Adaptive Trend Estimation with Recursive Least Squares

Summary

The article develops an online linear regression estimator for tracking price slope and producing a one-bar-ahead forecast. Recursive Least Squares (RLS) updates the coefficient estimate and inverse covariance state with each new observation, avoiding the repeated full-window recalculation used by ordinary least squares. The author presents two indicator outputs: a forecast line on the price chart and a signed slope histogram that can help describe trend direction, acceleration, or possible fading momentum.

A forgetting factor controls how quickly older observations lose influence, with an effective-window interpretation offered to guide selection. The article explains initialization and the recursive update, and describes a test against a noise-free linear sequence to check recovery of known coefficients. These are implementation and estimator checks, not evidence of trading profitability. The indicators are framed as measurements to combine with separate decision rules, and the fixed two-feature implementation does not directly generalize to arbitrary regressors.

Key ideas

• RLS updates a linear trend model incrementally at constant work per observation, rather than rebuilding a rolling regression.
• The forgetting factor controls the balance between responsiveness to recent prices and stability from older data.
• The estimator provides both a one-step forecast and a slope measure that can support trend analysis.
• A synthetic linear-sequence check verifies implementation behavior but does not validate a trading strategy.
• The indicators describe trend conditions and are not presented as standalone entry signals.

Tags

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