Simple Exponential Smoothing and Its Control Parameter: A Reassessment

  • Dipta Chaudhuri
  • Moloy Mukherjee
  • Mofazzal H. KhondekarEmail author
  • Koushik Ghosh
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 922)


Simple exponential smoothing (SES) is a popular form of smoothing which can be regarded as a recursive system with infinite impulse response (IIR). As a consequence, it suffers heavily from the threat of instability and phase nonlinearity. Here an effort has been made to get a finite impulse response (FIR) estimation of the SES to acquire the benefits of an optimal speed and computational efficiency in addition to the usual advantages like stability and phase linearity. The optimal order of the filter, its corresponding transfer function, has been worked out, and the frequency response has been estimated for this FIR form of the SES. The frequency response has been compared with the actual IIR form of the SES. In addition to this an effort has been made to get a suitable estimation of the control parameter also called smoothing constant (α) in order to have an effective smoothing taking the cut-off frequency, computational limitation of the transfer function, minimum MSE, SNR improvement and suitable window function realisation of the FIR form of SES into consideration. A magnitude of 0.5615 is found to the most suitable value of the control parameter.


Infinite impulse response (IIR) Finite impulse response (FIR) Simple exponential smoothing (SES) Smoothing constant 


  1. 1.
    Chatfield C, Koehler A, Ord K (2001) A new look at models for exponential smoothing. Stat 50 (Part 2):147–159Google Scholar
  2. 2.
    Gardner E (1985) Exponential smoothing: the state of the art. J Forecast 1–28Google Scholar
  3. 3.
    Gardner E (2006) Exponential smoothing: the state of the art–Part II. Int J Forecast 22:637–666CrossRefGoogle Scholar
  4. 4.
    Hyndman R, Koehler A, Ord J, Snyder R (2008) Forecasting with exponential smoothing: the state space approach. Springer, Berlin HeidelbergCrossRefGoogle Scholar
  5. 5.
    Brown RG (1959) Statistical forecasting for inventory. McGraw-Hill, New YorkzbMATHGoogle Scholar
  6. 6.
    Holt CC (1957) Forecasting trends and seasonals by exponentially. O.N.R. Memorandum, p 52Google Scholar
  7. 7.
    Ge SY, Zheng CJ, Hou MM (2013) Forecast of bus passenger traffic based on exponential smoothing and trend moving average method. Appl Mech Mater 1374:433–435Google Scholar
  8. 8.
    Lai KK, Yu L, Wang S, Huang W (2006) Hybridizing exponential smoothing and neural network for financial time series predication. In Lecture notes in computer science 3994, pp 493–500Google Scholar
  9. 9.
    Chusyairi A, Ramadar NSP, Bagio (2017) The use of exponential smoothing method to predict missing service e-report. In: 2nd international conferences on information technology, information systems and electrical engineering (ICITISEE), Yogyakarta, IndonesiaGoogle Scholar
  10. 10.
    Rahamneh A (2017) Using single and double exponential smoothing for estimating the number of injuries and fatalities resulted from traffic accidents in Jordan (1981–2016). Middle-East J Sci Res 25(7):1544–1552Google Scholar
  11. 11.
    Ray S, Ray R, Khondekar M, Ghosh K (2018) Scaling analysis and model estimation of solar Corona index. Adv Space Res 61(8):2214–2226CrossRefGoogle Scholar
  12. 12.
    Sarkar T, Ray R, Khondekar M, Banerjee S (2015) Periodicity and chaos of solar wind speed: cycle 23. Astrophys Space Sci 357(2):128CrossRefGoogle Scholar
  13. 13.
    Ray R, Khondekar M, Ghosh K, Bhattacharjee AK (2016) Memory persistency and nonlinearity in daily mean dew point across India. Theoret Appl Climatol 124(1–2):119–128CrossRefGoogle Scholar
  14. 14.
    Kalekar PS (2004) Time series forecasting using holt-wintersGoogle Scholar
  15. 15.
    Roberts S (1959) Control chart tests based on geometric moving average. Technometrics 42(1):97–101CrossRefGoogle Scholar
  16. 16.
    Romer M (2016) Smoothing time series: PennState Eberly college of science (Online). Available: Accessed 20 Dec 2016
  17. 17.
    Hunter J (1986) The exponentially weighted moving average. J Qual Technol 18(4):203–210CrossRefGoogle Scholar
  18. 18.
    Paul SK (2011) Determination of exponential smoothing constant to minimize mean square error and mean absolute deviation. Global J Res Eng 11(3)Google Scholar
  19. 19.
    Dalrymple D (1987) Sales forecasting practices: results from a United States Survey. Int J Forecast 3(3–4):379–391CrossRefGoogle Scholar
  20. 20.
    Winklhofer H, Diamantopoulos A, Witt S (1996) Forecasting practice: a review of the empirical literature and an agent for future research. Int J Forecast 12(2):193–221CrossRefGoogle Scholar
  21. 21.
    Dwivedi S, Shrivastav P (2015) Survey paper on digital IIR filter using evolutionary algorithms. Int J Innov Res Comput Commun Eng 5106–5111Google Scholar
  22. 22.
    Yapar G, Yavuz I, Selamlar HT (2017) Why and how does exponential smoothing fail? An in depth comparison of ATA-simple and simple exponential smoothing. Turk J Forecast 01(1):30–39Google Scholar
  23. 23.
    Sahu P, Kumar R (2013) Survey of demand fluctuation of dairy products at Raipur Dugdh Sangh, Chhattisgarh, India for selection of appropriate forecasting. Uncertain Supply Chain Management. Uncertain Supply Chain Manag 1(3):133–144Google Scholar
  24. 24.
    Kumar R, Sahu PK (2013) Demand forecasting for sales of milk product (Paneer) in Chhattisgarh. Int J Inventive Eng Sci (IJIES) 1(9):10–13Google Scholar
  25. 25.
    Ravinder HV (2013) Determining the optimal values of exponential smoothing constants—does solver really work? Am J Bus Educ 1(3):347–360Google Scholar
  26. 26.
    Engineering Statistics Handbook (Online). Available:
  27. 27.
    Booranawong T, Booranawong A (2017) Simple and double exponential smoothing methods with designed input data for forecasting a seasonal time series: in an application for lime prices in Thailand. Suranaree J Sci Technol 24(3):301–310Google Scholar
  28. 28.
    Valkenburg MV (2014) Network analysis, 3rd edn. PHI Learning, pp 383–384Google Scholar
  29. 29.
    Das N, Chakraborty M (2017) Performance analysis of FIR and IIR filters for ECG signal denoising based on SNR. In: 2017 Third international conference on research in computational intelligence and communication networks (ICRCICN), KolkataGoogle Scholar
  30. 30.
    Huang X, Jing S, Wang Z, Xu Y, Zheng Y (2016) Closed-form FIR filter design based on convolution window spectrum interpolation. IEEE Trans Sig Process 64(5):1173–1186MathSciNetzbMATHGoogle Scholar
  31. 31.
    Loganathan M, Deepa D (2018) Performance analysis of FIR filter design for secure applications-a review. Int J Adv Inf Eng Technol 5(3):11–23Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Dipta Chaudhuri
    • 1
  • Moloy Mukherjee
    • 1
  • Mofazzal H. Khondekar
    • 2
    Email author
  • Koushik Ghosh
    • 3
  1. 1.Department of Electronics and Communication EngineeringDr. B.C. Roy Engineering CollegeDurgapurIndia
  2. 2.Department of Applied Electronics and Instrumentation EngineeringDr. B. C. Roy Engineering CollegeDurgapurIndia
  3. 3.Department of MathematicsUniversity Institute of Technology, University of BurdwanBurdwanIndia

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