Using Random Quasi-Monte-Carlo Within Particle Filters, With Application to Financial Time Series.

This article presents a new particle filter algorithm which uses random quasi-Monte-Carlo to propagate particles. The filter can be used generally, but here it is shown that for one-dimensional state-space models, if the number of particles is N, then the rate of convergence of this algorithm is N−1. This compares favorably with the N−1/2 convergence rate of standard particle filters. The computational complexity of the new filter is quadratic in the number of particles, as opposed to the linear computational complexity of standard methods. I demonstrate the new filter on two important financial time series models, an ARCH model and a stochastic volatility model. Simulation studies show that for fixed CPU time, the new filter can be orders of magnitude more accurate than existing particle filters. The new filter is particularly efficient at estimating smooth functions of the states, where empirical rates of convergence are N−3/2; and for performing smoothing, where both the new and existing filters have the same computational complexity

Seasonality, density dependence, and population cycles in Hokkaido voles

Voles and lemmings show extensive variation in population dynamics regulated across and within species. In an attempt to develop and test generic hypotheses explaining these differences, we studied 84 populations of the gray-sided vole (Clethrionomys rufocanus) in Hokkaido, Japan. We show that these populations are limited by a combination of density-independent factors (such as climate) and density-dependent processes (such as specialist predators). We show that density-dependent regulation primarily occurs in winter months, so that populations experiencing longer winters tend to have a stronger delayed density-dependence and, as a result, exhibit regular density cycles. Altogether, we demonstrate that seasonality plays a key role in determining whether a vole population is cyclic or not