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Using ARCH/GARCH to Assess Conditional Heteroskedasticity

Article Quant Q&A · Author: accpnt
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Summary

The document discusses using ARCH or GARCH models to describe time-varying volatility in a financial series, prompted by a researcher studying copper prices. These models relate current conditional variance to past observations or shocks. The proposed diagnostic is to estimate the model and examine whether its coefficients are statistically distinguishable from zero: significant coefficients can indicate dependence in volatility, while insignificant ones may suggest that the chosen model and inputs do not capture it.

This is a preliminary indicator rather than a complete test of heteroskedasticity. The exchange discusses no formal test procedure, fitted results, model selection, or residual diagnostics, and the absence of significant coefficients does not establish constant variance in general. For a copper-price thesis, the approach therefore gives a starting point for investigating volatility clustering, but the result depends on the specified model and series representation.

Key ideas

  • ARCH/GARCH models represent conditional volatility using information from past observations or shocks.
  • Significant variance-model coefficients can indicate time dependence in volatility.
  • Insignificant coefficients only suggest that the selected model did not capture such dependence.
  • The document offers a preliminary interpretation rather than a complete testing workflow.

Tags

CommoditiesVolatilityStatistics
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# Quantifying volatility: a step by step approach?


# Quantifying volatility: a step by step approach?












I am a former electronics engineer and I'm fairly new to financial time series analysis. I'm currently working on a thesis on copper determinants and what factors influence its price from an economic perspective. I'd like quantify its volatility over time in order to show the complexity of its price forecasting.

Alternative techniques for forecasting mineral commodity prices from Tapia Cortez et al. conclude that time series modelling is somewhat limited for mineral commodities price forecasting.

I think I understand the maths behind ARCH/GARCH models but I lack financial knowledge. There are several tutorials on how to apply these models but very few in my opinion on why we use them. My prior idea would be showing that there is conditional heteroskedasticity. Am I right ? How would I test this assumption ? I am getting confused on which tools and models would be used to infer my hypothesis.

## Answer by FP0 (score 1)

https://quant.stackexchange.com/a/71681

Indeed, one of the purposes of ARCH/GARCH is to model the volatility of a time series using past values of the times series. If you fit an ARCH/GARCH model, then you are going to estimate coefficients which determine how the volatility of your process at time $t$ depends on previous observations of your time series. If you see that none of these coefficients are significantly different than 0, then you could assume that there is no heteroscedasticity (or at least that it is not determined by the dependent variables you have used in your model). If at least one coefficient is significantly different from 0, then it would be a good indicator that there is indeed heteroscedasticity in your time series.

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.