`DEMA`#

Description#

DEMA (Double Exponential Moving Average, Patrick Mulloy 1994) is a low-lag smoother defined as:

\[ \text{DEMA}[t] = 2 \cdot \text{EMA}(x)[t] - \text{EMA}(\text{EMA}(x))[t] \]

The construction subtracts the lag of a single EMA from twice that EMA. The result tracks the input more closely than a plain EMA of the same span, while still smoothing high-frequency noise.

Parameters#

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

NaN handling: NaN values should be preprocessed.

Implementation Details#

Algorithm#

DEMA is a pure composition of two chained EwMean instances. The class holds them as members and combines their outputs as 2*e1 - e2. There is no warmup: each EwMean returns a valid value from t=0 (sum_x / sum_w is x[0]/1 = x[0] after one append), so DEMA[0] = 2*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 DEMA, EwMean

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

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

# Algorithmically equivalent composition (the test suite verifies bit-equality)
e1 = EwMean(span=10)(x)
e2 = EwMean(span=10)(e1)
np.testing.assert_allclose(ours, 2*e1 - e2, atol=1e-12)

Reference#

Equivalent to TA-Lib's DEMA. Validated in tests/test_moving_averages.py against the explicit 2*EwMean - EwMean(EwMean) composition for four span values.

DEMA#