Rademacher Functions for Trend Filtering, Forecasts, and State Modeling
Summary
The article explores Rademacher functions as tools for analyzing noisy price series. It describes using an expanded function period to smooth trend components, then combining function levels into a price filter whose values depend on both prices and their order. It also proposes estimating empirical distributions for function values: a cumulative distribution can frame possible trend exhaustion near its extremes and trend confirmation around its midpoint. A related procedure uses the distribution of first-order function changes to form forecast bands for a moving average.
For a more complex forecast, the author builds an oscillator from deviations between price and smoothed Rademacher levels, classifies market conditions as uptrend, flat, or downtrend, and uses a Markov transition matrix to project states and inform a trading strategy. The article says the strategy tests were encouraging, but the supplied text gives no quantitative performance results or validation details. It also acknowledges that the functions are incomplete, have constrained periodicity, and that window updates can make the oscillator repaint, so the methods remain experimental.
Key ideas
- Rademacher function periods can be expanded to smooth trend signals and reduce sensitivity to noise.
- A price filter based on function levels reflects the sequence order as well as the observed prices.
- Empirical distributions and cumulative probabilities are used to construct trend cues and moving average forecast bands.
- A Rademacher oscillator can be paired with Markov transitions among trend, flat, and downtrend states.
- The approach has constraints, including incomplete reconstruction, periodicity limits, repainting behavior, and unquantified test claims.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.