Forecasting non-stationary time series by wavelet process modelling

Fryźlewicz, Piotr; Bellegem, Sébastien Van; Sachs, Rainer von

doi:10.1007/bf02523391

Cited by 93 publications

(67 citation statements)

References 18 publications

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“…We note that, in particular, Assumption 2.2 is satisfied if X t,T is the standard white noise process, for which Fryzlewicz, Van Bellegem and von Sachs (2003)]. …”

Section: Empirical Wavelet Spectrummentioning

confidence: 99%

Consistent Classification of Nonstationary Time Series Using Stochastic Wavelet Representations

Fryźlewicz

Ombao

2009

Journal of the American Statistical Association

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A method is proposed for classifying an observed non-stationary time series using a bias-corrected non-decimated wavelet transform. Wavelets are ideal for identifying highly discriminant local time and scale features. We view the observed signals as realizations of locally stationary wavelet (LSW) processes. The LSW model provides a time-scale decomposition of the signals under which we can define and rigorously estimate the evolutionary wavelet spectrum. The evolutionary spectrum, which contains the second-moment information on the signals, is used as the classification signature. For each time series to be classified, we compute the empirical wavelet spectrum and the divergence from the wavelet spectrum of each group. It is then assigned it to the group to which it is the least dissimilar. Under the LSW framework, we rigorously demonstrate that the classification procedure is consistent, i.e., misclassification probability goes to zero at the rate that is proportional to divergence between the true spectra. The method is illustrated using seismic signals and is demonstrated to work very well in simulation studies.

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“…We note that, in particular, Assumption 2.2 is satisfied if X t,T is the standard white noise process, for which Fryzlewicz, Van Bellegem and von Sachs (2003)]. …”

Section: Empirical Wavelet Spectrummentioning

confidence: 99%

Consistent Classification of Nonstationary Time Series Using Stochastic Wavelet Representations

Fryźlewicz

Ombao

2009

Journal of the American Statistical Association

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“…Concerning this book, the authors works primarily with the discontinuous Haar wavelet which in general forbids to use any of these scale-limited extrapolation techniques. Other forecasting algorithms are proposed in [1,2,9,25,32]. A book is devoted to wavelet techniques for time series analysis, see [22].…”

Section: Preprint Submitted To Elsevier Sciencementioning

confidence: 99%

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

Gosse¹

2010

Nonlinear Analysis: Real World Applications

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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.

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“…The MSE or Mean Square Prediction Error (MSPE)) is defined by [18], the time-varying auto-covariance structure (non-stationary time series) was modeled rigorously by using the wavelet transform and the concept of "local stationary" random processes [17][18] (see Subsection III.F for the definition of local stationary.) The method was then extended in [20] to model the series whose auto-covariance changes very suddenly in time.…”

Section: Wavelet Based Dpm (Wbdpm) Policymentioning

confidence: 99%