Simulating Cointegrated Price Pairs with AR(1) Processes

Summary

This documentation describes a simulator for autoregressive series and pairs whose cointegration error follows an AR(1) process. One series is modeled through its changes, while a linear combination of the two series represents the spread or cointegration error. Both the error and the price-change process have configurable autoregressive coefficients, constants, and noise variances; the hedge relationship is controlled by a user-specified coefficient. Simulations can be generated in batches, and the module provides methods to check the estimated cointegration relationship and plot a pair alongside its error.

The example demonstrates generating multiple synthetic pairs, setting model parameters, simulating the data, and checking whether the estimated coefficient agrees with the chosen value. The page says the module follows research on minimum-profit bounds for pairs trading, but it does not explain or test those bounds here. Simulated cointegration depends on the assumed model and parameter choices, so these series do not establish that a real asset pair is cointegrated, stable, or profitable to trade. The page provides no comparative performance results or empirical validation on market data.

Key ideas

• The simulator generates autoregressive processes and pairs with an autoregressive cointegration error.
• Users can set the autoregressive coefficients, constants, noise variances, and pair coefficient.
• Batch simulation supports generating many synthetic pairs for analysis.
• The example checks the estimated cointegration coefficient and plots a pair with its error series.
• The simulated relationship depends on model assumptions and does not establish real-world trading profitability.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.