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On the Stationary Marginal Distributions of Subclasses of Multivariate Setar Processes of Order One
Author(s) -
Das Soumya,
Genton Marc G.
Publication year - 2020
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12514
Subject(s) - setar , mathematics , marginal distribution , autoregressive model , skew , multivariate statistics , stationary process , econometrics , distribution (mathematics) , statistics , statistical physics , star model , mathematical analysis , autoregressive integrated moving average , computer science , random variable , time series , telecommunications , physics
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 oneMSETAR d ( 1 ) with multivariate normal innovations is shown to belong to the unified skew‐normal ( ) family and characterized under a fairly broad condition. This article also characterizes the stationary marginal distributions of a subclass of theMSETAR d ( 1 ) 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, anMSETAR d ( 1 ) process, with stationary marginal distribution identical to the given skew‐distribution, can be associated. Furthermore, this article illustrates a diagnostic of anMSETAR 2 ( 1 ) model using the corresponding stationary marginal density.