Lesson 3.1: Introduction to Volatility Modeling
Understanding volatility clustering and why constant variance models fail for financial data.
The Stylized Fact of Financial Markets
The ARIMA models we've studied assume the variance of the error term () is constant. This is called **homoskedasticity**. A quick glance at any stock return chart shows this is false.
The Core Phenomenon: Volatility Clustering
Volatility clustering is the empirical observation that:
"Large changes tend to be followed by large changes, and small changes tend to be followed by small changes."
Markets experience periods of high turmoil (large price swings) and periods of calm. This means volatility is **autocorrelated** and, therefore, predictable. We need a model for this time-varying, or **heteroskedastic**, variance.
Imagine a plot of stock returns. You would see quiet periods with small fluctuations, and turbulent periods (like 2008 or 2020) with huge fluctuations.
What's Next? Modeling the Variance
The observation of volatility clustering motivates a new class of models designed to capture the dynamics of the conditional variance.
In the next lesson, we will introduce the first formal model for this phenomenon: the **Autoregressive Conditional Heteroskedasticity (ARCH) model**.