Non-linear Functional Approximation of Heterogeneous Dynamics
نویسنده
چکیده
In modeling phenomena continuously observed and/or sampled at discrete time sequences, on problem is that often dynamics come from heterogeneous sources of uncertainty. This turns out particularly challenging with a low signal-to-noise ratio, due to the structural or experimental conditions; for instance, information appears dispersed in a wide spectrum of frequency bands or resolution levels. We aim to design ad hoc approximation instruments dealing with a particularly complex class of random processes, the one that generates financial returns, or their aggregates as index returns. The underlying volatility function is subject to the signature of noise and the masking effect of non-stationary superimposed dynamics, together with multiscaling regimes. Due to the unobserved nature of the volatility function, its recovery represents an inverse problem that can be cast in a latent variable model designed to account for both switching multi-scaling regimes and cascade system dynamics. We emphasize the role of independent component analysis, or ICA, for achieving dimensionality reduction of the addressed inverse problem, and also stress the relevance of atomic functional dictionaries in improving the volatility feature detection power. Then we show the good performance of greedy approximation algorithms in delivering sparse representations and coherent decompositions of the return sequences. keywords: Cascade Systems; Non-linear Sparse and Greedy Approximation; Independent Component Analysis; Multi-scaling; Volatility Recovery.
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تاریخ انتشار 2005