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

Abstract

To cite this version:Laurent Gosse. Analysis and short-time extrapolation of stock market indexes through projection onto discrete wavelet subspaces. Nonlinear Analysis Real World Applications, 2010Applications, , 11, pp.3139-3154. <10.1016Applications, /j.nonrwa.2009 Analysis and short-time extrapolation of stock market indexes through projection onto discrete wavelet subspaces Laurent GosseIAC-CNR "Mauro Picone" (sezione di Bari) Via Amendola 122/I -70126 Bari, Italy AbstractWe 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 [29,28,14,15]. 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 (R). 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 GerchbergPapoulis (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.

Effective band-limited extrapolation relying on Slepian series and ℓ1 regularization

“…We repeat the simple test-case of producing a 15% (i.e. α = 1.15) extrapolation of the function (14) observed in the interval [−1, 1] using the ROMP algorithm. The sparsity level has been fixed as s = 8 and a Fourier measurement matrix was used with N the integer part of s log(K) where K = 256 is the number of discretization points in [−1, 1].…”

Estimates for the SVD of the truncated Fourier transform on L2(exp(b|$\times$|)) and stable analytic continuation

“…Extrapolating an analytic square integrable function f from its observation with error on [−c, c] to R has a wide range of applications, for example in imaging and signal processing [26], in geostatistics and with big data [18], and finance [25]. A researcher may want to estimate a density from censored data.…”