Structural Break Detection

A classic frequentist test for a single structural break at a known point in time. It fits separate regressions on two sub-samples and tests whether the coefficient vectors are statistically identical.

• Null hypothesis: No structural break exists
• Requires the break date to be specified a priori
• Computes an F-statistic comparing restricted vs. unrestricted residual sums of squares
• Sensitive to heteroskedasticity; use robust standard errors
• Example: Testing whether a stock's beta changed after a known corporate event date

Also known as the Sup-Wald test, this generalizes the Chow test when the break date is unknown. It computes the Chow test statistic at every possible break point and takes the maximum.

• Scans a trimmed range (typically the middle 70%) to avoid edge effects
• The supremum of the F-statistics identifies the most likely break location
• Critical values are non-standard; use Andrews (1993) or Hansen (1997) tables
• Detects a single dominant break in the sample
• Foundation for more complex sequential break detection procedures

A comprehensive framework for detecting multiple unknown structural breaks in linear regression models. It sequentially tests for additional breaks using a dynamic programming algorithm.

• Global optimization: Minimizes the sum of squared residuals across all possible partitions
• Uses the BIC or a sequential sup-F test to determine the number of breaks
• Allows for heterogeneous error distributions across segments
• Handles both pure structural changes (coefficient shifts) and partial changes
• Widely used for identifying regime shifts in macroeconomic and financial time series

Recursive residual-based tests that detect parameter instability without specifying a break date. They plot cumulative sums of standardized residuals against confidence bounds.

• CUSUM: Detects shifts in the intercept or systematic parameter drift
• CUSUM of Squares: Detects changes in variance or coefficient stability
• Computed recursively as each new observation is added to the estimation window
• Boundary crossing signals a structural break at that observation
• Particularly useful for real-time monitoring in online changepoint detection systems

Tests for a unit root while endogenously allowing for a single structural break in the series. Traditional unit root tests (ADF, Phillips-Perron) lose power when breaks are present.

• Three model variants: break in intercept, break in trend, or break in both
• The break date is estimated as the point that gives the least favorable view of the unit root null
• Critical values differ from standard unit root tests
• Prevents misclassifying a trend-stationary process with a break as a random walk
• Essential for distinguishing regime shifts from non-stationarity in asset prices

The Iterated Cumulative Sums of Squares algorithm detects multiple discrete shifts in the unconditional variance of a time series. It identifies variance change points without specifying the number of breaks.

• Based on the statistic D_k = (C_k / C_T) - (k / T), where C_k is the cumulative sum of squared returns
• Iteratively applies the test to segments between previously identified break points
• Critical values derived from the distribution of the maximum absolute D_k statistic
• Detects volatility regime shifts characteristic of financial crises
• Often used as a pre-processing step before fitting MS-GARCH models

A classic econometric test for a structural break at a known point in time. It fits a model on the full dataset and on two sub-samples split at the breakpoint, then uses an F-test to determine if the coefficients are statistically different. Key limitations: requires the break date to be known a priori and assumes constant error variance across sub-samples. For unknown break dates, the Quandt Likelihood Ratio (QLR) test is preferred.

The gold standard for detecting multiple unknown structural breaks in linear regression models. It uses a dynamic programming algorithm to globally minimize the sum of squared residuals across all possible partitions of the data. The procedure sequentially tests l vs. l+1 breaks using sup-F statistics. Critical for identifying regime shifts in factor models and macroeconomic relationships without prior knowledge of break dates.

Recursive residual-based tests that detect parameter instability over time without specifying a break date. The CUSUM statistic plots the cumulative sum of standardized one-step-ahead forecast errors; crossing a critical boundary signals a structural change. The CUSUM of Squares variant is sensitive to variance shifts. Both are widely used for real-time monitoring of model stability in algorithmic trading systems.

A family of tests for a single unknown breakpoint where the test statistic is computed for every possible break date, and the maximum (supremum) value is compared to a non-standard critical distribution. Variants include the sup-Wald, ave-Wald, and exp-Wald statistics. Developed by Andrews (1993), these tests are robust to heteroskedasticity and form the basis of many modern break detection procedures in the strucchange R package.

A unit root test that allows for a single endogenous structural break in the intercept, trend, or both. Standard ADF tests lose power when structural breaks are present, often failing to reject the null of a unit root. The Zivot-Andrews procedure selects the break date that gives the least favorable view of the unit root null, distinguishing true non-stationarity from stationary processes with structural breaks.

Pruned Exact Linear Time (PELT) is an optimal changepoint detection algorithm for identifying multiple change points in a sequence. It uses a cost function (e.g., negative log-likelihood) with a penalty term to control the number of changepoints. A pruning step discards candidate points that can never be optimal, achieving O(n) computational complexity. Essential for high-frequency financial data where breaks must be detected in real-time.