Original title:
Bimodality testing of the stochastic cusp model
Authors:
Voříšek, Jan Document type: Papers Conference/Event: Mathematical Methods in Economics 2015 /33./, Cheb (CZ), 2015-09-09 / 2015-09-11
Year:
2015
Language:
eng Abstract:
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.
Keywords:
multimodal distributions; statistical bimodality test; stochastic cusp model Project no.: GA402/09/0965 (CEP) Funding provider: GA ČR Host item entry: Procedings of the 33rd International Conference Mathematical Methods in Economics MME 2015, ISBN 978-80-261-0539-8