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

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 articles [10], [11], [12] and [13]. 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 L2(R)L2(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 Gerchberg–Papoulis (GGP) algorithm is set up which is shown to converge toward the minimum L2L2 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.