Procedings of the 33rd International Conference Mathematical Methods in Economics MME 2015. - Plzeň : University of West Bohemia, Plzeň, 2015
- ISBN 978-80-261-0539-8
Pages
s. 888-893
Number of pages
6 s.
Publication form
Online - E
Action
Mathematical Methods in Economics 2015 /33./
Event date
09.09.2015-11.09.2015
VEvent location
Cheb
Country
CZ - Czech Republic
Event type
EUR
Language
eng - English
Country
CZ - Czech Republic
Keywords
multimodal distributions ; stochastic cusp model ; statistical bimodality test
Subject RIV
BB - Applied Statistics, Operational Research
OECD category
Statistics and probability
R&D Projects
GA402/09/0965 GA ČR - Czech Science Foundation (CSF)
Institutional support
UTIA-B - RVO:67985556
UT WOS
000387898900152
Annotation
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.
