CEU Electronic Theses and Dissertations, 2014
| Author | Mánfay, Máté |
|---|---|
| Title | Identification of stochastic systems driven by L\'evy processes |
| Summary | The research carried out in this thesis is motivated by my interest in the analysis of financial time series. From the technical point of view we study the identification of discrete time stochastic systems driven by the increments of Lévy processes. As an alternative to the maximum likelihood method we develop and analyze a novel identification method by adapting the so-called empirical characteristic function method originally devised for estimating parameters of characteristic functions from i.i.d. samples. First of all, we present an essentially asymptotically efficient three-stage identification method for the system and noise parameters of stable and inverse stable linear systems. Then we present an alternative extension of the empirical characteristic function (ECF) method applicable for stable, but possibly not inverse stable linear stochastic systems. Thirdly, we propose an essentially asymptotically efficient estimation method for the system parameters of general autoregressive conditional heteroscedasticity (GARCH) processes. For each of the above problems we precisely characterize the estimation error in the form of martingale representation theorems. After that we develop recursive estimation methods for stable and inverse stable linear systems along the line of arguments applied for the off-line identification of linear systems. Finally, we discuss a particular technical problem, the stability of time-varying stochastic systems driven or modulated by a Lévy process with discrete time interventions, such as parameter resettings |
| Supervisor | Gerencsér, László |
| Department | Mathematics PhD |
| Full text | https://www.etd.ceu.edu/2014/manfay_mate.pdf |
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