\`x^2+y_1+z_12^34\`
Advanced Search
Article Contents
Article Contents

Singular arma systems: A structure theory

Abstract Full Text(HTML) Related Papers Cited by
  • Singular vector ARMA systems are vector ARMA (VARMA) systems with singular innovation variance or equivalently with singular spectral density of the corresponding VARMA process. Such systems occur in linear dynamic factor models, e.g. if the dimension of the static factors is strictly larger than the dimension of the dynamic factors or in linear dynamic stochastic equilibrium models, if the number of outputs is strictly larger than the number of shocks. We describe the relation of factor models and singular ARMA systems and a realization procedure for singular ARMA systems. Finally we discuss kernel systems.

    Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

    Citation:

    \begin{equation} \\ \end{equation}
  • 加载中
  • [1] B. D. O. Anderson and M. Deistler, Properties of zero-free transfer function matrices, SICE Journal of Control, Measurement and System Integration, 1 (2008), 284-292.  doi: 10.1109/TAC.2009.2028976.
    [2] H. Akaike, Stochastic theory of minimal realization, IEEE-TAC, 19 (1974), 667-674.  doi: 10.1109/tac.1974.1100707.
    [3] M. Deistler and W. Scherrer, Modelle der Zeitreihenanalyse, Birkhuser-Springer, Cham, 2018.
    [4] M. DeistlerB. D. O. AndersonA. FillerC. Zinner and W. Chen, Generalized dynamic factor models - An approach via singular autoregressions, European Journal of Control, 16 (2010), 1-14.  doi: 10.3166/ejc.16.211-224.
    [5] M. ForniM. HallinM. Lippi and L. Reichlin, The generalized dynamic factor model: identification and estimation, The Review of Economics and Statistics, 82 (2000), 540-554. 
    [6] M. ForniM. HallinM. Lippi and P. Zaffaroni, Dynamic factor models with infinite dimensional factor spaces: one-sided representations, Journal of Econometrics, 185 (2015), 359-371.  doi: 10.1016/j.jeconom.2013.10.017.
    [7] E. J. Hannan, M. Deistler, The Statistical Theory of Linear Systems, SIAM Classics in Applied Mathematics, Philadelphia, 2012. doi: 10.1137/1.9781611972191.ch1.
    [8] B. L. Ho and R. E. Kalman, Effective construction of linear state-variable models from input/output functions, Regelungstechnik, 14 (1966), 545-592. 
    [9] I. Komunjer and S. Ng, Dynamic identification of dynamic stochastic general equilibrium models, Econometrica, 79 (2011), 1995-2032.  doi: 10.3982/ECTA8916.
    [10] Y. A. Rozanov, Stationary Random Processes, Holden Day, San Francisco, 1967.
    [11] W. Scherrer and M. Deistler, A structure theory for linear dynamic errors-in-variables models, SIAM J. Cont. Opt, 36 (1998), 2148-2175.  doi: 10.1137/S0363012994262464.
  • 加载中
SHARE

Article Metrics

HTML views(1742) PDF downloads(258) Cited by(0)

Access History

Other Articles By Authors

Catalog

    /

    DownLoad:  Full-Size Img  PowerPoint
    Return
    Return