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Smooth

In: ITSM: An Interactive Time Series Modelling Package for the PC

Author

Listed:
  • Peter J. Brockwell

    (Colorado State University, Department of Statistics)

  • Richard A. Davis

    (Colorado State University, Department of Statistics)

  • R. J. Hyndman

Abstract

To run the program SMOOTH, type SMOOTH↩. After entering the appropriate graphics code number you will be asked to specify the file name of the input series, {X t , t = 1,…, n}, which is to be smoothed. The program allows you to compute, plot and file the values of the smoothed series, $$\{ {\hat m_t},t = 1,...,n\}$$ which can be specified either as a symmetric moving average, $${\hat m_t} = \mathop \sum \limits_{j = - q}^q a(j){X_{t - j}},t = 1,...,n$$ where X t := X1 for t n, or a one-sided exponentially weighted moving average defined by the recursions, $${\hat m_1} = {X_1}$$ and $${\hat m_t} = a{X_t} + (1 - a){\hat m_{t - 1}},t = 2,...,n$$ where a is a specified smoothing constant (0 ≤ a ≤ 1).

Suggested Citation

  • Peter J. Brockwell & Richard A. Davis & R. J. Hyndman, 1991. "Smooth," Springer Books, in: ITSM: An Interactive Time Series Modelling Package for the PC, chapter 3, pages 57-60, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-3116-5_3
    DOI: 10.1007/978-1-4612-3116-5_3
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