Abstract
An original approach to digital moving trend based filters (MTF) design, based on Bode plots analysis is proposed, aimed at seasonal time series decomposition and prediction [5]. A number of polynomials of different range are discussed to be used in the MTF as the LS approximation formula. The Bode plots of the MTF are shown, and the best filter is selected. Results of a seasonal time series decomposition and prediction with the best MTF is presented and compared to the classical MTF calculations (involving the linear LS approximation). The MTF enhancementsareintroduced aimed at better change detection. Efficiency of low-frequency periodic signals reconstruction and step-wise changes is illustrated.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Askom, M.V., Chenouri, S., Mahmoodabadi, A.K.: ARCH and GARCH models. Department of Statistics and Actuarial Sciences, University of Waterloo, Waterloo (2001)
Box, G.E.P., Jenkins, G.M., Reinsnel, G.C.: Time Series Analysis, Forecasting and Control, 3rd edn. Prentice Hall, Englewood Cliffs (1994)
Cieślak, M. (Edt.): Economic Forecasting. Principles and practice. Polish Scientific Publishers PWN, Warsaw (2002)
Duda, J.T., Pelech-Pilichowski, T.: Enhancements of moving trend based filters aimed at time series prediction. Advances in systems science. Springer International Publishing, New York (2014)
Duda, J.T., Pelech-Pilichowski, T.: Moving trend based filters design in frequency domain. Federated Conference on Computer Science and Information Systems, 8–11 September, 2013, Kraków, Poland
Duda, J.T., Pelech-Pilichowski, T.: Opracowywanie prognoz sytuacji hydrogeologicznej i ostrzeżeń przed niebezpiecznymi zjawiskami zachodza̧cymi w strefach zasilania lub poboru wód podziemnych. Research Report, AGH University of Science and Technology, Faculty of Management, Kraków (2012)
Duda. J.T., Pelech-Pilichowski, T., Augustynek A.: Application of moving trend to analysis and prediction of financial time series. In: Howaniec, H., Waszkielewicz, W. (eds.) Determinants, metods and strategies of development of enterprises, ATHBielsko-Biała Publ., Poland (2013)
Hamilton, J.: Time Series Analysis. Princeton University Press, New Jersey (1994)
Oppenheim, A.V., Schafer R.W.: Digital Signal Processing. Prentice Hall (1975)
Otnes, R.K., Enochson, L.: Digital Time Series Analysis. Wiley, New York (1972)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Pełech-Pilichowski, T., Duda, J.T. (2015). Low-Frequency Signal Reconstruction and Abrupt Change Detection in Non-stationary Time Series by Enhanced Moving Trend Based Filters. In: Mach-Król, M., M. Olszak, C., Pełech-Pilichowski, T. (eds) Advances in ICT for Business, Industry and Public Sector. Studies in Computational Intelligence, vol 579. Springer, Cham. https://doi.org/10.1007/978-3-319-11328-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-319-11328-9_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-11327-2
Online ISBN: 978-3-319-11328-9
eBook Packages: EngineeringEngineering (R0)