Abstract
An autoregressive-moving average model in which all roots of the autoregressive polynomial are reciprocals of roots of the moving average polynomial and vice versa is called an all-pass time series model. All-pass models generate uncorrelated (white noise) time series, but these series are not independent in the non-Gaussian case. An approximate likelihood for a causal all-pass model is given and used to establish asymptotic normality for maximum likelihood estimators under general conditions. Behavior of the estimators for finite samples is studied via simulation. A two-step procedure using all-pass models to identify and estimate noninvertible autoregressive-moving average models is developed and used in the deconvolution of a simulated water gun seismogram.
Original language | English (US) |
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Pages (from-to) | 1638-1659 |
Number of pages | 22 |
Journal | Journal of Multivariate Analysis |
Volume | 97 |
Issue number | 7 |
DOIs | |
State | Published - Aug 2006 |
Keywords
- Gaussian mixture
- Non-Gaussian
- Noninvertible moving average
- White noise
ASJC Scopus subject areas
- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty