RT Report
T1 Mathematical framework for pseudo-spectra of linear stochastic difference equations
A1 Bujosa Brun, Marcos
A1 Bujosa Brun, Andrés
A1 García Ferrer, Antonio
AB Although spectral analysis of stationary stochastic processes has solid mathematical foundations, this is not always so for some non-stationary cases. Here, we establish a rigorous mathematical extension of the classic Fourier spectrum to the case in which there are AR roots in the unit circle, ie, the transfer function of the linear time-invariant filter has poles on the unit circle. To achieve it we: embed the classical problem in a wider framework, the Rigged Hilbert space, extend the Discrete Time Fourier Transform and defined a new Extended Fourier Transform pair pseudo-covariance function/pseudo-spectrum. Our approach is a proper extension of the classical spectral analysis, within which the Fourier Transform pair auto-covariance function/spectrum is a particular case. Consequently spectrum and pseudo-spectrum coincide when the first one is defined.
PB Facultad de CC Económicas y Empresariales. Instituto Complutense de Análisis Económico (ICAE)
YR 2013
FD 2013
LK https://hdl.handle.net/20.500.14352/41468
UL https://hdl.handle.net/20.500.14352/41468
LA eng
NO This working paper has been accepted for publication in a future issue of IEEE Transactions on Signal Processing. Content may change prior to final publication. Citation information: DOI:10.1109/TSP.2015.2469640.1053-587X copy right 2015 IEEE. Personal use of this material is permitted. However, permission to use this material for any other purposes must be obtained from the IEEE by sending a request to pubs-permissions@ieee.org See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.
DS Docta Complutense
RD 28 abr 2025