Stochastic cusp catastrophe model and its Bayesian computations

Fundamental and speculative components of the cryptocurrency pricing dynamics

“…Diks and Wang (2016) applied an alternative numerical method to that of Cobb (1978), which is based on Euler discretization to approximate the model dynamics and obtain estimates of the parameters using nonlinear least squares. Recently, there has been an innovative attempt at Bayesian estimation of this model by Chen et al (2021). However, the "industry standard" used in this study is the cusp package version 2.3.3, available in R (Grasman et al 2009), which implements and extends the method in Cobb et al (1983).…”

“…Most recently, Kukacka and Kristoufek (2020) studied the complexity of nine financial agent-based models, including the cusp, and Kukacka and Kristoufek (2021) extended this research topic with a sensitivity analysis concerning model parameter settings. Chen et al (2021) developed an innovative Bayesian approach based on two different likelihood approximations and estimated the cusp catastrophe model using USD/EUR exchange rate data. Finally, Lux (2021) estimated cusp as a benchmark model using monthly S &P 500 data until 2015 to explain index mispricing compared to the ex-post rational price.…”

Bayesian Inference for Stochastic Cusp Catastrophe Model with Partially Observed Data

“…Under the partial observations scenario, data points are assumed to be observed more sparsely in time than the complete observations scenario studied by the work of [11]. Figure 1 is a simulated sample trajectory of stochastic cusp catastrophe model with parameters α = 1, β = 3.…”

“…In our recent work, we proposed a Bayesian approach inference method that combines Hamiltonian Monte Carlo with two different transition density approximation methods, namely Euler method and Hermite expansion [11]. By extensive simulation studies and empirical example, we showed that the proposed methods achieved satisfactory results in statistical inference to stochastic cusp catastrophe models with different model parameter settings.…”

“…To better illustrate the contributions of this paper, including how this paper addresses a different problem from our recent work [11], Figure 1 shows a sample trajectory of stochastic cusp catastrophe model with parameters α = 1, β = 3. The upper plot is a sample trajectory assuming no missing values, and our recent work [11] has addressed the statistical inference problem under this so-called "complete" observations settings. The lower plot is the same sample trajectory assuming missing values.…”