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The ACR Model: A Multivariate Dynamic Mixture Autoregression *
Author(s) -
Bec Frédérique,
Rahbek Anders,
Shephard Neil
Publication year - 2008
Publication title -
oxford bulletin of economics and statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.131
H-Index - 73
eISSN - 1468-0084
pISSN - 0305-9049
DOI - 10.1111/j.1468-0084.2008.00512.x
Subject(s) - autoregressive model , ergodicity , econometrics , estimator , mathematics , multivariate statistics , star model , series (stratigraphy) , markov chain , unit root , nonlinear system , time series , statistics , autoregressive integrated moving average , paleontology , physics , quantum mechanics , biology
This paper proposes and analyses the autoregressive conditional root (ACR) time‐series model. This multivariate dynamic mixture autoregression allows for non‐stationary epochs. It proves to be an appealing alternative to existing nonlinear models, e.g. the threshold autoregressive or Markov switching class of models, which are commonly used to describe nonlinear dynamics as implied by arbitrage in presence of transaction costs. Simple conditions on the parameters of the ACR process and its innovations are shown to imply geometric ergodicity, stationarity and existence of moments. Furthermore, consistency and asymptotic normality of the maximum likelihood estimators are established. An application to real exchange rate data illustrates the analysis.