Ensemble prediction systems aim to account for uncertainties of initial conditions and model error. Ensemble forecasting is sometimes viewed as a method of obtaining (objective) probabilistic forecasts. How is one to judge the quality of an ensemble at forecasting a system? The probability that...

Presents a latent trait and a latent class model for analyzing the relationships among a set of mixed manifest variables using 1 or more latent variables. The set of manifest variables contains metric (continuous or discrete) and binary items. For the latent trait model the latent variables are...

We consider local least absolute deviation (LLAD) estimation for trend functions of time series with heavy tails which are characterised via a symmetric stable law distribution. The setting includes both causal stable ARMA model and fractional stable ARIMA model as special cases. The asymptotic...

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 semiparametric local Whittle or Gaussian estimate of the long memory parameter is known to have especially nice limiting distributional properties, being asymptotically normal with a limiting variance that is completely known. However in moderate samples the normal approximation may not be...

Semiparametric estimates of long memory seem useful in the analysis of long financial time series because they are consistent under much broader conditions than parametric estimates. However, recent large sample theory for semiparametric estimates forbids conditional heteroskedasticity. We show...

Forecast evaluation based on single predictions, each determined from an imperfectly observed initial state, is incomplete; observational uncertainty implies that an ensemble of initial states of the system is consistent with a given observation. In a nonlinear system, this initial distribution...

It is now generally recognized that very simple dynamical systems can produce apparently random behaviour. Attention has recently turned to focus on the flip-side of this coin: random-looking time series (or random-looking patterns in space) may indeed be the result of very complicated processes...

The self-consistent prediction of nonlinear, potentially chaotic, systems must account for observational noise both when constructing the model and when determining the current state of the system to be used as `the' initial condition. In fact, there exists an ensemble of initial states of the...

We introduce a new point process, the dynamic contagion process, by generalising the self excited Hawkes process (with exponential decay) by Hawkes (1971) and the Cox process with shot noise intensity by Dassios and Jang (2003). Our process includes both self excited and externally excited...