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J. Risk Financial Manag. 2018, 11(3), 45;

Stationary Threshold Vector Autoregressive Models

Department of Economics, University of Western Ontario, Social Science Centre, London, ON N6A 5C2, Canada
Department of Statistical and Actuarial Sciences, University of Western Ontario, Western Science Centre, London, ON N6A 5B7, Canada
Author to whom correspondence should be addressed.
Received: 15 June 2018 / Revised: 20 July 2018 / Accepted: 3 August 2018 / Published: 5 August 2018
(This article belongs to the Special Issue Financial Econometrics)
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This paper examines the steady state properties of the Threshold Vector Autoregressive model. Assuming that the trigger variable is exogenous and the regime process follows a Bernoulli distribution, necessary and sufficient conditions for the existence of stationary distribution are derived. A situation related to so-called “locally explosive models”, where the stationary distribution exists though the model is explosive in one regime, is analysed. Simulations show that locally explosive models can generate some of the key properties of financial and economic data. They also show that assessing the stationarity of threshold models based on simulations might well lead to wrong conclusions. View Full-Text
Keywords: asset price bubbles; explosive regimes; multivariate nonlinear time series; steady state distributions; TVAR models asset price bubbles; explosive regimes; multivariate nonlinear time series; steady state distributions; TVAR models

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Grynkiv, G.; Stentoft, L. Stationary Threshold Vector Autoregressive Models. J. Risk Financial Manag. 2018, 11, 45.

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