Continuous processes derived from the solution of generalized Langevin equation: theoretical properties and estimation
| Autor: | Sílvia R. C. Lopes, J. Stein, A. V. Medino |
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| Rok vydání: | 2016 |
| Předmět: |
Statistics and Probability
Class (set theory) Mathematical optimization Stochastic process Applied Mathematics 010102 general mathematics Covariance 01 natural sciences Measure (mathematics) Langevin equation 010104 statistics & probability Autocovariance Modeling and Simulation Trigonometric functions Statistical physics 0101 mathematics Statistics Probability and Uncertainty Well-defined Mathematics |
| Zdroj: | Journal of Statistical Computation and Simulation. 86:2819-2845 |
| ISSN: | 1563-5163 0094-9655 |
| Popis: | In this paper we present a class of continuous-time processes arising from the solution of the generalized Langevin equation and show some of its properties. We define the theoretical and empirical codifference as a measure of dependence for stochastic processes. As an alternative dependence measure we also consider the spectral covariance. These dependence measures replace the autocovariance function when it is not well defined. Results for the theoretical codifference and theoretical spectral covariance functions for the mentioned process are presented. The maximum likelihood estimation procedure is proposed to estimate the parameters of the process arising from the classical Langevin equation, i.e. the Ornstein–Uhlenbeck process, and of the so-called Cosine process. We also present a simulation study for particular processes arising from this class showing the generation, and the theoretical and empirical counterpart for both codifference and spectral covariance measures. |
| Databáze: | OpenAIRE |
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