Partial Autocorrelation Calculator
Compute partial autocorrelations with the Durbin-Levinson recursion over the sample autocorrelation sequence (the classical Yule-Walker-style estimator).
Description
Calculate Yule-Walker-style partial autocorrelations with Durbin-Levinson recursion.
Partial autocorrelation measures the association between a series and a lag after accounting for shorter lags. It is commonly inspected when identifying autoregressive time-series structure.
When to use Partial Autocorrelation Calculator
- Inspect candidate autoregressive lag order
- Separate direct lag association from intervening lags
- Compare PACF with ordinary autocorrelation
How the calculation works
The series is mean-centered, biased sample autocorrelations are formed, and Durbin-Levinson recursion yields diagonal coefficients φ(k,k). The reported ±1.96/√n bound is a rough white-noise reference.
Interpreting the result
A coefficient at lag k describes remaining linear association after lags 1 through k−1 are controlled in the recursion. The bound is approximate and should not be treated as a multiple-testing-adjusted decision rule.
Important limitations
- Constant and degenerate series are rejected.
- At most 40 lags are reported.
- Nonstationarity, seasonal structure, missing data, and model diagnostics require additional analysis.