Edgeworth’s time series model: Not AR(1) but same covariance structure

Stephen Portnoy

Journal of Econometrics, 2019, vol. 213, issue 1, 281-288

Abstract: In an 1886 paper, Edgeworth developed a method for simulating time series processes with substantial dependence. A version of this process with normal errors has the same means and covariance structure as an AR(1) process, but is actually a mixture of a very large number of processes, some of which are not stationary. That is, joint distributions of lag 3 or greater are not normal but are mixtures of normals (even though all successive pairs are bivariate normal). Thus, it serves as a cautionary example for time series analysis: though the AR(1) process cannot be distinguished from the Edgeworth Process by second order properties, inferences based on an AR(1) assumption can fail under the Edgeworth model. This model has many additional surprising features, among which is that it has Markov structure, but is not generated by a one-step transition operator.

Keywords: Edgeworth process; AR(1); Model diagnostics; Counterexample (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:213:y:2019:i:1:p:281-288

DOI: 10.1016/j.jeconom.2019.04.015

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