A minimum variance property of Levinson predictors using variograms

✍ Scribed by G. Bastin; E. Henriet

• Publisher: Elsevier Science
• Year: 1982
• Tongue: English
• Weight: 319 KB
• Volume: 2
• Category: Article
• ISSN: 0167-6911
• DOI: 10.1016/s0167-6911(82)80039-x

✦ Synopsis

The classical way to solve the problem of predicting future values of a stationary non-zero mean stochastic process having known model is (i) to remove the mean of the process from the past data, (ii) to apply an optimal predictor (Wiener, Levinson. Kalman,.

. ) to the zero-mean purely stochastic residuals. In most practical applications, however, the mean of the process is not given a priori but must be estimated, in a preliminary step, from a sequence of available data. Using the concept of 'variogram', we propose in this paper an alternative way to derive the Levinson predictor, which does not require any preliminary knowledge of the mean. We prove that this predictor is better than the classical one. in the sense that it leads to a smaller prediction error variance when the mean is unknown, though it applies not only to (wide sense) stationary processes but also to non-stationary processes with stationary increments.