1. Copulas related to piecewise monotone functions of the interval and associated processes.
- Author
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Pumi, Guilherme and Lopes, Sílvia R. C.
- Subjects
- *
COPULA functions , *MONOTONE operators , *INTERVAL analysis , *STOCHASTIC processes , *ITERATIVE methods (Mathematics) - Abstract
In this work, we derive the copulas related to vectors obtained from the so-called chaotic stochastic processes. These are defined by the iteration of certain piecewise monotone functions of the interval [0, 1] to some initial random variable. We study some of its properties and present some examples. Since often these types of copulas do not have closed formulas, we provide a general approximation method which converges uniformly to the true copula. Our results cover a wide class of processes, including the so-called Manneville–Pomeau processes. The general theory is applied to the parametric estimation in certain chaotic processes. A Monte Carlo simulation study is also presented. [ABSTRACT FROM PUBLISHER]
- Published
- 2017
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