Abstract
This paper revitalizes the investigation of the classical cusp catastrophe model in catastrophe theory and tackles the unsolved statistical inference problem concerning stochastic cusp differential equation. This model is challenging because its associated transition density hence the likelihood function is analytically intractable. We propose a novel Bayesian approach combining Hamiltonian Monte Carlo with two likelihood approximation methods, namely, Euler approximation and Hermite expansion. We validate this novel approach through a series of simulation studies. We further demonstrate potential application of this novel approach using the real USD/EUR exchange rate.
2010 Mathematics Subject Classification:
Acknowledgements
The authors would like to thank the two anonymous reviewers, the associate editor and the editor-in-chief (Professor Jie Chen, Biostatistics and Data Science, Augusta University, USA) for their comments and suggestions, which have significantly improved the quality of this chapter.
Disclosure statement
No potential conflict of interest was reported by the author(s).