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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. Kasparis, Ioannis, 2010. "The Bierens test for certain nonstationary models," Journal of Econometrics, Elsevier, vol. 158(2), pages 221-230, October.
    2. Bierens, H.J., 1988. "Conditioning and dependence," Serie Research Memoranda 0062, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    3. de Jong, Robert M., 1996. "The Bierens test under data dependence," Journal of Econometrics, Elsevier, vol. 72(1-2), pages 1-32.
    4. 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.
    5. 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.

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