Creating “Complex” price from “Real” price
Hilbert Transform, Technical Indicators November 21st. 2007, 9:52pmThere are many benefits of converting price data in complex number form. The presence of an Imaginary component gives one the freedom to create other kinds of indicators which can provide further insight into the statistical properties of the asset price. For example, indicators that fall into the categories below can only be derived from complex price data:
- Signal to Noise ratio (SNR)
- Cycle Period
- Phasor diagrams
- Predictive Indicators (i.e. filters with Negative Lag)
- Power Spectral Density of the price
A complex number takes the form
where
Real price data only have an component, aka the InPhase component. The aim is to derive the corresponding Quadrature component using the InPhase data of the price at a given bar. The Hilbert Transform provides a way of doing this, and an excellent description can be found at wikipedia.
To complement the notes we can think of the Hilbert Transform as a control system, the simplest of which looks like:
Note that represents the z-domain delay operator. It remembers its input value for
samples into the future.
We shall discuss Indicators based on Complex Price Data in due course.
