The Annals of Applied Probability

Parametric Signal Modelling using Laguerre Filters

B. Wahlberg and E. J. Hannan

Full-text: Open access

Abstract

Autoregressive (AR) modelling is generalized by replacing the delay operator by discrete Laguerre filters. The motivation is to reduce the number of parameters needed to obtain useful approximate models of stochastic processes, without increasing the computational complexity. Asymptotic statistical properties are investigated. Several AR model estimation results are extended to Laguerre models. In particular, it is shown how the choice of Laguerre time constant affects the resulting estimates. A Levinson-type algorithm for computing the Laguerre model estimates in an efficient way is also given. The Laguerre technique is illustrated by two simple examples.

Article information

Source
Ann. Appl. Probab., Volume 3, Number 2 (1993), 467-496.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177005434

Digital Object Identifier
doi:10.1214/aoap/1177005434

Mathematical Reviews number (MathSciNet)
MR1221162

Zentralblatt MATH identifier
0784.62080

JSTOR
links.jstor.org

Subjects
Primary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 62F12: Asymptotic properties of estimators 60G12: General second-order processes 60F05: Central limit and other weak theorems 60G10: Stationary processes

Keywords
Autoregression network modeling time series spectral analysis Laguerre functions

Citation

Wahlberg, B.; Hannan, E. J. Parametric Signal Modelling using Laguerre Filters. Ann. Appl. Probab. 3 (1993), no. 2, 467--496. doi:10.1214/aoap/1177005434. https://projecteuclid.org/euclid.aoap/1177005434


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