Stationary‐Increment Variance‐Gamma and t Models: Simulation and Parameter Estimation

Abstract

Summary We detail a method of simulating data from long range dependent processes with variance‐gamma or t distributed increments, test various estimation procedures [method of moments (MOM), product‐density maximum likelihood (PMLE), non‐standard minimumχ2and empirical characteristic function estimation] on the data, and assess the performance of each. The investigation is motivated by the apparent poor performance of the MOM technique using real data (Tjetjep & Seneta, 2006); and the need to assess the performance of PMLE for our dependent data models. In the simulations considered the product‐density method performs favourably.

Bayesian Inference on the Memory Parameter for Gamma-Modulated Regression Models

“…Observe, in the first scatterplot, the sharp and negative posterior correlation between α and τ , as expected by Equation (3). Furthermore, the e-values for the hypotheses α 0 = −0.5 and α 0 = 0 are clearly zero, as confirmed by both graphs.…”

“…It is worth noting the symmetry of the sampling distribution of the posterior mean for µ, as well as the asymmetry of the sampling distribution of the posterior mean for τ , as it was supposed to be by Equation (3). Furthermore, the estimates are consistent around the nominal value.…”

“…Many extensions to the classic diffusion model have been developed in recent years, addressing such diverse issues as asymmetry, kurtosis, heteroscedasticity and long memory; see, for instance, [3].…”

Guaranteed stop orders as portfolio insurance – An analysis for the German stock market

“…Following Cont and Tankov (2004), there are two main approaches: the method of moments (MoM) and the maximum likelihood estimation. Recently, Finlay and Seneta (2008) have shown that the minimum χ 2 procedure produces an acceptable approximation of the marginal distribution in connection with a low calculation time. The χ 2 procedure corresponds to the goodness-of-fit test of the same name and tries to minimize the squared difference between observed absolute frequency and the number of observations derived from the theoretical probability.…”

“…According to Finlay and Seneta (2008), we split the data set into 100 equal-sized sample bands. Owing to the different time series, we fitted the overnight parameters (c ON , θ ON , κ ON , σ ON ) and the intraday parameters (c ID , θ ID , κ ID , σ ID ) separately (for example, the dot at c stands for either ON or ID) ( Table 1).…”