`TRIX`#

Description#

TRIX(span) is the one-step rate of change of a triple-smoothed EMA -- a momentum oscillator that filters short-term noise via two extra layers of exponential smoothing before measuring change.

\[\begin{split} \begin{aligned} \text{ema}_1[t] &= \text{EwMean}(\text{span})(x)[t] \\ \text{ema}_2[t] &= \text{EwMean}(\text{span})(\text{ema}_1)[t] \\ \text{ema}_3[t] &= \text{EwMean}(\text{span})(\text{ema}_2)[t] \\ \text{TRIX}[t] &= 100 \cdot \frac{\text{ema}_3[t] - \text{ema}_3[t-1]}{\text{ema}_3[t-1]} \end{aligned} \end{split}\]

Parameters:

span (int, positive): the span for every EMA stage (all three use the same value).

Warmup: only the first sample is NaN (no prev_ema3 yet). Each EwMean is well-defined from t=0, so from t=1 onward TRIX is finite.

NaN handling: NaN inputs propagate through the EMA arithmetic.

Implementation Details#

Pure composition of three chained EwMean instances plus a single scalar holding prev_ema3. O(1) per step.

The underlying EMA is pandas's adjust=True (bias-corrected weighted mean -- the form we use throughout the library). TA-Lib's TRIX uses adjust=False with an SMA-seeded warmup, so ours differs from TA-Lib by a few percent during early samples; see conventions.

NaN handling#

Policy: ignore. A NaN in any input at index t causes the function to skip that step: output at t is NaN and internal state is unchanged. Subsequent finite samples are processed as if step t had not occurred.

Examples#

Usage example#

import numpy as np, pandas as pd
from screamer import TRIX

x = 100 + np.cumsum(np.random.default_rng(0).standard_normal(200))
trix = TRIX(14)(x)

# Algorithmically equivalent composition (pandas adjust=True):
s = pd.Series(x)
e3 = s.ewm(span=14, adjust=True).mean().ewm(span=14, adjust=True).mean().ewm(span=14, adjust=True).mean()
np.testing.assert_allclose(trix, 100 * e3.pct_change(), equal_nan=True, atol=1e-12)

Reference#

Equivalent to pandas.Series.ewm(span=..., adjust=True).mean() triple composition followed by 100 * pct_change. Cross-validated in tests/test_third_party_alignment.py: bit-exact vs pandas composition; documented divergence vs TA-Lib's TRIX.

TRIX#