Contents
1. Daily exchange rate values to date (currently from 1 Jan. 2004).
2. Entropy filtered data.
3. One day ahead forecast.
This web page is recreated each day at 06:00 local time.

Some References

• F. Murtagh, J.L. Starck and O. Renaud, On neuro-wavelet modeling, Journal of Decision Support Systems, special issue Data Mining for Financial Decision Making, 37, 475-484, 2004.
• O. Renaud, J.-L. Starck, F. Murtagh, Prediction Based on a Multiscale Decomposition, International Journal of Wavelets, Multiresolution and Information Processing, Vol. 1, No. 2, 1-16, 2003. Abstract (and access to journal site).
• O. Renaud, J.-L. Starck, F. Murtagh, Wavelet-based combined signal filtering and prediction, IEEE Transactions on Systems, Man, and Cybernetics, B - Cybernetics, 2005, in press.

1. Daily exchange rate values. This is the data we are analyzing. There is an additional value each day. The abscissa on the plot is the day number. The ordinate is the number of Euros corresponding to 1 US dollar.

2. Filtered data. This is based on optimizing the separation of signal and noise at the different resolution levels of an à trous wavelet transform. Gaussian noise is assumed and the optimization uses an entropy characterization of signal and noise. (Signal modeled as stationary here.)

3. Forecast. This is based on an MAR (multiresoludionn autoregressive) model of the entropy-filtered data stream, with automatic estimate of AR order. Note that filtering is not used here (cf. Renaud et al., 2005) - the forecast is based on the Haar à trous wavelet transform only. Our one-step ahead forecast of the number of EUR corresponding to 1 USD is: