`TEMA`#

Description#

TEMA (Triple Exponential Moving Average, Patrick Mulloy 1994) extends the DEMA construction by one more level:

\[ \text{TEMA}[t] = 3 \cdot \text{EMA}(x)[t] - 3 \cdot \text{EMA}(\text{EMA}(x))[t] + \text{EMA}(\text{EMA}(\text{EMA}(x)))[t] \]

The three-term combination further reduces lag: TEMA typically tracks faster than DEMA and much faster than a plain EMA of the same span, in exchange for slightly less smoothing.

Parameters#

Same com / span / halflife / alpha mutex as EwMean -- specify exactly one. The same value is used for all three internal EMAs.

NaN handling: NaN values should be preprocessed.

Implementation Details#

Algorithm#

Pure composition of three chained EwMean instances. No explicit warmup: each EwMean returns a valid value from t=0, so TEMA[0] = 3*x[0] - 3*x[0] + x[0] = x[0].

Complexity#

Time complexity: O(1) per step.
Space complexity: O(1).

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
from screamer import TEMA, EwMean

x = np.cumsum(np.random.randn(100))

# Direct
ours = TEMA(span=10)(x)

# Algorithmically equivalent composition (the test suite verifies equality)
e1 = EwMean(span=10)(x)
e2 = EwMean(span=10)(e1)
e3 = EwMean(span=10)(e2)
np.testing.assert_allclose(ours, 3*e1 - 3*e2 + e3, atol=1e-12)

Reference#

Equivalent to TA-Lib's TEMA. Validated in tests/test_moving_averages.py against the explicit composition for four span values.

TEMA#