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Mixed autoregressive-moving average multivariate processes with time-dependent coefficients

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  • Hallin, Marc

Abstract

Conditions for mixed autoregressive-moving average processes with time-dependent coefficients to be purely nondeterministic and invertible can be obtained from classical difference equations theory. These conditions involve one-sided Green's functions or their matricial equivalents. A recursive computation of these functions is proposed, which allows one to drop the assumption of nondegeneracy classicaly made about the highest order matrix of difference operators; it constitutes thus a generalized definition of these functions.

Suggested Citation

  • Hallin, Marc, 1978. "Mixed autoregressive-moving average multivariate processes with time-dependent coefficients," Journal of Multivariate Analysis, Elsevier, vol. 8(4), pages 567-572, December.
    • Handle: RePEc:eee:jmvana:v:8:y:1978:i:4:p:567-572
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    Cited by:

    1. Alj, Abdelkamel & Jónasson, Kristján & Mélard, Guy, 2016. "The exact Gaussian likelihood estimation of time-dependent VARMA models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 633-644.
    2. Peter Robinson, 2007. "On Discrete Sampling Of Time-Varyingcontinuous-Time Systems," STICERD - Econometrics Paper Series 520, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Rajae Azrak & Guy Melard, 1998. "The exact quasi-likelihood of time dependent ARMA models," ULB Institutional Repository 2013/13740, ULB -- Universite Libre de Bruxelles.
    4. Beran, Jan, 2007. "On parameter estimation for locally stationary long-memory processes," CoFE Discussion Papers 07/13, University of Konstanz, Center of Finance and Econometrics (CoFE).
    5. Karanasos, Menelaos & Paraskevopoulos,Alexandros & Canepa, Alessandra, 2020. "Unified Theory for the Large Family of Time Varying Models with Arma Representations: One Solution Fits All," Department of Economics and Statistics Cognetti de Martiis. Working Papers 202008, University of Turin.
    6. Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
    7. M. Shelton Peiris & Manabu Asai, 2016. "Generalized Fractional Processes with Long Memory and Time Dependent Volatility Revisited," Econometrics, MDPI, vol. 4(3), pages 1-21, September.
    8. Kley, Tobias & Preuss, Philip & Fryzlewicz, Piotr, 2019. "Predictive, finite-sample model choice for time series under stationarity and non-stationarity," LSE Research Online Documents on Economics 101748, London School of Economics and Political Science, LSE Library.
    9. Robinson, Peter, 2007. "On discrete sampling of time-varying continuous-time systems," LSE Research Online Documents on Economics 6795, London School of Economics and Political Science, LSE Library.

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