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A Gaussian Mixture Autoregressive Model for Univariate Time Series
Author(s) -
Kalliovirta Leena,
Meitz Mika,
Saikkonen Pentti
Publication year - 2015
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.12108
Subject(s) - autoregressive model , mathematics , star model , series (stratigraphy) , ergodicity , nonlinear autoregressive exogenous model , setar , gaussian , mixture model , mixing (physics) , autoregressive integrated moving average , univariate , econometrics , conditional probability distribution , parametric model , stationary process , parametric statistics , statistics , time series , multivariate statistics , quantum mechanics , biology , paleontology , physics
The Gaussian mixture autoregressive model studied in this article belongs to the family of mixture autoregressive models, but it differs from its previous alternatives in several advantageous ways. A major theoretical advantage is that, by the definition of the model, conditions for stationarity and ergodicity are always met and these properties are much more straightforward to establish than is common in nonlinear autoregressive models. Another major advantage is that, for a p th‐order model, explicit expressions of the stationary distributions of dimension p + 1 or smaller are known and given by mixtures of Gaussian distributions with constant mixing weights. In contrast, the conditional distribution given the past observations is a Gaussian mixture with time‐varying mixing weights that depend on p lagged values of the series in a natural and parsimonious way. Because of the known stationary distribution, exact maximum likelihood estimation is feasible and one can assess the applicability of the model in advance by using a non‐parametric estimate of the stationary density. An empirical example with interest rate series illustrates the practical usefulness and flexibility of the model, particularly in allowing for level shifts and temporary changes in variance. Copyright © 2014 Wiley Publishing Ltd