We introduce a dynamic Skellam model that measures stochastic volatility from high-frequency tick-by-tick discrete stock price changes. The likelihood function for our model is analytically intractable and requires Monte Carlo integration methods for its numerical evaluation. The proposed...

Locally explosive behavior is observed in many economic and financial time series when bubbles are formed. We introduce a time-varying parameter model that is capable of describing this behavior in time series data. Our proposed model can be used to predict the emergence, existence and burst of...

We introduce a dynamic statistical model for Skellam distributed random variables. The Skellam distribution can be obtained by taking differences between two Poisson distributed random variables. We treat cases where observations are measured over time and where possible serial correlation is...

We introduce conditional score residuals and provide a general framework for the diagnostic analysis of time series models. A key feature of conditional score residuals is that they account for the shape of the conditional distribution. These residuals offer reliable and powerful diagnostic...

We propose a new methodology for designing flexible proposal densities for the joint posterior density of parameters and states in a nonlinear, non-Gaussian state space model. We show that a highly efficient Bayesian procedure emerges when these proposal densities are used in an independent...