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Joint Estimation of GARCH Volatility and a Simultaneous Equation

Article Quant Q&A · Author: ZebrasInPjs
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Summary

The document raises an econometric modeling question involving a GARCH(1,1) volatility equation and a fourth equation in a simultaneous system. A variable from the fourth equation enters the GARCH specification as an exogenous regressor, while the conditional volatility produced by the GARCH model enters the fourth equation as an explanatory variable. This creates feedback between the equations and motivates asking whether their parameters can be estimated jointly and whether doing so is appropriate.

No full equations, estimation strategy, assumptions, data, or empirical findings are provided. In particular, the document does not resolve how to handle the endogenous relationship or establish identification and distributional conditions. It is therefore a useful statement of a modeling issue rather than a worked method: an answer would need the complete system and a specified likelihood or other estimator before judging simultaneous estimation.

Key ideas

  • A GARCH(1,1) conditional volatility equation is linked to another equation in a simultaneous system.
  • A variable from the fourth equation enters the volatility equation as a regressor.
  • Conditional volatility from the GARCH model enters the fourth equation as an explanatory variable.
  • The document asks about joint estimation but provides no estimator or conditions for valid inference.

Tags

StatisticsVolatilityMachine learning
Full text
# GARCH model within a system of simultaneous equations


# GARCH model within a system of simultaneous equations












This is a system of simultaneous equations. The first equations is a GARCH(1,1) model with a exogenous variable.

The dependent variable (x) from the fourth equation is exogenous independent variable in the GARCH equation and the conditional volatility variable from GARCH(1,1) model is an explanatory variable in the fourth equation.

I wonder if it is possible and appropriate to estimate the parameters of these two equations simultaneously.

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