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ARMA Memory Index Modeling of Economic Time Series

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  • Bierens, Herman J.

Abstract

In this paper, it will be shown that if we condition a k-variate rational-valued time series process on its entire past, it is possible to capture all relevant information on the past of the process by a single random variable. This scalar random variable can be formed as an autoregressive moving average of past observations; Since economic data are usually reported in a finite number of digits, this result applies to virtually all economic time series. Therefore, economic time series regressions generally take the form of a nonlinear function of an autoregressive moving average of past observations. This approach is applied to model specification testing of nonlinear ARX models.

Suggested Citation

  • Bierens, Herman J., 1988. "ARMA Memory Index Modeling of Economic Time Series," Econometric Theory, Cambridge University Press, vol. 4(1), pages 35-59, April.
    • Handle: RePEc:cup:etheor:v:4:y:1988:i:01:p:35-59_01
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    Cited by:

    1. Bierens, H.J., 1988. "Conditioning and dependence," Serie Research Memoranda 0062, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    2. Jungyoon Lee & Peter C.B. Phillips & Francesca Rossi, 2020. "Consistent Misspecification Testing in Spatial Autoregressive Models," Cowles Foundation Discussion Papers 2256, Cowles Foundation for Research in Economics, Yale University.
    3. Bierens, Herman J. & Swanson, Norman R., 2000. "The econometric consequences of the ceteris paribus condition in economic theory," Journal of Econometrics, Elsevier, vol. 95(2), pages 223-253, April.
    4. Kasparis, Ioannis, 2010. "The Bierens test for certain nonstationary models," Journal of Econometrics, Elsevier, vol. 158(2), pages 221-230, October.
    5. de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 1-32.

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