Wavelet packet transfer function modelling of nonstationary time series

Some New Methods for Prediction of Time Series by Wavelets

Extended Abstract. Forecasting is one of the most important purposes of time series analysis. For many years, classical methods were used for this aim. But these methods do not give good performance results for real time series due to non-linearity and non-stationarity of these data sets. On one hand, most of real world time series data display a time-varying second order structure. On th...

Wavelet packet modelling of nonstationary time series

This article models the relationship between a response time series, fYtgt2Zand an explanatory time series fXtgt2Z. We hope that any model we choose might be interesting in its own right but we shall also be interested in using it to predict future values of Yt from future values of Xt. When both time series fall into the class of ARMA type models then it is appropriate to use \transfer functio...

Wavelet packet modelling of nonstationary time seriesGuy

Statistical modelling of time series using non-decimated wavelet representations

This article proposes the use of time-ordered non-decimated wavelet or nondecimated wavelet packet transforms to provide flexible representations of a time series (explanatory). The resulting representations are then used as variables in a statistical model to provide predictions of another (response) time series. The statistical model provides valuable information about which components in the...

Spectral Correction for Locally Stationary Shannon Wavelet Processes

It is well-known that if a time series is not sampled at a fast enough rate to capture all the high frequencies then aliasing may occur. Aliasing is a distortion of the spectrum of a series which can cause severe problems for time series modelling and forecasting. The situation is more complex and more interesting for nonstationary series as aliasing can be intermittent. Recent work has shown t...