qis.compute_ar_residuals

qis.compute_ar_residuals(data)

fit an AR(1) per column and return the residuals on complete lag pairs.

A lag pair at t is usable when every column is observed at both t and t-1. Estimating and residualising on that same set is what keeps the returned arrays aligned, and what stops a gap being read as a one-period step. Rows must be complete across all columns because bootstrap_ar_process resamples rows jointly to preserve the cross-section.

The coefficient is the conditional maximum likelihood estimate, which for an AR(1) is ordinary least squares of the series on its own lag.

Parameters:

data (Series | DataFrame) – observations, one column per series

Returns:

Tuple of (residuals, intercept, beta). residuals has one row per usable lag pair and one column per series, and contains no NaN. intercept and beta have one entry per series

Raises:

ValueError – if no column is present, or if fewer than three usable lag pairs survive, below which an AR(1) is not identified

Return type:

Tuple[ndarray, ndarray, ndarray]