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Interpreting Standardized Residuals in Markov-Switching GARCH

Article Quant Q&A · Author: Chp
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Summary

The document asks whether residuals from the MSGARCH R package should have unit variance within each latent regime. The user reports that the overall residual standard deviation is near one, while regime-specific standard deviations differ substantially, and wonders whether this reflects how the package’s volatility function constructs residuals.

It offers no answer or technical explanation: the text ends with a reproducibility observation across datasets. As a result, it does not establish whether the residuals are standardized conditionally on the inferred regime, how regimes are assigned, or whether the reported differences indicate a modeling or interpretation issue. It is useful as a focused question about regime-conditioned diagnostics, but it provides no evidence beyond the reported pattern and should not be treated as guidance on MSGARCH residual behavior.

Key ideas

  • The question concerns whether MSGARCH residuals should have unit variance within each regime.
  • The reported overall residual standard deviation is near one, while regime-specific values differ.
  • The document provides no answer explaining the package’s volatility output or validating the diagnostic.

Tags

StatisticsVolatility
Full text
# Is variance of residuals of Markov switching GARCH model regime specific?


# Is variance of residuals of Markov switching GARCH model regime specific?












I'm using MSGARCH package in R. By return_data/Volatility(fit.model), I get the residuals. When I calculate the standard deviation of the residuals, it turns out that it's close to 1 for all residuals. However, the standard deviation in each regime differs greatly. It's about 0.7 in one and 1.6 in the other.

Is this reasonable? I imagine that the residual would have unit variance in each regime respectively, since in each regime it's filtered by a GARCH model.

This result can be reproduced by any data I tried, so it's more about how the function Volatility works.

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