Online Changepoint Detection

Maintains a posterior distribution over run-lengths—the time since the last changepoint—updated recursively with each new observation. This probabilistic framework quantifies uncertainty about whether a change has occurred rather than making hard binary decisions.

• Computes the run-length posterior using recursive message-passing
• Naturally handles multiple changepoints without pre-specifying the number
• Provides a change probability at each time step for threshold-based alerts

Sequential probability ratio tests and martingale-based methods continuously monitor for deviations from a null hypothesis of stationarity. When the cumulative evidence crosses a threshold, a changepoint is declared with statistical guarantees.

• CUSUM (Cumulative Sum) detects shifts in mean with minimal detection delay
• Page-Hinkley test identifies sustained deviations from historical averages
• Provides controlled false alarm rates through threshold calibration

Compares the empirical distribution of recent observations against a reference window using divergence measures like Kullback-Leibler or Maximum Mean Discrepancy. A changepoint is flagged when the two distributions differ significantly.

• Kernel density estimators capture non-parametric distributional shifts
• MMD-based tests detect changes in high-dimensional feature spaces
• Window sizes trade off detection speed vs. false positive rate

Leverages stochastic gradient descent on a loss function computed over streaming data. A changepoint is detected when the gradient magnitude spikes, indicating the current model no longer fits recent observations.

• Monitors the Fisher information matrix for structural breaks
• Integrates naturally with online learning models already in production
• Detects changes in regression coefficients and model parameters in real-time

The canonical algorithm combining conjugate-exponential models with recursive message-passing. For each possible run-length, it computes the predictive probability of the next observation and updates beliefs analytically.

• Uses conjugate priors for closed-form updates (Gaussian, Poisson, etc.)
• Hazard rate parameter controls expected segment duration
• Forms the foundation for extensions like Gaussian Process BOCPD for nonparametric detection

Specialized detectors for regime shifts in second-order statistics, critical for identifying transitions from low-volatility to high-volatility market states. These methods monitor variance, covariance, and correlation structures.

• Exponentially weighted moving variance tracks evolving volatility
• GARCH residual monitoring detects when volatility dynamics change
• Covariance matrix equality tests identify correlation breakdowns across assets

Pairs trading strategies rely on a stable cointegration relationship between two assets. When an online changepoint detector identifies a structural break in this relationship, the system can immediately flatten the position or recalibrate the hedge ratio. This prevents catastrophic losses during correlation breakdowns that occur during market crises, where historical relationships suddenly invert.

Option market-making systems use online changepoint detection to identify shifts between low-volatility and high-volatility regimes in real-time. Upon detecting a changepoint, the system immediately widens bid-ask spreads and adjusts delta-hedging frequency. This is critical during events like flash crashes, where volatility can spike 10x within seconds, and stale parameters lead to significant inventory risk.

VWAP and TWAP execution algorithms assume stable intraday volume profiles. An online changepoint detector monitoring order book imbalance and trade intensity can identify when the market microstructure has fundamentally shifted—such as the arrival of a large institutional order. The algorithm then switches from a passive to an aggressive execution strategy to minimize implementation shortfall.

A single asset can exhibit momentum behavior in trending regimes and mean-reverting behavior in range-bound regimes. Online changepoint detection on price series or Hurst exponent estimates allows a trading system to dynamically switch between trend-following and contrarian signal generators. This avoids the classic pitfall of applying a momentum strategy during a choppy, sideways market.

Quantitative equity strategies often rely on multi-factor models where factor exposures are assumed stable. Online changepoint detection applied to the residual returns of a Barra-style risk model signals when a stock's sensitivity to factors like value, momentum, or size has permanently shifted. This triggers immediate portfolio rebalancing before the stale factor model generates erroneous risk forecasts.

A market maker's inventory is exposed to adverse selection when informed traders enter the market. Online changepoint detection on the order flow toxicity metric (e.g., VPIN) identifies when the probability of informed trading has abruptly increased. The system responds by reducing position limits, skewing quotes away from the direction of toxic flow, and hedging residual inventory more aggressively.