We present a new drift condition which implies rates of convergence to the stationary distribution of the iterates of a -irreducible aperiodic and positive recurrent transition kernel. This condition, extending a condition introduced by Jarner and Roberts (2002) for polynomial convergence rates, turns out to be very convenient to prove subgeometric rates of convergence. Several applications are presented including nonlinear autoregressive models, stochastic unit root models and multidimensional random walk Hastings Metropolis algorithms.

Abstract: We review the past 25 years of research into time series forecasting. In this silver jubilee issue, we naturally highlight results published in journals managed by the International Institute of Forecasters (Journal of Forecasting 1982–1985; International Journal of Forecasting 1985–2005). During this period, over one third of all papers published in these journals concerned time series forecasting. We also review highly influential works on time series forecasting that have been published elsewhere during this period. Enormous progress has been made in many areas, but we find that there are a large number of topics in need of further development. We conclude with comments on

Abstract: Intermittent demand commonly occurs with inventory data, with many time periods having no demand and small demand in the other periods. Croston’s method is a widely used procedure for intermittent demand forecasting. However, it is an ad hoc method with no properly formulated underlying stochastic model. In this paper, we explore possible models underlying Croston’s method and three related methods, and we show that any underlying model will be inconsistent with the properties of intermittent demand data. However, we find that the point forecasts and prediction intervals based on such underlying models may still be useful. Keywords: Croston’s method, exponential smoothing, forecasting, intermittent demand. 1.

We consider a class of observation-driven Poisson count processes where the current value of the accompanying intensity process depends on previous values of both processes. We show under a contractive condition that the bivariate process has a unique stationary distribution and that the stationary version of the count process is absolutely regular. Moreover, since the intensities can be written as measurable functionals of the count variables we conclude that the bivariate process is ergodic. As an important application of these results, we show how a test method previously used in the case of independent Poisson data can be used in the case of Poisson count processes.

Stochastic models underlying Croston’s method for intermittent demand forecasting

Stochastic models underlying Croston's method for