Applied Probability and Time Series Modelling

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DMS-0308109PI: Peter J. BrockwellTitle: Applied probability and Time Series modeling Abstract:Properties and applications in finance of Levy-driven linear and non-linear continuous-time autoregressive-moving average (ARMA) processes will be investigated. Questions concerning existence of stationary solutions for non-linear continuous-time models and relations between discrete-time models and their continuous-time analogues will also be addressed. In discrete time, the stochastic stability of generalized linear versions of ARMA models will be studied with a view to modeling time series of counts. Efficient estimation techniques for these models and for all-pass models driven by non-Gaussian noise will be developed. The results for the latter processes will be applied to the problem of identification and estimation for non-causal and/or non-invertible ARMA models. In the last decade there has been a widely recognized need for the development of new models and techniques for the analysis of time-series data from scientific, engineering, biomedical and financial applications. Major features giving rise to this need include non-linearity, complex dependence structures and strong deviations from normality, with discrete-valued data arising in many genetic and biomedical applications. In financial applications there is a need for continuous-time models exhibiting these characteristics. The proposal addresses these needs, with the goal of enhancing scientific understanding of the physic and economic processes represented by the models.