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 |
Funding
We would like to thank two anonymous reviewers for their helpful comments and Professor Keh-Shin Lii for supplying the water gun wavelet used in Section 4.3. Also, the work reported here was developed in part under STAR Research Assistance Agreement CR-829095 awarded by the U.S. Environmental Protection Agency (EPA) to Colorado State University. This manuscript has not been formally reviewed by EPA. The views expressed here are solely those of the authors. EPA does not endorse any products or commercial services mentioned in this report. ∗Corresponding author. E-mail address: [email protected] (B. Andrews). 1Supported in part by NSF Grants DMS9972015 and DMS0308109. 2Supported in part by EPA STAR Grant CR-829095.
Keywords
- Gaussian mixture
- Non-Gaussian
- Noninvertible moving average
- White noise
ASJC Scopus subject areas
- Statistics and Probability
- Numerical Analysis
- Statistics, Probability and Uncertainty