Use this calculation to reproduce a defined quantitative method when the observations, units, sampling process, and assumptions match the method shown here.

Values

Required list. Observations in time order.

Maximum lag

Optional integer. Highest lag to report; zero selects the smaller of the sample size minus one and forty.

The cited overview of Statistics supplies background for the terminology and domain context used by this tool.^[1]

Compute partial autocorrelations with the Durbin-Levinson recursion over the sample autocorrelation sequence (the classical Yule-Walker-style estimator). Inputs are interpreted exactly in the displayed units and the calculation returns the following fields without presentation rounding.

Coefficients

Returned list. Partial autocorrelations phi(1,1) through phi(K,K).

Critical bound

Returned number. Approximate plus-or-minus white-noise significance bound at 1.96 over the square root of the sample size.

Lag count

Returned integer. Number of reported lags.

• A numerical result does not by itself establish data quality, causation, representativeness, independence, distributional fit, or practical significance.
• Maximum lag must be at least 0.
• Use finite inputs in the displayed units, preserve source measurements and assumptions, and independently verify consequential decisions.

Inspect the underlying data, visualize its distribution, report uncertainty and sample size, and compare the result with a robust or domain-specific method where appropriate.

• Autocorrelation Calculator

  Compute sample autocorrelation coefficients for lags one through a maximum lag.

• Kaplan-Meier Survival Estimator

  Estimate survival over time with the product-limit estimator from right-censored durations.

• Benford's Law First-Digit Checker

  Count leading nonzero decimal digits 1–9 in nonzero observations for comparison with Benford's logarithmic proportions. A small or range-restricted sample alone is not evidence of fraud.