Simulating Cointegrated Series with a Drifting Hedge Ratio

Summary

The document asks how to simulate two cointegrated time series when their beta coefficient changes gradually, rather than remaining fixed. It distinguishes this goal from simply generating returns with a constant correlation, and seeks a model that can produce a stationary relationship while allowing the coefficient to drift.

The sole proposed construction is to multiply one series by a beta coefficient whose own evolution follows a random walk, then use the result to form the second series. The author presents this tentatively and provides no equations, simulation results, or analysis showing that the resulting spread is stationary. A random-walking coefficient can itself affect the stability of the relationship, so the suggestion should be treated as an idea to validate rather than a demonstrated cointegration model.

Key ideas

• Correlated returns alone do not specify a cointegrated relationship between price series.
• The question seeks a simulation with a beta coefficient that drifts over time.
• The proposed construction lets beta follow a random walk and uses it to scale one series.
• The excerpt offers no evidence that this construction produces a stationary spread.

Tags

# Simulating Co-Integrated Assets


# Simulating Co-Integrated Assets












I know how to simulate correlated returns, but I do not know how to simulate Co-Integrated assets. I would like to simulate a co-integrated time series where the Beta Co-Efficient is not constant, but rather has some degree of drift. An equation or model for doing so would be very helpful, thanks very much Quant SE!

## Answer by FX_NINJA (score 1)

https://quant.stackexchange.com/a/30069

I think I just figured it out, and kinda feel dumb. It appears It could be solved by multiplying one time series by the beta co-efficient, and having a random walk model the drift of the beta co-efficient, thus a stationary time series could be contrived by the two co-integrated assets.

I am not for sure however, so if I am wrong please correct me.

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