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Analysis and short-time extrapolation of stock market indexes through projection onto discrete wavelet subspaces

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  • Laurent Gosse

    (IAC - Istituto per le Applicazioni del Calcolo "Mauro Picone" - CNR - National Research Council of Italy | Consiglio Nazionale delle Ricerche)

Abstract

We consider the problem of short-time extrapolation of blue chips' stocks indexes in the context of wavelet subspaces following the theory proposed by X.-G. Xia and co-workers in a series of papers \cite{XLK,XKZ,LK,LXK}. The idea is first to approximate the oscillations of the corresponding stock index at some scale by means of the scaling function which is part of a given multi-resolution analysis of $L^2(\Re)$. Then, since oscillations at a finer scale are discarded, it becomes possible to extend such a signal up to a certain time in the future; the finer the approximation, the shorter this extrapolation interval. At the numerical level, a so--called Generalized Gerchberg-Papoulis (GGP) algorithm is set up which is shown to converge toward the minimum $L^2$ norm solution of the extrapolation problem. When it comes to implementation, an acceleration by means of a Conjugate Gradient (CG) routine is necessary in order to obtain quickly a satisfying accuracy. Several examples are investigated with different international stock market indexes.

Suggested Citation

  • Laurent Gosse, 2010. "Analysis and short-time extrapolation of stock market indexes through projection onto discrete wavelet subspaces," Post-Print hal-00414210, HAL.
    • Handle: RePEc:hal:journl:hal-00414210
    DOI: 10.1016/j.nonrwa.2009.11.009
    Note: View the original document on HAL open archive server: https://hal.science/hal-00414210
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    References listed on IDEAS

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    1. Miguel A. Ario, "undated". "Forecasting Time Series via Discrete Wavelet Transform," Computing in Economics and Finance 1996 _005, Society for Computational Economics.
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    Cited by:

    1. Gautier, Eric & Gaillac, Christophe, 2019. "Estimates for the SVD of the Truncated Fourier Transform on L2(cosh(b.)) and Stable Analytic Continuation," TSE Working Papers 19-1013, Toulouse School of Economics (TSE).

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