Circular Statistics and Robust Trend Channels for Trading Indicators

Summary

This article adapts angle-based analysis to trading indicators and trend estimation. For comparing two currency instruments, it scales prices into comparable point units and interprets their relative values as an angle, with the indicator intended to show relative overbought or oversold conditions. Because angles wrap around, it recommends computing their mean from sine and cosine components and estimating angular dispersion with the Yamartino method, then comparing deviations with that spread.

For price trends, the article distinguishes slope angles from angles formed by comparable measurements and fits a linear trend using the robust Theil–Sen estimator. It derives an error spread from median absolute deviations and uses that to construct trend channels and fans, described as analogous to volatility bands and possible support or resistance levels. A synthetic example contrasts the robust estimate with least squares under noise, while noting the robust method’s advantage is most relevant when errors are not normally distributed. The article offers indicator construction methods, not evidence of trading profitability.

Key ideas

• Angles between scaled currency prices can represent one instrument’s relative overbought or oversold condition against another.
• Circular means should account for wraparound, so angles near the zero-degree boundary are not averaged as if they were far apart.
• Theil–Sen estimation uses medians of pairwise slopes and intercepts to fit a trend with less sensitivity to outliers than least squares.
• Median absolute deviations from the fitted trend can define robust channels, while slope estimates can form trend fans.
• The article describes indicator designs and a synthetic comparison, but it does not demonstrate that these tools improve trading results.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.