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

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  • Portnoy, Stephen

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.

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  • Portnoy, Stephen, 2019. "Edgeworth’s time series model: Not AR(1) but same covariance structure," Journal of Econometrics, Elsevier, vol. 213(1), pages 281-288.
    • Handle: RePEc:eee:econom:v:213:y:2019:i:1:p:281-288
    DOI: 10.1016/j.jeconom.2019.04.015
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    1. Koenker, Roger & Xiao, Zhijie, 2006. "Quantile Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 980-990, September.
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    Cited by:

    1. Weiß, Christian H., 2021. "On Edgeworth models for count time series," Statistics & Probability Letters, Elsevier, vol. 171(C).

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