In this paper, the spectral properties of matrices associated to trend filters are investigated and connected to the frequency domain properties of the associated filters. The analytical form of the eigenvalues is derived, with an approximation measured by the size of the perturbation that diffeerent boundary conditions apport to the eigenvalues of matrices belonging to algebras with known spectral properties. The boundary conditions are interpreted in terms of hypotheses on the future behavior of the process underlying the observed series. A further topic investigated in the paper concerns a strategy for a filter design in time domain. The key argument is that eigenanalysis consents to represent in time domain all the periodic latent component of a time series.
On the spectral properties of matrices associated to trend filters / A. Luati; T. Proietti. - ELETTRONICO. - (2007), pp. ---. (Intervento presentato al convegno 56th Session of the International Statistical Institute tenutosi a Lisboa, Portugal nel 22-29 agosto 2007).
On the spectral properties of matrices associated to trend filters
LUATI, ALESSANDRA;
2007
Abstract
In this paper, the spectral properties of matrices associated to trend filters are investigated and connected to the frequency domain properties of the associated filters. The analytical form of the eigenvalues is derived, with an approximation measured by the size of the perturbation that diffeerent boundary conditions apport to the eigenvalues of matrices belonging to algebras with known spectral properties. The boundary conditions are interpreted in terms of hypotheses on the future behavior of the process underlying the observed series. A further topic investigated in the paper concerns a strategy for a filter design in time domain. The key argument is that eigenanalysis consents to represent in time domain all the periodic latent component of a time series.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
