I wish to start discussing wavelets, which is yet another branch of signal processing that has had success in feature extraction and volatility forecasting for time series. I suggest the following three excellent books for the reader who is interested in wavelets:
Additionally there are numerous web resources on wavelets and the like, with about two million hits via google search.
In addition to Matlab, The Mathworks offer a product called Simulink which is a design platform for implementing and testing model-based systems. Most of my experience using Simulink borders on modelling Control Systems and DSP architectures. However, as the Mathworks have pointed out in a recent webinar, Simulink can be extended to develop and test finance based models such as a trading system or sub-systems that form part of a larger model.
I decided to implemented a Hilbert Transformer model for price data using Simulink which is shown below:
The model has input “simin” which takes the price data from the matlab workspace as discrete points one at a time and applies unit delay (represented by “1/Z”) and gain which is basically multiplication by the shown number. Individual Real and Complex parts are combined to create complex numbers which is then outputted to the workspace.
Simply put, the Hilbert Transform converts price data into complex number form so that one may go about calculating different measures that are not possible to calculate using just the price itself. My previous post mentions measures that are calculated using hilbert transformed price. The relationship between the actual price and the hilbert transformed price is
for a hilbert price
.
As one would expect the model implemented above suffers lag. This is confirmed by comparing the Actual price with the price reconstructed from the hilbert complex numbers:
The model does not induce any loss or gain in magnitude, but there is a lag of 4 bars. This implies that the hilbert price for the current bar actually corresponds to the price 4 bars ago - something we should consider when using hilbert prices to deduce other measures.
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