Measuring Volatility Clustering with Hidden Markov Models

Summary

The document proposes comparing volatility clustering in return series by fitting hidden Markov models with multiple volatility states. An information criterion such as AIC or BIC can help select the number of states, after which standard HMM estimation yields the states and transition probabilities. The method offers two possible comparison measures: the probability that volatility remains in its current state, and the fit of a regression relating squared demeaned returns to estimated squared volatility.

These measures capture related but distinct properties: state persistence and the strength of the relationship between estimated volatility and squared returns. The document provides no empirical comparison of particular stocks or commodities, despite the question asking which assets show the feature most clearly. Results would depend on model specification, state selection, and estimation quality, so the proposed metrics are a framework for analysis rather than evidence that one asset class clusters more than another.

Key ideas

• Fit an HMM with several volatility states to represent changes in volatility regimes.
• Use AIC or BIC as an objective criterion for choosing the number of states.
• Measure volatility persistence by the probability of remaining in the same state.
• Measure the cluster effect using the regression fit between squared returns and estimated squared volatility.
• The document does not identify which stocks or commodities exhibit stronger clustering.

Tags

# Answer by stans (score 1)


# Which method would you use to compare if a time series of financial returns has more "clusterized volatility" than another?












It is known that the historical series of financial returns are characterized by the so-called volatility clustering. Suppose we approximate the number of two-type clusters, namely the high and low volatility cluster.

Which method would you use to compare if a time series of financial returns has more "clusterized volatility" than another?

On the basis of your knowledge or your studies, would you be able to indicate which stocks or commodities present this feature more clearly?

## Answer by stans (score 1)

https://quant.stackexchange.com/a/41307

You can model the return as a Hidden Markov Model (HMM) with several volatility states. The number of states can be chosen based on an objective model selection criterion, like AIC or BIC. For any particular number of volatility states, the model can be estimated using standard HMM algorithms. Then

1) the "volatility persistence" can be measured as the probability that the Markov chain describing volatility stays in the same state tomorrow;

2) the "cluster effect" can be measured as the R-square in regressing $(\rm{Return} - \mu)^2$ on the estimated level of $\rm{Volatility}^2$.

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