Tomáš Cipra (1989)
Aplikace matematiky
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The paper deals with some practical problems connected with the classical exponential smoothing in time series. The fundamental theorem of the exponential smoothing is extended to the case with missing observations and an interpolation procedure in the framework of the exponential smoothing is described. A simple method of the exponential smoothing for multivariate time series is suggested.
Tomás Cipra, Asunción Rubio, José Trujillo (1991)
Extracta Mathematicae
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The recursive methods are popular in time series analysis since they are computationally efficient and flexible enough to treat various changes in character of data. This paper gives a survey of the most important type of these methods including their classification and relationships existing among them. Special attention is devoted to i) robustification of some recursive methods, capable of facing outliers in time series, and ii) modifications of recursive methods for time series with...
Tomáš Ratinger (1996)
Applications of Mathematics
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Popular exponential smoothing methods dealt originally only with equally spaced observations. When time series contains gaps, smoothing constants have to be adjusted. Cipra et al., following Wright’s approach of irregularly spaced observations, have suggested ad hoc modification of smoothing constants for the Holt-Winters smoothing method. In this article the fact that the underlying model of the Holt-Winters method is a certain seasonal ARIMA is used. Minimum mean square error smoothing...
T. G. McLaughlin (1972)
Compositio Mathematica
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Włodzimierz Greblicki (2001)
International Journal of Applied Mathematics and Computer Science
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A Wiener system, i.e. a cascade system consisting of a linear dynamic subsystem and a nonlinear memoryless subsystem is identified. The a priori information is nonparametric, i.e. neither the functional form of the nonlinear characteristic nor the order of the dynamic part are known. Both the input signal and the disturbance are Gaussian white random processes. Recursive algorithms to estimate the nonlinear characteristic are proposed and their convergence is shown. Results of numerical...
Christophe Croux, Sarah Gelper, Roland Fried (2008)
Applications of Mathematics
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To obtain a robust version of exponential and Holt-Winters smoothing the idea of -estimation can be used. The difficulty is the formulation of an easy-to-use recursive formula for its computation. A first attempt was made by Cipra (Robust exponential smoothing, J. Forecast. (1992), 57–69). The recursive formulation presented there, however, is unstable. In this paper, a new recursive computing scheme is proposed. A simulation study illustrates that the new recursions result in smaller...