 The Correspondence Between Stochastic Linear Difference and Differential EquationsD.S.G. Pollock () No 19/07, Discussion Papers in Economics from Division of Economics, School of Business, University of Leicester Abstract: The relationship between autoregressive moving-average (ARMA) models in discrete time and the corresponding models in continuous time is examined in this paper. The linear stochastic models that are commonly regarded as the counterparts of the ARMA models are driven by a forcing function that consists of the increments of a Wiener Process. This function is unbounded in frequency. In cases where the periodogram of the data indicates that there is a clear upper bound to its frequency content, we propose an alternative frequency- limited white-noise forcing function. Then, there is a straightforward translation from the ARMA model to a differential equation, which is based of the principle of impulse invariance. Whenever there is no perceptible limit to the frequency content, the translation must be based on a principle of autocovariance equivalence. On the website of the author, there is a computer program that effects both of these discrete-to-continuous translations. New Economics Papers: this item is included in nep-ecm and nep-ets Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:lec:leecon:19/07 Ordering information: This working paper can be ordered from Access Statistics for this paper More papers in Discussion Papers in Economics from Division of Economics, School of Business, University of Leicester School of Business, University of Leicester, University Road. Leicester. LE1 7RH. UK Provider-Homepage: https://le.ac.uk/school-of-business. Contact information at EDIRC. |
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