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On cross-correlogram IRF’s estimators of two-output systems in spaces of continuous functions

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  • Irina Blazhievska
  • Vladimir Zaiats

Abstract

In this article, single input–double output linear time-invariant systems are studied. Both components of system’s impulse response function are supposed to be real-valued and L2-integrable. One component is unknown while the second one is controlled. The problem is to estimate the unknown component after observations of the other component. For this purpose, we apply cross-correlating of the outputs given that the input is a standard Wiener process on R. Weak asymptotic normality of appropriately centered estimators in spaces of continuous functions is proved. This enables us to construct confidence intervals in these spaces. Our results employ techniques related to Gaussian processes and bilinear forms of Gaussian processes.

Suggested Citation

  • Irina Blazhievska & Vladimir Zaiats, 2021. "On cross-correlogram IRF’s estimators of two-output systems in spaces of continuous functions," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 50(24), pages 6024-6048, November.
    • Handle: RePEc:taf:lstaxx:v:50:y:2021:i:24:p:6024-6048
    DOI: 10.1080/03610926.2020.1738490
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