Using Walsh Functions and Markov Chains for Trading Analysis
Summary
The article explains how Walsh functions can decompose price series into components used to study smoothing, trend, and noise. It describes using the zero-order function as an SMA-like measure and higher-order functions to estimate changes in that measure. Historical probability distributions for these changes are combined to form expected future SMA and trend values; the article says the gap between forecasts and actual values may also signal volatility or changing conditions.
It then modifies the functions to allow periods beyond powers of two and to calculate values once per bar, addressing period constraints and repainting. For a strategy concept, it proposes encoding an indicator’s up or down movement as Markov states, estimating transition probabilities from history, and using them to forecast. The examples are conceptual rather than a documented performance study. The author warns that forecasts can be inaccurate, function outputs may be ambiguous, and the number of Markov states affects predictive usefulness.
Key ideas
- Walsh functions are orthogonal components that the article uses to distinguish smoothing, trend, and noise in price series.
- The zero-order Walsh function is presented as an SMA-like measure, while higher orders describe trend and changes in trend.
- Historical probability distributions of Walsh function changes can be used to estimate future SMA or trend values.
- Modified periods and one-time bar calculations are proposed to reduce period restrictions and repainting.
- A Markov model can forecast indicator direction from estimated transitions between up and down states.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.