The paper refines Lenk’s concept of improving the performance of the computed harmonic mean estimator (HME) in three directions. First, the adjusted HME is derived from an exact analytical identity. Second, Lenk’s assumption concerning the appropriate subset A of the parameter space is significantly weakened. Third, it is shown that, under certain restrictions imposed on A, a fundamental identity underlying the HME also holds for improper prior densities, which substantially extends applicability of the adjusted HME.
News might trigger jump arrivals in financial time series. The “bad” news and “good” news seem to have distinct impact. In the research, a double exponential jump distribution is applied to model downward and upward jumps. Bayesian double exponential jump-diffusion model is proposed. Theorems stated in the paper enable estimation of the model’s parameters, detection of jumps and analysis of jump frequency. The methodology, founded upon the idea of latent variables, is illustrated with simulated data.
A Bayesian stochastic volatility model with a leverage effect, normal errors and jump component with the double exponential distribution of a jump value is proposed. The ready to use Gibbs sampler is presented, which enables one to conduct statistical inference. In the empirical study, the SVLEDEJ model is applied to model logarithmic growth rates of one month forward gas prices. The results reveal an important role of both jump and stochastic volatility components.