`RollingMedianAD`#

Description#

RollingMedianAD computes the rolling median absolute deviation (MAD): for the trailing window it takes the median of the absolute deviations from the window median,

\[ \text{MAD}_t = \text{median}_{i \in W_t}\; \bigl| x_i - \text{median}(W_t) \bigr|. \]

Unlike RollingMad, which is the mean absolute deviation, this is a robust scale estimate: a few extreme samples cannot inflate it. It is the scale primitive behind the Hampel and ImpulseClip despikers. The raw MAD is returned; multiply by 1.4826 for a Gaussian-consistent standard-deviation estimate.

Parameters:

window_size: (int) Trailing-window length. Must be positive.
start_policy: How the initial phase is handled before window_size samples are available:
- "strict": NaN until the window is full.
- "expanding": compute over the samples seen so far, from the first sample.
- "zero": treat missing samples as zeros (a full window of zeros to start).

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 RollingMedianAD

x = np.array([1.0, 2.0, 1.0, 2.0, 50.0, 2.0, 1.0])
print(RollingMedianAD(5)(x))   # robust scale, barely moved by the spike

Implementation Details#

O(W) per step: the window median shifts every step, so the absolute deviations cannot be updated incrementally. Each step copies the active window, finds the median with std::nth_element, then finds the median of the absolute deviations the same way. Strictly causal.

RollingMedianAD#