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A Unified Approach To The Study Of Sums, Products, Time‐Aggregation And Other Functions Of Arma Processes

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  • E. M. R. A. Engel

Abstract

. Conditions under which sums, products and time‐aggregation of ARMA processes follow ARMA models are derived from a single theorem. This characterizes these processes in terms of difference equations satisfied by their autocovariance function. From this we obtain necessary and sufficient conditions for a function of a Gaussian ARMA process and the product of two possibly dependent Gaussian ARMA processes to be ARMA. We show that the sum and product of two ARMA processes related by a Box and Jenkins transfer function model belong to the ARMA family.

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  • E. M. R. A. Engel, 1984. "A Unified Approach To The Study Of Sums, Products, Time‐Aggregation And Other Functions Of Arma Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 5(3), pages 159-171, May.
    • Handle: RePEc:bla:jtsera:v:5:y:1984:i:3:p:159-171
    DOI: 10.1111/j.1467-9892.1984.tb00384.x
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    Cited by:

    1. Gong, Fangxiong & Remolona, Eli M, 1997. "Two Factors along the Yield Curve," The Manchester School of Economic & Social Studies, University of Manchester, vol. 65(0), pages 1-31, Supplemen.
    2. Ricardo J. Caballero & Eduardo M.R.A. Engel, 2003. "Missing Aggregate Dynamics: On the Slow Convergence of Lumpy Adjustment Models," Cowles Foundation Discussion Papers 1430, Cowles Foundation for Research in Economics, Yale University, revised Apr 2008.
    3. Cordis, Adriana S. & Kirby, Chris, 2014. "Discrete stochastic autoregressive volatility," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 160-178.
    4. Caballero, Ricardo J. & Engel, Eduardo M.R.A., 2003. "Adjustment is Much Slower than You Think," Center Discussion Papers 28419, Yale University, Economic Growth Center.
    5. Dionne, Georges & Pacurar, Maria & Zhou, Xiaozhou, 2015. "Liquidity-adjusted Intraday Value at Risk modeling and risk management: An application to data from Deutsche Börse," Journal of Banking & Finance, Elsevier, vol. 59(C), pages 202-219.
    6. Jeff Fleming & Chris Kirby, 2013. "Component-Driven Regime-Switching Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 11(2), pages 263-301, March.
    7. Abeysinghe Tilak & Choy Keen, 2002. "On the Use of Innovation Correlations to Study Cyclical Co-Movements in GDP and Its Components," International Economic Journal, Taylor & Francis Journals, vol. 16(2), pages 37-45.
    8. Kilian, Lutz, 1999. "Exchange Rates and Monetary Fundamentals: What Do We Learn from Long-Horizon Regressions?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(5), pages 491-510, Sept.-Oct.

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