena, G. C. Tiao and R. S. Tsay, “A Course in Time Series Analysis,” John Wiley & Sons, Hoboken, 2001.
[11] P. Stoica and R. Moses, “Spectral Analysis of Signals,” Pearson Prentice Hall, New Jersey, 2005.
[12] Q. Song and A. O. Esogbue, “A New Algorithm for Automated Modeling of Seasonal Time Series Using Box-Jenkins Techniques,” International Journal of Industrial Engineering and Management Systems, Vol. 7, No.1, 2008, pp. 9-22.

comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.