A Note on the Threshold Ar(1) Model With Cauchy Innovations

Anděl, Jiří; Bartoň, Tomáŝ

doi:10.1111/j.1467-9892.1986.tb00481.x

Cited by 13 publications

(4 citation statements)

References 5 publications

(1 reference statement)

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“…See Tong (1990) for a thorough review of results for the more general TAR models. Explicit formulae for the stationary solutions of such simple TAR models have been found when the noise distributions are normal, Cauchy and Laplace (Andel and Barton, 1986;Andel et al, 1984;Loges, 2004). More specifically, when = − , for the simplest TAR model with t a standard normal white-noise process, Andel et al (1984) have shown that its stationary distribution is of the form…”

Section: Connection Between the Simplest Tar Model And Sn Distributionsmentioning

confidence: 97%

Skew-Normal ARMA Models with Nonlinear Heteroscedastic Predictors

Pourahmadi

2007

Communications in Statistics - Theory and Methods

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Multivariate skew-normal (SN) distributions (Azzalini and Dalla Valle, 1996) enjoy some of the useful properties of normal distributions, have nonlinear heteroscedastic predictors but lack the closure property of normal distributions (the sum of independent SN random variables is not SN). Recently, there has been a proliferation of classes of SN distributions with certain closure properties, one of the most promising being the closed skew-normal (CSN) distributions of González-Farías et al. (2004). We study the construction of stationary SN ARMA models for colored SN noise and show that their finite-dimensional distributions are skew-normal, seldom strictly stationary and their covariance functions differ from their normal ARMA counterparts in that they do not converge to zero for large lags. The situation is better for ARMA models driven by CSN noise, but at the additional cost of considerable computational complexity and a less explicit skewness parameter. In view of these results, the widespread use of such classes of SN distributions in the framework of ARMA models seem doubtful.

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Section: Connection Between the Simplest Tar Model And Sn Distributionsmentioning

confidence: 97%

Skew-Normal ARMA Models with Nonlinear Heteroscedastic Predictors

Pourahmadi

2007

Communications in Statistics - Theory and Methods

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“…The Seasonal and Cyclical Long Memory (SCLM ) filter is defined by convolution. Any of the factors in (8) may be expanded as a binomial series given by Anděl et al (1986):…”

Section: Gegenbauer Arfisma-sαs Processmentioning

confidence: 99%

Infinite variance stable Gegenbaeur Arfisma models

Keita¹,

Hili²,

Kanga³

2021

jas

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This paper develops the theory of the Gegenbauer AutoRegressive Fractionally Integrated Seasonal Moving Average (GARFISMA) process with alpha-stable innovations.We establish its conditions for causality and invertibility. This is a finite parameter process which exhibits high variability, long memory, cyclical, and seasonality in financial, hydrological data studies, and more. We perform some simulations to illustrate the behavior of our process.

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“…While there is an extensive study on obtaining explicit forms of the stationary marginal densities of such models (e.g. Anděl et al, ; Anděl and Bartoň, ; Chan and Tong, ; Loges, ), little work has been done to characterize them. By and large, our current work is intended to link the stationary marginal densities of certain MSETAR models to the skew‐symmetric densities (Genton, ; Azzalini and Capitanio, ) and to characterize them under certain additional but fairly broad assumptions.…”

Section: Introductionmentioning

confidence: 99%

On the Stationary Marginal Distributions of Subclasses of Multivariate Setar Processes of Order One

Das

Genton

2019

Journal Time Series Analysis

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To introduce more flexibility in process‐parameters through a regime‐switching behavior, the classical autoregressive (AR) processes have been extended to self‐exciting threshold autoregressive (SETAR) processes. However, the stationary marginal distributions of SETAR processes are usually difficult to obtain in explicit forms and, therefore, they lack appropriate characterizations. The stationary marginal distribution of a multivariate (d‐dimensional) SETAR process of order one ()MSETARdfalse(1false) with multivariate normal innovations is shown to belong to the unified skew‐normal (𝒮𝒰𝒩) family and characterized under a fairly broad condition. This article also characterizes the stationary marginal distributions of a subclass of the MSETARdfalse(1false) processes with symmetric multivariate stable innovations. To characterize the stationary marginal distributions of these processes, the authors show that they belong to specific skew‐distribution families, and for a given skew‐distribution from the corresponding family, an MSETARdfalse(1false) process, with stationary marginal distribution identical to the given skew‐distribution, can be associated. Furthermore, this article illustrates a diagnostic of an MSETAR2false(1false) model using the corresponding stationary marginal density.

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A Note on the Threshold Ar(1) Model With Cauchy Innovations

Cited by 13 publications

References 5 publications

Skew-Normal ARMA Models with Nonlinear Heteroscedastic Predictors

Skew-Normal ARMA Models with Nonlinear Heteroscedastic Predictors

Infinite variance stable Gegenbaeur Arfisma models

On the Stationary Marginal Distributions of Subclasses of Multivariate Setar Processes of Order One

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