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• W1039920355 abstract "Non-stationarity is a negative concept. A class of non-stationary time series, class (KF), has been introduced for its covariance analysis. A model of the “signal plus noise” form had been studied where the signal is a time series with zero mean and a periodic covariance and the noise is a stationary series with zero mean; it is termed “asymptotically stationary.” The class (KF) is one of the main results asserts that the class of harmonizable time series belongs to class (KF), and then an ergodic theorem is established. The class (KF) has been analyzed and an almost harmonizable class is introduced and shown to be of class (KF). This contains the harmonizable case, but the generalization gives a better insight, and shows the essential simplicity of the class (KF). The consistency of an estimator of the averaged mean function and a weak law of large numbers are established. This chapter focuses on the covariance analysis of time series governed by difference schemes with not necessarily constant coefficients. The basic sample function continuity of the solutions, the conditions under which they belong to class (KF), and the fact that they always belong to class (C), among others, have been established." @default.
• W1039920355 created "2016-06-24" @default.
• W1039920355 creator A5031690413 @default.
• W1039920355 date "1978-01-01" @default.
• W1039920355 modified "2023-09-25" @default.
• W1039920355 title "Covariance Analysis of Nonstationary Time Series† †This work was sponsored partly by the Air Force Aerospace Research Laboratories, Air Force Systems Command, USAF, Contract F33615-74-C-4009; and partly by the National Science Foundation under grants MPS 75-13881 and MCS 76-15544. Reproduction in whole or in part is permitted for any purpose of the U.S. government." @default.
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• W1039920355 doi "https://doi.org/10.1016/b978-0-12-426601-8.50010-3" @default.
• W1039920355 hasPublicationYear "1978" @default.
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