Advanced Linear Regression Channels with OLS & T-Critical Bands — Strategy by asifhkin
By asifhkin
Performance Metrics
- Author: asifhkin
- Symbol: BITSTAMP:BTCUSD
- Timeframe: 15 minutes
- Win Rate: 47.4%
- Profit Factor: 1.135
Description
OverviewStandard channel indicators often rely on simple, static standard deviations or lagging moving averages that fail to adapt to changing market volatility. This strategy utilizes a highly sophisticated quantitative approach to map out price boundaries: it manually calculates Ordinary Least Squares (OLS) Regression in real-time and pairs it with an accurate inverse normal distribution and Student's t-critical approximation.By calculating dynamic confidence and prediction intervals based on degrees of freedom ($n - 2$), this script creates a statistically sound framework for both Mean Reversion and Breakout trading.How It Works: The MathematicsThe script avoids built-in approximations and instead evaluates the statistical properties of the price series over your chosen lookback window ($n$): OLS Regression Baseline (Yellow Line): This represents the line of best fit for the asset's price within the lookback window, calculating the exact sample means ($\bar{x}, \bar{y}$), sum of squares ($S_{xx}$), and covariance ($S_{xy}$). Confidence Bands (Teal Lines): These intervals estimate the range in which the true population regression line lies. Prediction Bands (Fuchsia Lines): These intervals are wider than the confidence bands because they account for both the uncertainty of the regression line and the variance of individual future data points. The script evaluates these either at the current "Edge" or calculates a "One-Step-Ahead" boundary.The Built-In Trading FrameworkTo prevent the classic pitfalls of basic channel indicators, this strategy integrates an institutional-grade modular filter system:1. Macro Trend Filter (MTF)Mean reversion strategies inherently struggle in strong, one-sided trending markets. When toggled on, the script looks at a Higher Timeframe (HTF) EMA (e.g., 4-Hour or Daily) to determine macro market structure. It will completely block short positions in a macro uptrend and block long positions in a macro downtrend.2. Volume Surge FilterFor Breakout mode, false breakouts are filtered out by requiring a volume expansion. A breakout is only triggered if the breakout bar's volume is at least 1.5x higher than its 20-period Simple Moving Average.3. Dynamic ATR Trailing StopIn addition to the standard band-based stop loss, users can activate a trailing stop driven by the Average True Range (ATR). This locks in profits adaptively as price moves in your favor, protecting capital before a counter-trend reversal occurs.4. Real-Time Performance DashboardAn on-chart UI table tracks your strategy's exact statistics (Total Trades, Win Rate, and Net Profit) in real-time based on your current chart settings, allowing for rapid parameter optimization without constantly switching tabs.Recommended Strategy RulesMode A: Macro-Aligned Mean ReversionMarket Environment: High-liquidity assets (EURUSD, XAUUSD, BTCUSD).Timeframe: 15-Minute (15m) or 1-Hour (1H).Lookback (len): 100 or 150.Macro Trend Filter: ON (HTF set to 240 for the 15m chart).Execution: Buy only when the price dips below the lower fuchsia Prediction Band while the macro trend is bullish, and exit when the price reverts to the yellow baseline or opposite teal confidence band.Mode B: Momentum BreakoutMarket Environment: High-volatility expansion phases.Trade Mode: Breakout.Volume Filter: ON.Execution: Enter long when the price aggressively breaks above the upper fuchsia Prediction Band on a positive slope, accompanied by a verified volume surge.DisclaimerPast performance does not guarantee future results. There is no "holy grail" in quantitative trading. Linear regression assumes a degree of continuous distribution that can be disrupted during black swan events or extreme macroeconomic data releases. Always forward-test and practice strict risk management.