Abstract
The classical paradigm of statistics assumes that data is generated by a stochastic process whose structure is entirely known save for a fixed number of parameters. Of course there are many departures from this assumption and consequent statistical methods are useful over a much wider range than the paradigm suggests. In time series analysis the paradigm is rarely relevant, which partly explains the wide use of Fourier methods, which are non-parametric. The other major part of time series analysis is that based on autoregressive-moving average (ARMA) models. Much of the literature associated with these acts as if the data are actually generated by such a model though this attitude has been modified in some of the systems and control literature (Rissanen, 1983) and in the work of Akaike and Shibata (see Shibata, 1980). Here the point of view will, also, be taken that the ARMA models are fitted as approximations. A complete treatment will be impossible because of the space available and also the state of the development of the ideas.
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© 1987 D. Reidel Publishing Company
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Hannan, E.J. (1987). Approximation of Linear Systems. In: MacNeill, I.B., Umphrey, G.J., Carter, R.A.L., McLeod, A.I., Ullah, A. (eds) Time Series and Econometric Modelling. The University of Western Ontario Series in Philosophy of Science, vol 36. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-4790-0_1
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DOI: https://doi.org/10.1007/978-94-009-4790-0_1
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