Range Of Stochastic Models Research Articles

How Stochasticity Influences Leading Indicators of Critical Transitions.

Many complex systems exhibit critical transitions. Of considerable interest are bifurcations, small smooth changes in underlying drivers that produce abrupt shifts in system state. Before reaching the bifurcation point, the system gradually loses stability ('critical slowing down'). Signals of critical slowing down may be detected through measurement of summary statistics, but how extrinsic and intrinsic noises influence statistical patterns prior to a transition is unclear. Here, we consider a range of stochastic models that exhibit transcritical, saddle-node and pitchfork bifurcations. Noise was assumed to be either intrinsic or extrinsic. We derived expressions for the stationary variance, autocorrelation and power spectrum for all cases. Trends in summary statistics signaling the approach of each bifurcation depend on the form of noise. For example, models with intrinsic stochasticity may predict an increase in or a decline in variance as the bifurcation parameter changes, whereas models with extrinsic noise applied additively predict an increase in variance. The ability to classify trends of summary statistics for a broad class of models enhances our understanding of how critical slowing down manifests in complex systems approaching a transition.

Prequential omnibus goodness-of-fit tests for stochastic processes: A numerical study

ABSTRACTThis article is a contribution to the study of an omnibus goodness-of-fit (Gof) test based on Rosenblatt Probability Integral Transform (RPIT) within Dawid's prequential framework. This Gof test is easy to use since it has a common test statistic (with apparently the same asymptotic distribution) for a wide range of stochastic models. Intensive Monte-Carlo simulations are presented to investigate the behavior of this test for several stochastic models: renewal, autoregressive (AR, ARMA, ARCH, GARCH) and Poisson processes, generalized linear models... These simulations suggest that the RPIT test could be used to test the fit of a wide range of stochastic models but it may be not powerful when compared to Gof tests specifically designed for the tested processes. It is also conjectured that this test is still appropriate for testing the Gof of any discrete-time stochastic process provided that efficient estimators are used.

An investigation into stochastic claims reserving models and the chain-ladder technique

This paper considers a range of stochastic models which give the same reserve estimates as the chain-ladder technique. The relationship between the models described by Renshaw and Verrall (Renshaw, A.E., Verrall, R.J., 1998. British Actuarial Journal 4, 903–923) and Mack (Mack, T., 1993. ASTIN Bulletin 23, 213–225) is explored in more detail than previously. Several new models are suggested and some new ways to allow for negative incremental claims for the chain-ladder technique and other claims reserving methods are put forward.