auto_correlation: Gnostic Auto-Correlation Metric

The auto_correlation function computes the Gnostic auto-correlation coefficient for a data sample. This metric measures the similarity between a data sample and a lagged version of itself, using robust gnostic theory principles for reliable diagnostics—even in the presence of noise or outliers.

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Overview

Auto-correlation quantifies how much a data sample resembles itself when shifted by a specified lag. Unlike classical auto-correlation, the Gnostic version uses irrelevance measures from gnostic theory, providing robust, assumption-free estimates that reflect the true structure of your data.

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Parameters

Parameter	Type	Description
data	np.ndarray	Data sample (1D numpy array, no NaN/Inf).
lag	int	Lag value (non-negative, less than length of data). Default:0.
case	str	Geometry type:'i' for estimation (EGDF), 'j' for quantifying (QGDF). Default: 'i'.
verbose	bool	If True, enables detailed logging for debugging. Default:False.

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Returns

• float The Gnostic auto-correlation coefficient for the given lag.

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Raises

• ValueError If input is not a 1D numpy array, is empty, contains NaN/Inf, or if lag/case is invalid.

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Example Usage

import numpy as np
from machinegnostics.metrics import auto_correlation

# Example 1: Compute auto-correlation for a simple dataset
data = np.array([1, 2, 3, 4, 5])
lag = 1
auto_corr = auto_correlation(data, lag=lag, case='i', verbose=False)
print(f"Auto-Correlation (lag={lag}, case='i'): {auto_corr}")

# Example 2: Using quantifying geometry
auto_corr_j = auto_correlation(data, lag=2, case='j', verbose=True)
print(f"Auto-Correlation (lag=2, case='j'): {auto_corr_j}")

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Notes

• The metric is robust to data uncertainty, noise, and outliers.
• Input data must be preprocessed and cleaned for optimal results.
• If data homogeneity is not met, the function automatically adjusts scale parameters for better reliability.
• The Gnostic auto-correlation uses irrelevance measures rather than classical means, providing deeper insight into temporal relationships in your data.
• Supports both estimation and quantification geometries for flexible analysis.

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Gnostic vs. Classical Auto-Correlation

Note: Unlike classical auto-correlation metrics that rely on statistical means, the Gnostic auto-correlation uses irrelevance measures derived from gnostic theory. This approach is assumption-free and designed to reveal true temporal relationships, even in the presence of outliers or non-normal distributions.

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Author: Nirmal Parmar
Date: 2025-09-24

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