Tilson T3 Moving Average
period = 8 (3–50) • volume_factor = 0.7 (0–1) Overview
The Tilson T3 Moving Average represents a revolutionary approach to price smoothing, earning its place as one of the "Better Moving Averages" as Tim Tillson titled his 1998 article in Technical Analysis of Stocks and Commodities. The T3 is technically a six-pole non-linear Kalman filter that applies exponential smoothing six times through a sophisticated weighted combination. This complex calculation produces an indicator that is both composite and adaptive, significantly reducing lag while maintaining smoother curves than any traditional moving average.
The magic of T3 lies in its unique formula that combines six EMAs using specific coefficients derived from a volume factor (typically 0.7). The calculation uses the formula: T3 = c1×e6 + c2×e5 + c3×e4 + c4×e3, where each 'e' represents successive EMAs and the coefficients are calculated from the volume factor. This approach builds on the Generalized Double EMA (DEMA) concept but extends it dramatically, resulting in backtests showing 33.59% annual returns compared to 20.20% for simple moving averages, demonstrating its superior performance in trend-following systems.
Interpretation & Trading Signals
Primary Trading Signals:
- Retracement Buy: Price falls to rising T3 = buy opportunity
- Retracement Sell: Price rises to falling T3 = sell opportunity
- Trend Support: T3 acts as dynamic support/resistance during trends
- Penetration Signal: Confirmed break of T3 often signals trend end
Dual T3 Crossover Strategy:
- Buy Signal: Fast T3 crosses above slow T3 - trend positive
- Sell Signal: Fast T3 crosses below slow T3 - trend negative
- Early Entry: T3 provides earlier signals with fewer false positives
- Optimal Periods: Backtests show 5-8 periods work best
Advanced Applications:
- Volume Factor: 0.7 recommended, 0.618 for more smoothing
- Trend Quality: Price rarely touches T3 during strong trends
- Combine Tools: Use with channels, oscillators, volume analysis
- Building Block: Excellent base for custom indicators
Example Usage
Code examples will be available once the Rust implementation is complete.
Performance Analysis
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