Expolynomial smoothing of autocorrelated time series
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In the following, causal pattern buried in autocorrelated noise is considered. The causal pattern may be described by models such as trends, polynomial trajectories, growing sines. Based on a new criterion — called expolynomial — estimators of coefficients of a polynomial model are obtained. Characteristic functions of the estimators are derived and the first two moments calculated. Continuous time series are briefly studied to show similarities between discrete and continuous observations. Popular exponential smoothing is a special case of the expolynomial smoothing.
KeywordsTime Series Stochastic Process Sine Characteristic Function Probability Theory
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