This volume is based on lectures presented at the AMS Special Session on Algebraic Methods in Statistics and Probability--held March 27-29, 2009, at the University of Illinois at Urbana-Champaign--and on contributed articles solicited for this volume. A decade after the publication of...

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...

Parameter estimation in nonlinear models is a common task, and one for which there is no general solution at present. In the case of linear models, the distribution of forecast errors provides a reliable guide to parameter estimation, but in nonlinear models the facts that predictability may...

Cointegrated bivariate nonstationary time series are considered in a fractional context, without allowance for deterministic trends. Both the observable series and the cointegrating error can be fractional processes. The familiar situation in which the respective integration orders are 1 and 0...

For linear processes, semiparametric estimation of the memory parameter, based on the log-periodogram and local Whittle estimators, has been exhaustively examined and their properties well established. However, except for some specific cases, little is known about the estimation of the memory...

We examine a test for the hypothesis of weak dependence against strong cyclical components. We show that the limiting distribution of the test is a Gumbel distribution, denoted G(·). However, since G(·) may be a poor approximation to the finite sample distribution, being the rate of the...

Order selection based on criteria by Akaike (IEEE Trans. Automat. Control AC-19 (1974) 716), AIC, Schwarz (Ann. Stat. (1978) 461), BIC or Hannan and Quinn's (J. R. Stat. Soc. Ser. B (1979) 190) HIC is often applied in empirical examples. They have been used in the context of order selection of...

Many medical studies involve modelling the relationship between an outcomevariable and a series of one or more continuous/interval scaled discrete explanatoryvariables. It is common practice in many of these studies for some, or indeed all, ofthe continuous/interval scaled discrete explanatory...

Financial modelling in the area of option pricing involves the understanding of the correlations between asset and movements of buy/sell in order to reduce risk in investment. Such activities depend on financial analysis tools being available to the trader with which he can make rapid and...

Successful integrated pest management (IPM) control programmes depend on many factors which include host-parasitoid ratios, starting densities, timings of parasitoid releases, dosages and timings of insecticide applications and levels of host-feeding and parasitism. Mathematical models can help...