Volatility is not just “how much a price moves.” In many real-world time series—stock returns, exchange rates, commodity prices, even some demand and energy signals—volatility changes over time in a patterned way. Calm periods tend to cluster together, and turbulent periods do the same. This behaviour is called volatility clustering, and it breaks a common assumption in basic time-series models: that the variance of errors is constant.
GARCH (Generalized Autoregressive Conditional Heteroskedasticity) models were designed to capture this time-varying variance directly. If you are learning forecasting, risk analytics, or financial modelling through a data scientist course in Coimbatore, understanding GARCH is useful because it teaches you how to model uncertainty itself—not just the average trend.
Why Standard Models Struggle With Volatility Clustering
Traditional models like ARIMA focus on modelling the conditional mean of a series (the expected value given past values). They often assume the error term has constant variance. But in financial returns, errors tend to show bursts:
- A market shock leads to large swings for several days or weeks.
- A stable period leads to small swings for a while.
This matters because many decisions depend on volatility: risk limits, margin requirements, Value at Risk (VaR), hedging, and stress testing. When variance changes over time, treating it as constant can understate risk during turbulent periods and overstate it during calm periods.
GARCH models address this by modelling the conditional variance—how volatility evolves based on past information.
From ARCH to GARCH: The Core Idea
Before GARCH, there was ARCH (Autoregressive Conditional Heteroskedasticity). ARCH models volatility as a function of past squared errors (past shocks). The challenge is that pure ARCH often needs many lag terms to fit real data well.
GARCH generalises this by adding a term for past variance. In simple terms:
- Big shocks tend to increase volatility.
- High volatility tends to persist for a while.
This is why GARCH is widely used: it captures both shock impact and volatility persistence with relatively few parameters. In applied learning environments—like a data scientist course in Coimbatore focused on time series—GARCH becomes a practical example of building models that align with how data behaves in the real world.
How a Basic GARCH(1,1) Model Works
The most common form is GARCH(1,1). Let returns be rtr_trt, and the error term be ϵt\epsilon_tϵt. We usually write:
- Mean equation (simplified): rt=μ+ϵtr_t = \mu + \epsilon_trt=μ+ϵt
- Error decomposition: ϵt=σtzt\epsilon_t = \sigma_t z_tϵt=σtzt, where ztz_tzt is typically assumed to be i.i.d. with mean 0 and variance 1
- Variance equation:
σt2=ω+αϵt−12+βσt−12\sigma_t^2 = \omega + \alpha \epsilon_{t-1}^2 + \beta \sigma_{t-1}^2σt2=ω+αϵt−12+βσt−12
What these parameters mean:
- ω\omegaω: baseline variance level (must be positive)
- α\alphaα: how strongly volatility reacts to the most recent shock (news impact)
- β\betaβ: how strongly volatility persists over time (memory)
A useful rule of thumb is α+β\alpha + \betaα+β:
- If it’s close to 1, volatility is highly persistent (shocks fade slowly).
- If it’s much smaller, volatility mean-reverts faster.
This structure is why GARCH is effective: it allows volatility to update each period using both new information (shock) and old information (past variance).
Estimation and Model Checking in Practice
GARCH models are typically fit using maximum likelihood estimation (MLE). In practice, you also choose an error distribution. Financial returns often have heavy tails, so using Student’s t errors can improve realism compared to assuming normal errors.
A practical workflow looks like this:
- Work with returns, not raw prices (log returns are common).
- Fit a mean model first (sometimes a simple constant mean is enough; sometimes AR terms help).
- Test for ARCH effects in residuals (an ARCH-LM test is commonly used). If residual variance shows dependence, GARCH is justified.
- Fit a GARCH model and check diagnostics:
- Standardised residuals should look closer to white noise.
- Squared standardised residuals should show reduced autocorrelation.
- Compare models using AIC/BIC, and validate out-of-sample where possible.
This is exactly the kind of modelling discipline that translates well beyond finance. Anyone doing serious forecasting—often covered in a data scientist course in Coimbatore—benefits from learning how to test assumptions rather than blindly applying models.
Extensions and Where GARCH Adds Value
Real markets sometimes show asymmetry: negative returns increase future volatility more than positive returns of the same size (the “leverage effect”). Standard GARCH cannot fully capture this, so extensions are used:
- EGARCH: models log variance and can represent asymmetry without forcing positivity constraints the same way.
- GJR-GARCH: explicitly adds a term that reacts differently to negative shocks.
Common use cases where GARCH is valuable:
- Risk management: estimating time-varying volatility for VaR and risk limits
- Portfolio analytics: understanding when correlation and volatility regimes change
- Options and hedging: volatility forecasts influence pricing and hedge ratios
- Operational forecasting with uncertainty: in some domains (like energy load variability), modelling changing variance improves planning
Conclusion
GARCH models are powerful because they treat volatility as a dynamic process rather than a fixed number. They capture two key realities: shocks affect volatility, and volatility tends to persist. A well-fitted GARCH model can improve risk estimates, make forecasts more realistic, and help decision-makers prepare for changing uncertainty.
If you are building strong time-series foundations through a data scientist course in Coimbatore, GARCH is a practical milestone: it shifts your thinking from “predict the next value” to “predict the next level of uncertainty,” which is often what real-world decisions depend on.
