Wavelet for time series

Question

I am trying to use wavelets coefficients as feature for neural networks on a time series data and I am bit confused on usage of the same. Do I need to find the coefficients on entire time series at once, or use a sliding window for finding the same. I mean, will finding coefficients on entire time series for once, include the future data points while determining those coefficients? What should be the approach to go about using Wavelets on a time series data without look ahead bias if any?

Answer 1

It is hard to provide you with a detailed answer without knowing what you are trying to achieve.

In a nutshell, you first need to decide whether you want to apply a discrete (DWT) or a continous (CWT) wavelet transform to your time series.

A DWT will allow you to decompose your input data into a set of discrete levels, providing you with information about the frequency content of the signal i.e. determining whether the signal contains high frequency variations or low frequency trends. Think of it as applying several band-pass filters to your input data.

I do not think that you should apply a DWT to your entire time series at once. Since you are working with financial data, maybe decomposing your input signal into 1-day windows and applying a DWT on these subsets would do the trick for you.

In any case, I would suggest:

• Installing the pywt toolbox and playing with a dummy time series to understand how wavelet decomposition works.
• Checking out the abundant literature available about wavelet analysis of financial data. For instance, if you are interested into financial time series forecasting, you might want to read this paper.
• Posting your future questions on the DSP stack exchange, unless you have a specific coding-related answer.