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A New Method For Obtaining The Autocovariance Of An Arma Model: An Exact Form Solution

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  • Karanasos, M.

Abstract

In this article we present a new method for computing the theoretical autocovariance function of an autoregressive moving average model. The importance of our theorem is that it yields two interesting results: First, a closed-form solution is derived in terms of the roots of the autoregressive polynomial and the parameters of the moving average part. Second, a sufficient condition for the lack of model redundancy is obtained.

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  • Karanasos, M., 1998. "A New Method For Obtaining The Autocovariance Of An Arma Model: An Exact Form Solution," Econometric Theory, Cambridge University Press, vol. 14(5), pages 622-640, October.
    • Handle: RePEc:cup:etheor:v:14:y:1998:i:05:p:622-640_14
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    Cited by:

    1. Menelaos Karanasos, "undated". "Prediction in ARMA models with GARCH in Mean Effects," Discussion Papers 99/11, Department of Economics, University of York.
    2. Xingwu Zhou & Martin Solberger, 2017. "A Lagrange Multiplier-Type Test for Idiosyncratic Unit Roots in the Exact Factor Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(1), pages 22-50, January.
    3. Zheng, Wei & Jin, Yong & Zhang, Guoyi, 2016. "Recursive estimation of time-average variance constants through prewhitening," Statistics & Probability Letters, Elsevier, vol. 114(C), pages 30-37.
    4. Menelaos Karanasos, "undated". "The Covariance Structure of Mixed ARMA Models," Discussion Papers 00/10, Department of Economics, University of York.
    5. Karanasos, Menelaos & Paraskevopoulos, Alexandros & Magdalinos, Anastasios & Canepa, Alessandra, 2024. "A Unified Theory for Arma Models with Varying Coefficients: One Solution Fits All," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202413, University of Turin.
    6. Menelaos Karanasos & Alexandros Paraskevopoulos & Faek Menla Ali & Michail Karoglou & Stavroula Yfanti, 2014. "Modelling Returns and Volatilities During Financial Crises: a Time Varying Coefficient Approach," Papers 1403.7179, arXiv.org.
    7. Zhou, X. & Solberger, M., 2013. "A Lagrange multiplier-type test for idiosyncratic unit roots in the exact factor model under misspecification," Research Memorandum 058, Maastricht University, Graduate School of Business and Economics (GSBE).

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