Bimodality testing of the stochastic cusp model

0507386 - ÚTIA 2020 RIV CZ eng C - Konferenční příspěvek (zahraniční konf.)
Voříšek, Jan
Bimodality testing of the stochastic cusp model.
Procedings of the 33rd International Conference Mathematical Methods in Economics MME 2015. Plzeň: University of West Bohemia, Plzeň, 2015, s. 888-893. ISBN 978-80-261-0539-8.
[Mathematical Methods in Economics 2015 /33./. Cheb (CZ), 09.09.2015-11.09.2015]
Grant CEP: GA ČR GA402/09/0965
Institucionální podpora: RVO:67985556
Klíčová slova: multimodal distributions * stochastic cusp model * statistical bimodality test
Obor OECD: Statistics and probability
http://library.utia.cas.cz/separaty/2019/E/vorisek-0507386.pdf

Multimodal distributions are popular in many areas: biology (fish and shark population), engineering (material collapse under pressure, stability of ships), psychology (attitude transitions), physics (freezing of water) etc. There were a few attempts to utilize multimodal distributions in financial mathematics as well. Cobb et al. described a class of multimodal distributions belonging to the exponential family, which has unique maximum likelihood estimators and showed a connection to the stationary distribution of the stochastic cusp catastrophe model. Moreover was shown, how to identify bimodality for given parameters of the stochastic cusp model using the sign of Cardans discriminant. A statistical test for bimodality of the stochastic cusp model using maximum likelihood estimates is proposed in the paper as well as the necessary condition for bimodality which can be used for s simplified testing to reject bimodality. By proposed methods is tested the bimodality of exchange rate between USD and GBP in the periods within the years 1975 - 2014.
Trvalý link: http://hdl.handle.net/11104/0298682