Stochastic cusp catastrophe model and its Bayesian computations

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.