Using the Discrete Hartley Transform to Filter Financial Time Series
Summary
The article introduces the discrete Hartley transform (DHT) as a real-valued method for moving a discrete signal between time and frequency representations. It applies DHT to price series, where individual harmonics can be removed, attenuated, selected by strength, or sign-reversed before reconstructing a filtered signal. Examples include smoothing prices by suppressing higher frequencies and processing prices through an indicator's frequency response. It also outlines constructing indicator coefficients from a desired spectrum, with a proposed spectrum-matched indicator intended to lag less than a moving average.
The article extends the discussion to colored noise, relating different spectral energy distributions to market movement characteristics and describing how to build noise levels and indicators from those spectra. These are signal-processing concepts and indicator construction examples, rather than evidence of a predictive trading edge. Claims about trends, ranges, hidden patterns, or improved forecasting are presented as possible uses; the supplied material does not provide rigorous out-of-sample performance tests or trading results.
Key ideas
- DHT represents real-valued time series in a real-valued frequency domain and supports inverse reconstruction.
- Removing or reducing selected harmonics can smooth price data before applying conventional indicators.
- An indicator's frequency response can filter a price spectrum, while a chosen spectrum can be transformed into indicator coefficients.
- Colored-noise spectra offer a way to describe frequency-dependent energy in market movements and to build related indicators.
- The proposed market applications are exploratory signal processing and are not validated evidence of trading profitability.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.