Minimum-Variance and Maximum-Likelihood Deconvolution for Noncausal Channel Models

Hsueh, A.; Mendel, Jerry M.

doi:10.1109/tgrs.1985.289464

Cited by 19 publications

(2 citation statements)

References 12 publications

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“…including deconvolution of seismic signals [Wiggins (1978), Donoho (1981), Hsueh and Mendel (1985)], and analysis of astronomical data [Scargle (1981)]. Recent years have witnessed the emergence of a significant line of research on noncausal models in the econometric literature [see e.g., Lanne, Nyberg and Saarinen (2012), Lanne, Saikkonen (2011), Davis and Song (2012), Chen, Choi and Escanciano (2012), Hencic and Gouriéroux (2015), Velasco and Lobato (2015), Hecq, Lieb and Telg (2016, 2017a, 2017b, Cavaliere, Nielsen and Rahbek (2017)].…”

Section: Introductionmentioning

confidence: 99%

Mixed Causal-Noncausal Ar Processes and the Modelling of Explosive Bubbles

Fries

Zakoïan²

2019

Econom. Theory

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Noncausal autoregressive models with heavy-tailed errors generate locally explosive processes and, therefore, provide a convenient framework for modelling bubbles in economic and financial time series. We investigate the probability properties of mixed causal-noncausal autoregressive processes, assuming the errors follow a stable non-Gaussian distribution. Extending the study of the noncausal AR(1) model by Gouriéroux and Zakoian (2017), we show that the conditional distribution in direct time is lighter-tailed than the errors distribution, and we emphasize the presence of ARCH effects in a causal representation of the process. Under the assumption that the errors belong to the domain of attraction of a stable distribution, we show that a causal AR representation with non-i.i.d. errors can be consistently estimated by classical least-squares. We derive a portmanteau test to check the validity of the estimated AR representation and propose a method based on extreme residuals clustering to determine whether the AR generating process is causal, noncausal, or mixed. An empirical study on simulated and real data illustrates the potential usefulness of the results.

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Section: Introductionmentioning

confidence: 99%

Mixed Causal-Noncausal Ar Processes and the Modelling of Explosive Bubbles

Fries

Zakoïan²

2019

Econom. Theory

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“…We use them in this paper in the deconvolution of a simulated water gun seismogram. Other deconvolution approaches are discussed in Blass and Halsey [3], Donoho [11], Godfrey and Rocca [13], Hsueh and Mendel [15], Lii and Rosenblatt [17], Ooe and Ulrych [20], and Wiggins [21].…”

Section: Introductionmentioning

confidence: 99%

Maximum likelihood estimation for all-pass time series models

Andrews

Davis

Breidt

2006

Journal of Multivariate Analysis

125

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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.

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