Volatility Modeling with ARCH and GARCH in R: A Hands-On Interactive Course

A stock index does not swing by the same amount every day. Quiet weeks and violent weeks arrive in runs, and a forecast that ignores that gives intervals that are too wide when the market is calm and far too narrow when it is not. This six-lesson interactive course starts from that pattern and builds the models that describe it, from ARCH and GARCH through to Value at Risk and time-varying correlation.

The first lesson shows the pattern in real DAX returns, before any model is fitted: the returns look unpredictable, but their squares do not. From there the course writes the ARCH idea as one equation, adds yesterday's variance to get the GARCH(1,1) workhorse, fits it in R, and then puts the fitted model to work, forecasting volatility, turning it into a one-day Value at Risk number, and letting the correlation between two series move over time.

Each lesson is a guided, interactive experience: you run real R code in the page, answer checkpoints, and work with one real dataset per idea. No setup, no installs.

The six lessons

Lesson 1: Conditional heteroskedasticity and volatility clustering

See why a returns series has a steady mean but a variance that moves. Compute a 60-day rolling standard deviation on the DAX, compare the ACF of the returns with the ACF of the squared returns, and count how often a constant-variance 95% interval actually covers the calm days and the violent ones.

Start Lesson 1: Conditional heteroskedasticity and volatility clustering

Lesson 2: ARCH models

Write the ARCH(q) idea as one equation, today's variance as a function of recent squared shocks. Simulate one so the clustering appears in front of you, test for ARCH effects with a Ljung-Box test on squared residuals, and read the fitted conditional variance against the realised series.

Lesson 2 is coming soon.

Lesson 3: The GARCH family of volatility models

See why ARCH needs a long lag order and GARCH does not. Read alpha and beta in GARCH(1,1) as shock and persistence, see what alpha plus beta close to 1 means for how long a shock lasts, and meet the asymmetric extensions that let bad news raise volatility more than good news.

Lesson 3 is coming soon.

Lesson 4: Fitting GARCH in R

Fit GARCH(1,1) end to end on a real returns series with tseries::garch(), then again with fGarch::garchFit() for the richer output. Read the coefficient table, extract the fitted conditional standard deviation, check the standardised residuals, and compare Normal against Student-t errors.

Lesson 4 is coming soon.

Lesson 5: Forecasting volatility and Value at Risk

Forecast the conditional variance forward and watch multi-step forecasts decay towards the unconditional variance. Turn a volatility forecast into a one-day Value at Risk number, then backtest it by counting exceedances against the nominal rate.

Lesson 5 is coming soon.

Lesson 6: Multivariate volatility and DCC-GARCH

When two series move together, the covariance moves too. Fit a univariate GARCH to each series, then let the correlation itself vary over time, and see what that means for a portfolio when correlations spike exactly when you need diversification. The rugarch and rmgarch workflow is shown as code to read, not run in the browser.

Lesson 6 is coming soon.

Who this is for

Anyone comfortable reading an ACF plot and fitting a time series model in R, for example from the ARIMA and Seasonal ARIMA course. You do not need any finance background: every idea is introduced on real daily stock returns. By the end you will be able to spot volatility clustering, fit and check ARCH and GARCH models, and use a fitted model to forecast volatility and estimate Value at Risk.

What you will be able to do

• Spot volatility clustering in a returns series, and say why the ACF of squared returns shows what the ACF of the returns hides
• Explain why a constant-variance prediction interval is too wide in calm stretches and too narrow in violent ones
• Write an ARCH(q) and a GARCH(1,1) model, and read alpha and beta as shock and persistence
• Fit ARCH and GARCH models in R with tseries and fGarch, and check the standardised residuals
• Forecast conditional variance, turn it into a one-day Value at Risk, and backtest it
• Let the correlation between two series vary over time with a DCC-GARCH model

This course is part of the Forecaster track.

Ready? Begin with Lesson 1: Conditional heteroskedasticity and volatility clustering.