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structural_breaks

Concept Overview

Three families of break test. Chow-type statistics test for a break at a known or scanned candidate date. Chu-Stinchcombe-White is a sequential monitoring statistic that can be run online as data arrives. SADF — the supremum of ADF statistics over expanding windows — tests for explosive rather than merely non-stationary behaviour, which is the econometric signature of a bubble: an autoregressive coefficient that exceeds 1 rather than approaching it from below.

When to Use

Use SADF as a regime guard on any model whose parameters are estimated: a break means the training distribution no longer describes the present, and refitting then becomes a decision rather than a formality. Use the sequential statistics for online monitoring between refits. SADF cost grows quadratically with series length, because every endpoint re-runs an expanding-window regression, so keep long-window scenarios on a nightly path rather than in an interactive loop.

Mathematical Foundations

ADF Regression

$\Delta y_t=\alpha+\beta y_{t-1}+\sum_{i=1}^{k}\phi_i\Delta y_{t-i}+\epsilon_t$

SADF

$SADF=\sup_{r_2\in[r_0,1]} ADF_0^{r_2}$

Usage Examples

Rust

Compute SADF statistic

use openquant::structural_breaks::{get_sadf, SadfLags};

// SADF is defined on log prices.
let log_prices: Vec<f64> =
    (0..160).map(|i| (100.0 + i as f64 * 0.1 + ((i / 40) as f64) * 5.0).ln()).collect();

// (series, model, add_const, min_length, lags). `model` selects the regression
// specification — "linear", "quadratic", "sm_poly_1", "sm_poly_2", "sm_exp",
// "sm_power" — and `min_length` is the shortest window a statistic is computed on.
let sadf = get_sadf(&log_prices, "linear", true, 20, SadfLags::Fixed(1))?;

let peak = sadf.iter().cloned().fold(f64::NEG_INFINITY, f64::max);
println!("{} SADF values, peak = {peak:.4}", sadf.len());

API Reference

Python API

structural_breaks.get_chow_type_stat
structural_breaks.get_chu_stinchcombe_white_statistics
structural_breaks.get_sadf

Rust API

get_chow_type_stat
get_chu_stinchcombe_white_statistics
get_sadf
SadfLags

Risk Notes and Caveats

SADF can be computationally expensive on long windows.
Use dedicated slow/nightly test paths for heavy scenarios.