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Extending Kalman Regression to Three Asset Prices

Article Quant Q&A · Author: Pman70
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Summary

The document asks how to extend a Kalman filter regression commonly used to estimate a rolling spread between two asset price series. The proposed relationship models one asset’s price as a linear combination of two other asset prices, with an optional intercept. The aim is to estimate both coefficients over time rather than maintain a single static regression.

The author mentions using Python and the pykalman library and requests an example, but the document contains no answer, implementation, or empirical evidence. It therefore identifies the regression structure and estimation goal without explaining how to define the state vector, transition model, or observation noise. Those choices would be needed to turn the question into a working model, and the document does not establish whether the resulting spread is stationary or suitable for a trading strategy.

Key ideas

  • A Kalman regression can be framed to estimate time-varying coefficients for multiple asset prices.
  • The proposed relationship uses one dependent asset price and two explanatory asset prices.
  • An intercept may optionally be included in the regression.
  • The document asks for an implementation example but does not provide filter equations or trading evidence.

Tags

EquitiesStatisticsPairs tradingMean reversion
Full text
# Kalman Filter for Multiple Regression?


# Kalman Filter for Multiple Regression?












I'm using Kalman Filter to calculate a rolling spread between two asset price series as commonly described by Chan and many others. I would like to extend this regression to the price of three assets, according to:

Asset_0 = c1 * Asset_1 + c2 * Asset_2 ( + intercept)

Question: How can I extend the Kalman regression to calculate c1 and c2? I'm using Python and pykalman, but any example that could explain this would be greatly appreciated.

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