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How ARCH and GARCH Explain Volatility Clustering

Article Quant Q&A · Author: Oneday
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Summary

The document asks whether persistent realized volatility reflects slowly changing latent volatility or whether observed volatility shocks cause future latent volatility to rise. It presents the latter as closer to the usual market consensus, then describes volatility clustering through ARCH and GARCH models.

The explanation distinguishes returns from their magnitude: returns may show little serial correlation, while squared returns can remain positively correlated. ARCH and GARCH represent this persistence by making current return variance depend on past squared returns and, in GARCH, past variance estimates. The document offers this modeling framework as an explanation rather than a causal test. It does not provide data, empirical comparisons, model specifications, or evidence that separates causation from persistent latent volatility, so its answer should be read as a summary of common modeling practice rather than proof of a causal mechanism.

Key ideas

  • Returns can be weakly autocorrelated even when their squared values show persistence.
  • ARCH and GARCH models represent volatility clustering through dependence on past shocks and variance estimates.
  • The document favors a causal interpretation but does not present evidence that establishes causality.

Tags

VolatilityStatistics
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# Answer by QuantCalc.net (score 0)


# Is realized volatility autocorrelation due to causal relationships between current realized volatility and future latent volatility?












Realized volatility is autocorrelated, that could be due to either:

- Latent volatility takes time to change, thus, time periods close together have similar latent volatility.

- There's a causal relationship between realized and latent volatility. Higher realized volatility now causes higher latent volatility later.

Which one is correct?

## Answer by QuantCalc.net (score 0)

https://quant.stackexchange.com/a/85290

Short answer is that the second one is more close to market consensus.

Volatility autocorrelation (also known as volatility clustering or conditional heteroscedasticity) is typically modeled using ARCH (Autoregressive Conditional Heteroskedasticity) and GARCH (Generalized Autoregressive Conditional Heteroskedasticity) models.

- Autocorrelation in Shocks (Squared Returns): While daily returns (the actual percentage price change) are generally uncorrelated with previous returns (making the market "efficient"), their magnitude is not. If you look at the squared returns (a mathematical way to measure the size of the shocks, regardless of whether they are positive or negative), you'll see a strong positive correlation over time.

- The Role of GARCH Models: GARCH (Generalized Autoregressive Conditional Heteroskedasticity) models are essentially a formal, mathematical way to capture this persistence. They make the variance (volatility) of today's returns conditional on (dependent on) the squared returns and estimated variances from previous days.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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