The moving-mean method is one of the conventional approaches for trend-extraction from a data set. It is usually applied in an empirical way. The smoothing degree of the trend depends on the selections of window length and weighted coefficients, which are associated with the change pattern of the data. Are there any uniform criteria for determining them? The present article is a reaction to this fundamental problem. By investigating many kinds of data, the results show that: 1) Within a certain range, the more points which participate in moving-mean, the better the trend function. However, in case the window length is too long, the trend function may tend to the ordinary global mean. 2) For a given window length, what matters is the choice of weighted coefficients. As the five-point case concerned, the local-midpoint, local-mean and global-mean criteria hold. Among these three criteria, the local-mean one has the strongest adaptability, which is suggested for your usage.
References
[1]
Leon-Castro, E., Aviles-Ochoa, E. and Merigo, J.M. (2018) Induced Heavy Moving Averages. International Journal of Intelligent Systems, 33, 1823-1839. https://doi.org/10.1002/int.21916
[2]
Huang, K.M. (2006) Research on the Parameters of Sliding Averaging for Digital Filtering. Journal of Jimei University (Natural Science), 4, 381-384. (In Chinese)
[3]
Abujiya, M.R., Lee, M.H. and Riaz, M. (2014) Improving the Performance of Exponentially Weighted Moving Average Control Charts. Quality & Reliability Engineering International, 4, 571-590. https://doi.org/10.1002/qre.1509
[4]
Sun, H.X. (2007) Stochastic Processes. China Machine Press, Beijing. (In Chinese)
[5]
Zhu, S.H. and You, C.X. (2013) A Modified Average Filtering Algorithm. Computer Applications and Software, 12, 97-99. (In Chinese)
[6]
Wang, J.L. and Li, Z.J. (2013) Extreme-Point Symmetric Mode Decomposition Method for Data Analysis. Advances in Adaptive Data Analysis, 5, Article ID: 1350015. https://doi.org/10.1142/S1793536913500155 http://arxiv.org/abs/1303.6540
[7]
Wang, J.L. and Li, Z.J. (2015) Extreme-Point Symmetric Mode Decomposition Method: A New Approach for Data Analysis and Science Exploration. Higher Education Press, Beijing. (In Chinese)
[8]
Smith, J.S. (2005) The Local Mean Decomposition and Its Application to EEG Perception Data. Journal of the Royal Society Interface, 2, 443-454. https://doi.org/10.1098/rsif.2005.0058
[9]
Jiang, S. and Wang, J.L. (2018) Improvement of ESMD Algorithm for Asymmetric Data. Advances in Applied Mathematics, 7, 1500-1505. (In Chinese) https://doi.org/10.12677/AAM.2018.712174
