A resampling technique that draws contiguous blocks of a multivariate time series after applying a rotation to its coordinates, preserving short-run serial dependence and the joint cross-correlation structure of variables while remaining robust to structural breaks. Used to build confidence bands and probability estimates without assuming a fixed parametric model.
How it works
A standard block bootstrap resamples overlapping contiguous segments of a series to retain autocorrelation; the rotation step transforms the data so that the joint covariance structure across series (e.g. yields at different maturities) is preserved under resampling. Robustness to structural change comes from drawing blocks empirically rather than imposing a stationary parametric law.
Why it matters now
It underpins the New York Fed's updated yield-curve recession-probability work, where preserving the joint structure of Treasury yields matters for honest uncertainty bands after 2022-24 regime shifts in term premia and the inversion-to-steepening transition.
Example
The New York Fed's term-spread recession model uses a rotated block bootstrap to resample the joint path of Treasury yields, generating confidence intervals around its 12-month-ahead recession probability rather than relying on a single point estimate from a probit fit to historical inversions.
Frequently asked
- What is a rotated block bootstrap?
- A rotated block bootstrap is a resampling method that draws contiguous blocks from a multivariate time series after rotating its coordinates, preserving both short-run autocorrelation and the joint cross-correlation across series. It produces nonparametric confidence bands without assuming a fixed model, making it robust to structural breaks like the 2022-24 shift in Treasury term premia.
- How does a rotated block bootstrap differ from a standard block bootstrap?
- A rotated block bootstrap adds a coordinate rotation step that a standard block bootstrap lacks. Standard block bootstraps resample contiguous segments to retain each series' autocorrelation, but can distort the joint covariance across variables. The rotation transforms the data so cross-correlations among, say, yields at different maturities survive resampling intact, which matters for multivariate yield-curve models.
- Why does the New York Fed use a rotated block bootstrap for recession probabilities?
- The New York Fed uses it to put honest uncertainty bands around its term-spread recession model rather than reporting a single probit point estimate. Preserving the joint structure of Treasury yields matters because the 2022-24 inversion-to-steepening transition and term-premium regime shift make parametric stationarity assumptions unreliable, and the bootstrap stays robust without imposing them.
- Why does preserving joint structure matter for yield-curve resampling?
- Preserving joint structure matters because Treasury yields move together, and recession signals depend on spreads between maturities, not levels alone. Resampling each series independently would break the correlation that defines a curve inversion. The rotation step keeps the cross-maturity covariance intact, so bootstrapped paths remain plausible curves and the resulting confidence intervals are credible.
- Is a rotated block bootstrap parametric or nonparametric?
- A rotated block bootstrap is nonparametric: it draws blocks empirically from observed data rather than assuming a stationary parametric law. This is precisely what makes it robust to structural breaks, since no fixed distribution is imposed. The only tuning choices are block length and the rotation applied to the multivariate coordinates.