Multivariate stable distributions and generating densities

Fallahgoul, Hasan; Hashemiparast, S. M.; Fabozzi, Frank J.; Kim, Young S.

doi:10.1016/j.aml.2012.09.009

Cited by 4 publications

(1 citation statement)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, combining these two results, we characterize the

{MSETAR}_{d} false(1 false)

models with

bold-italicA \in {bold-scriptH}_{1} false(bold-italicA false)

and symmetric multivariate stable innovations. For an extensive study on multivariate stable distributions, see, for example, Press (), Nolan (), Fallahgoul et al (), and Teimouri et al ().…”

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

View full text Add to dashboard Cite

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.

show abstract

“…Thus, combining these two results, we characterize the

{MSETAR}_{d} false(1 false)

models with

bold-italicA \in {bold-scriptH}_{1} false(bold-italicA false)

and symmetric multivariate stable innovations. For an extensive study on multivariate stable distributions, see, for example, Press (), Nolan (), Fallahgoul et al (), and Teimouri et al ().…”

Section: Introductionmentioning

confidence: 99%