Indicator Formulas, Cross-Checked

Wilder's smoothing, in code

Three of the six indicators here depend on it, and it is the piece most published formulas leave out. It is an exponential average with alpha = 1/n, seeded with a simple average of the first n values:

import numpy as np

def wilder(x: np.ndarray, n: int) -> np.ndarray:
    """Wilder's smoothing (RMA). Not the same as an EMA of the same length."""
    out = np.full_like(x, np.nan, dtype=float)
    out[n - 1] = np.nanmean(x[:n])          # seed: simple average of the first n
    for i in range(n, len(x)):
        out[i] = out[i - 1] + (x[i] - out[i - 1]) / n
    return out

# Equivalent to an EMA with alpha = 1/n.  A standard EMA uses 2/(n+1):
#   n = 14  ->  Wilder alpha = 0.0714,  EMA alpha = 0.1333

The seed choice is what causes the long warm-up. Different libraries seed differently — some with a simple average, some by running the recursion from the first observation — and because the filter is recursive those choices take hundreds of bars to wash out, not fourteen.

Method

Each formula is implemented independently here in plain NumPy from its definition, then computed again with pandas_ta on the same real bars, and the two are compared over every point where both are defined. Agreement is evidence the published formula is the one the library implements; disagreement is published as a finding rather than hidden.

Agreement is judged on the converged region, with the warm-up measured separately. That distinction is the point: a single max-difference over the whole series conflates "the formula is wrong" with "the first bars are seeded differently", and those are completely different problems for someone implementing this. Tolerance: relative difference below 1e-6 against the series' own scale.

Regenerate with python -m pipeline.indicator_verify. Every figure is tagged with the library version that produced it, so it goes visibly stale rather than quietly wrong.

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