Theil-Sen Line Filter [BackQuant]

Theil-Sen Line Filter [BackQuant]
A robust, median-slope baseline that tracks price while resisting outliers. Designed for the chart pane as a clean, adaptive reference line with optional candle coloring and slope-flip alerts.

What this is
A trend filter that estimates the underlying slope of price using a Theil-Sen style median of past slopes, then advances a baseline by a controlled fraction of that slope each bar. The result is a smooth line that reacts to real directional change while staying calm through noise, gaps, and single-bar shocks.

Why Theil-Sen
Classical moving averages are sensitive to outliers and shape changes. Ordinary least squares is sensitive to large residuals. The Theil-Sen idea replaces a single fragile estimate with the median of many simple slopes, which is statistically robust and less influenced by a few extreme bars. That makes the baseline steadier in choppy conditions and cleaner around regime turns.

What it plots

• Filtered baseline that advances by a fraction of the robust slope each bar.
  
• Optional candle coloring by baseline slope sign for quick trend read.
  
• Alerts when the baseline slope turns up or down.
  

How it behaves (high level)

• Looks back over a fixed window and forms many “current vs past” bar-to-bar slopes.
  
• Takes the median of those slopes to get a robust estimate for the bar.
  
• Optionally caps the magnitude of that per-bar slope so a single volatile bar cannot yank the line.
  
• Moves the baseline forward by a user-controlled fraction of the estimated slope. Lower fractions are smoother. Higher fractions are more responsive.
  

Inputs and what they do

• Price Source — the series the filter tracks. Typical is close; HL2 or HLC3 can be smoother.
  
• Window Length — how many bars to consider for slopes. Larger windows are steadier and slower. Smaller windows are quicker and noisier.
  
• Response — fraction of the estimated slope applied each bar. 1.00 follows the robust slope closely; values below 1.00 dampen moves.
  
• Slope Cap Mode — optional guardrail on each bar’s slope:
  None — no cap.
  ATR — cap scales with recent true range.
  Percent — cap scales with price level.
  Points — fixed absolute cap in price points.
  
• ATR Length / Mult, Cap Percent, Cap Points — tune the chosen cap mode’s size.
  
• UI Settings — show or hide the line, paint candles by slope, choose long and short colors.
  

How to read it

• Up-slope baseline and green candles indicate a rising robust trend. Pullbacks that do not flip the slope often resolve in trend direction.
  
• Down-slope baseline and red candles indicate a falling robust trend. Bounces against the slope are lower-probability until proven otherwise.
  
• Flat or frequent flips suggest a range. Increase window length or decrease response if you want fewer whipsaws in sideways markets.
  

Use cases

• Bias filter — only take longs when slope is up, shorts when slope is down. It is a simple way to gate faster setups.
  
• Stop or trail reference — use the line as a trailing guide. If price closes beyond the line and the slope flips, consider reducing exposure.
  
• Regime detector — widen the window on higher timeframes to define major up vs down regimes for asset rotation or risk toggles.
  
• Noise control — enable a cap mode in very volatile symbols to retain the line’s continuity through event bars.
  

Tuning guidance

• Quick swing trading — shorter window, higher response, optionally add a percent cap to keep it stable on large moves.
  
• Position trading — longer window, moderate response. ATR cap tends to scale well across cycles.
  
• Low-liquidity or gappy charts — prefer longer window and a points or ATR cap. That reduces jumpiness around discontinuities.
  

Alerts included

• Theil-Sen Up Slope — baseline’s one-bar change crosses above zero.
  
• Theil-Sen Down Slope — baseline’s one-bar change crosses below zero.
  

Strengths

• Robust to outliers through median-based slope estimation.
  
• Continuously advances with price rather than re-anchoring, which reduces lag at turns.
  
• User-selectable slope caps to tame shock bars without over-smoothing everything.
  
• Minimal visuals with optional candle painting for fast regime recognition.
  

Notes
This is a filter, not a trading system. It does not account for execution, spreads, or gaps. Pair it with entry logic, risk management, and higher-timeframe context if you plan to use it for decisions.