TSI — True Strength Index

Momentum smoothed twice, divided by absolute momentum smoothed the same way. The double smoothing removes most of the noise from raw price change while the normalisation keeps the result on a −100 to +100 scale; the signal line makes it a crossover system.

Signature

TSI(long_period, short_period, signal_period, on=<source>)

Argument	Type	Required	Notes
long_period	int Param or literal	Yes	First smoothing. Default 25, bounds 1–200.
short_period	int Param or literal	Yes	Second smoothing. Default 13, bounds 1–200.
signal_period	int Param or literal	Yes	EMA of the TSI. Default 13, bounds 1–200.
on=	symbol, OHLCV field, or indicator	No	Source. Defaults to the trade symbol’s close.

Formula

$$ \text{TSI} = 100,\frac{\text{EMA}(\text{EMA}(\Delta C, r), s)}{\text{EMA}(\text{EMA}(|\Delta C|, r), s)} $$

Warmup

Both EMA chains start at zero and converge over roughly 3 × long_period bars.

Reading the value

tsi.tsi
tsi.signal
tsi.tsi > tsi.signal

Multi-value: cannot be chained onto or crossed.

Example

class TsiCross(Strategy):
    """Long while TSI leads its signal line above zero."""
    trade = Symbol()
    sizing = FixedCapital()

    def execute(self):
        tsi = TSI(25, 13, 13, on=self.trade)
        if tsi.tsi > tsi.signal and tsi.tsi > 0 and self.trade.is_flat:
            self.buy(self.trade, reason=f"TSI {tsi.tsi:.1f}")
        if tsi.tsi < tsi.signal and self.trade.is_long:
            self.sell(self.trade, self.trade.position, reason="TSI below signal")

Notes

• William Blau, Momentum, Direction and Divergence (1995).
• Proven by an assert-via-trade run on SPY daily (converged to an independent double-EMA replication within 0.5 once warm; zero alarm trades).
• SMIErgodic is the same construction on a 0–1 scale with different defaults.
• The recursion seeds from the first bar rather than from a warm-up window, so early values are not comparable with pandas_ta’s tsi(13, 25, 13), which seeds from an average of the first n; measured on a 300-bar tape the two agree to 1e-6 from bar 200 onward.