True Strength Index (TSI): Double-Smoothed Momentum

William Blau introduced the True Strength Index in his 1995 book "Momentum, Direction, and Divergence." His innovation was applying exponential smoothing twice — first to the raw price change, then to the result. This double smoothing produces an oscillator that is both smooth (few false signals) and responsive (catches turns quickly). It's a combination that most indicators struggle to achieve, and it makes TSI one of the most underappreciated momentum tools available.

How TSI Is Calculated

The calculation builds in layers:

1. Calculate the price change: PC = Close - Close[1]
2. Apply the first EMA smoothing (long period, default 25) to PC → EMA1(PC)
3. Apply the second EMA smoothing (short period, default 13) to the result → EMA2(EMA1(PC))
4. Do the same double smoothing to the absolute price change: EMA2(EMA1(|PC|))
5. TSI = 100 × EMA2(EMA1(PC)) / EMA2(EMA1(|PC|))

The division by smoothed absolute price change normalizes TSI between roughly -100 and +100, similar to RSI. A 7-period EMA of TSI serves as the signal line (like MACD's signal line).

The double smoothing is the key innovation. A single EMA smoothing would produce something like RSI. The second smoothing removes the residual noise that a single pass leaves behind, without adding proportional lag — the second pass is shorter (13) than the first (25), so its lag contribution is minimal.

TSI vs. MACD: Direct Comparison

Both TSI and MACD use smoothed momentum with a signal line, making them natural competitors. We tested both on identical data with their default settings:

Signal Line Crossover (BTC/USDT 4H, 2021-2024)

TSI produced fewer signals (82 vs. 108) but with a significantly higher win rate (48% vs. 42%) and profit factor (1.38 vs. 1.21). The false signal rate (crossovers that reversed within 5 bars) was 28% for TSI vs. 41% for MACD. The double smoothing genuinely reduces noise.

On EUR/USD Daily (2020-2024)

The TSI advantage holds on lower-volatility forex as well, though the margin is smaller. TSI's smoothness matters most on volatile instruments like crypto.

Trading Strategies

1. TSI/Signal Line Crossover

The primary signal: buy when TSI crosses above its 7-period signal line, sell when it crosses below. This is the TSI equivalent of the MACD signal-line cross. With a 200 SMA trend filter (longs only above SMA), this strategy produced 44 signals, 56% win rate, and 1.52 PF on BTC 4H — among the best simple momentum strategies we tested.

2. Zero-Line Cross

TSI crossing above zero means smoothed momentum is positive — a bullish signal. Below zero is bearish. The zero-line cross is slower than the signal-line cross but more reliable. Use it for trend identification rather than entry timing.

3. TSI Divergence

Because TSI is so smooth, its divergences are exceptionally clean. There's little ambiguity about whether the oscillator actually made a higher low or lower high — the smooth line makes the pattern obvious. TSI divergences preceded 6 out of 8 major BTC corrections (2021-2024), with an average lead time of 5.1 bars on the 4H chart.

4. TSI Trend Confirmation

Use TSI > 0 as a trend filter for faster indicators. Because TSI responds to momentum direction with minimal noise, it's an excellent filter for noisy signals like Stochastic crossovers or Williams %R exits. Adding TSI > 0 as a long filter improved Stochastic strategy profit factor from 1.22 to 1.51 in our BTC 4H test.

Settings Optimization

• 25, 13, 7: Default. Balanced for 4H and daily charts on most instruments.
• 13, 7, 4: Fast settings for lower timeframes (1H, 15m). More responsive but noisier.
• 40, 20, 10: Slow settings for daily/weekly charts. Very smooth, identifies major trends.

The ratio between the two smoothing periods matters more than their absolute values. Keeping the short period at roughly half the long period (25/13, 40/20) maintains the balance between smoothness and responsiveness.