Least absolute deviation estimation for all-pass time series models

Breidt, Y. F. Jay; Davis, Richard A.; Trindade, A. Alexandre

doi:10.1214/aos/1013699987

Cited by 47 publications

(21 citation statements)

References 30 publications

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“…With this definition, some noncausal ARMA processes (as in Example 2) are considered as nonlinear. This is also the case for the so-called all-pass models, which are causal ARMA models in which the roots of the AR polynomial are the reciprocals of the roots of the MA polynomial (see [28] and the references therein for details about all-pass models). The following example corresponds to the simplest all-pass model.…”

Section: Linear and Nonlinear Processesmentioning

confidence: 96%

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Concepts of and tools for Nonlinear Time‐Series Modelling

Amendola

Francq

2009

Handbook of Computational Econometrics

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Tools and approaches are provided for nonlinear time series modelling in econometrics. A wide range of topics is covered, including probabilistic properties, statistical inference and computational methods. The focus is on the applications but the ideas of the mathematical arguments are also provided. Techniques and concepts are illustrated by various examples, Monte Carlo experiments and a real application. 1

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Section: Linear and Nonlinear Processesmentioning

confidence: 96%

“…When (Z t ) is stationary, the term sup t can be omitted in the definitions (28) and (29). The process is said to be α-mixing (resp.…”

Section: Mixing Coefficientsmentioning

confidence: 99%

Concepts of and tools for Nonlinear Time‐Series Modelling

Amendola

Francq

2009

Handbook of Computational Econometrics

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“…There is now an extensive literature on inference for non‐Gaussian, non‐CI sequences including, for example, Lii and Rosenblatt (1996), Rosenblatt (2000), Breidt etal . (2001), Andrews et al (2006) and Davis and Zhang (2018).…”

Section: Introductionmentioning

confidence: 99%

“…They also arise very naturally in connection with one-dimensional spatial processes such as measurements along a river in which upstream and downstream shocks both affect the measurement at a given point. There is now an extensive literature on inference for non-Gaussian, non-CI sequences including, for example, Lii and Rosenblatt (1996), Rosenblatt (2000), Breidt et al (2001), Andrews et al (2006) and Davis and Zhang (2018). Rosenblatt (2000), Section 5.6, also considered analogous second-order non-CI non-Gaussian continuous-time CARMA (p, q) processes defined by a formal stochastic differential equation of the form…”

Section: Introductionmentioning

confidence: 99%

Aspects of non‐causal and non‐invertible CARMA processes

Brockwell

Lindner

2021

Journal Time Series Analysis

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A CARMA(p, q) process Y is a strictly stationary solution Y of the pth-order formal stochastic differential equation a(D)Y t = b(D)DL t , where L is a two-sided Lévy process, a(z) and b(z) are polynomials of degrees p and q respectively, with p > q, and D denotes differentiation with respect to t. Using a state-space formulation of the defining equation, Brockwell and Lindner (2009, Stochastic Processes and their Applications 119, 2660-2681) gave necessary and sufficient conditions on L, a(z) and b(z) for the existence and uniqueness of such a stationary solution and specified the kernel g in the representation of the solutionIf the zeros of a(z) all have strictly negative real parts, Y is said to be a causal function of L (or simply causal) since then Y t can be expressed in terms of the increments of L s , s ≤ t, and if the zeros of b(z) all have strictly negative real parts the process is said to be invertible since then the increments of L s , s ≤ t, can be expressed in terms of Y s , s ≤ t. In this article we are concerned with properties of CARMA processes for which these conditions on a and b do not necessarily hold.

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“…Then, estimation is performed using ML or approximate versions of it (e.g. Rosenblatt, 1992, 1996, for ARMA; Renne, 2017, andLanne, Meitz andSaikkonen, 2017, for SVAR; Gouriéroux et al, 2019, for SVARMA models) or non-Gaussian criteria like LAD or ranks Trindade, 2001, andAndrews, Davis andBreidt, 2007, in the univariate case). Methods based on higher order moments have been also developed, first for the univariate case in the frequency and time domains Rosenblatt, 1982, Gospodinov andNg, 2015, respectively).…”

Section: Introductionmentioning

confidence: 99%

Identification and estimation of Structural VARMA models using higher order dynamics

Velasco¹

2020

Preprint

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We use information from higher order moments to achieve identification of non-Gaussian structural vector autoregressive moving average (SVARMA) models, possibly non-fundamental or non-causal, through a frequency domain criterion based on a new representation of the higher order spectral density arrays of vector linear processes. This allows to identify the location of the roots of the determinantal lag matrix polynomials based on higher order cumulants dynamics and to identify the rotation of the model errors leading to the structural shocks up to sign and permutation. We describe sufficient conditions for global and local parameter identification that rely on simple rank assumptions on the linear dynamics and on finite order serial and component independence conditions for the structural innovations. We generalize previous univariate analysis to develop asymptotically normal and efficient estimates exploiting second and non-Gaussian higher order dynamics given a particular structural shocks ordering without assumptions on causality or invertibility. Bootstrap approximations to finite sample distributions and the properties of numerical methods are explored with real and simulated data.

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Least absolute deviation estimation for all-pass time series models

Cited by 47 publications

References 30 publications

Concepts of and tools for Nonlinear Time‐Series Modelling

Concepts of and tools for Nonlinear Time‐Series Modelling

Aspects of non‐causal and non‐invertible CARMA processes

Identification and estimation of Structural VARMA models using higher order dynamics

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