We use the Cox process (or a doubly stochastic Poisson process) to model the claim arrival process for catastrophic events. The shot noise process is used for the claim intensity function within the Cox process. The Cox process with shot noise intensity is examined by piecewise deterministic...

This paper presents a Markov chain Monte Carlo algorithm for a class of multivariate diffusion models with unobserved paths. This class is of high practical interest as it includes most diffusion driven stochastic volatility models. The algorithm is based on a data augmentation scheme where the...

The aim of an experiment is often to enable discrimination between competing forms for a response model. We consider this problem when there are two competing generalized linear models (GLMs) for a binomial response. These models are assumed to have a common link function with the linear...

We introduce a new point process, the dynamic contagion process, by gener- alising the Hawkes process and the Cox process with shot noise intensity. Our process includes both self-excited and externally excited jumps, which could be used to model the dynamic contagion impact from endogenous and...

Motivated by prediction problems for time series with heavy-tailed marginal distributions, we consider methods based on `local least absolute deviations' for estimating a regression median from dependent data. Unlike more conventional `local median' methods, which are in effect based on locally...

We investigate the time-varying ARCH (tvARCH) process. It is shown that it can be used to describe the slow decay of the sample autocorrelations of the squared returns often observed in financial time series, which warrants the further study of parameter estimation methods for the model. Since...

We consider a locally stationary model for financial log-returns whereby the returns are independent and the volatility is a piecewise-constant function with jumps of an unknown number and locations, defined on a compact interval to enable a meaningful estimation theory. We demonstrate that the...

The generalized varying coefficient partially linear model with growing number of predictors arises in many contemporary scientific endeavor. In this paper we set foot on both theoretical and practical sides of profile likelihood estimation and inference. When the number of parameters grows with...

We propose two new types of nonparametric tests for investigating multivariate regression functions. The tests are based on cumulative sums coupled with either minimum volume sets or inverse regression ideas; involving no multivariate nonparametric regression estimation. The methods proposed...

This paper concerns statistical tests for simple structures such as parametric models, lower order models and additivity in a general nonparametric autoregression setting. We propose to use a modified L2-distance between the nonparametric estimator of regression function and its counterpart...