Abstract
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 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.
Highlights
Correct theoretical and empirical modelling of financial time series remains challenging
We first obtain the conditions on the parameter matrices under which the locally explosive TVAR model remains stationary
It is noteworthy that the stationarity of the TVAR model does not rule out the possibility of an explosive regime, but it restricts the value of the own autoregressive coefficients
Summary
Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel. Suggested Citation: Grynkiv, Galyna; Stentoft, Lars (2018) : Stationary threshold vector autoregressive models, Journal of Risk and Financial Management, ISSN 1911-8074, MDPI, Basel, Vol 11, Iss. 3, pp. Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen. Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte.
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