Generalized AutoRegressive Conditional Heteroskedasticity (GARCH)

Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) is a statistical model used in analyzing financial time-series data. Heteroskedasticity describes the irregular pattern of variation of an error term, or variable, in a statistical model. Essentially, where there is heteroskedasticity, observations do not conform to a linear pattern. Instead, they tend to cluster. The result is that the conclusions and predictive value one can draw from the model will not be reliable.

Although Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) models can be used in the analysis of a number of different types of financial data, for instance, macroeconomic data, financial institutions typically use them to estimate the volatility of returns for stocks, bonds and market indices. They use the resulting information to help determine pricing and judge which assets will potentially provide higher returns, as well as to forecast the returns of current investments to help in their asset allocation, hedging, risk management and portfolio optimization decisions.

GARCH was formulated in the 1980s as a way to address the problem of forecasting volatility in asset prices. It built on Economist Robert Engle's breakthrough 1982 work in introducing the Autoregressive Conditional Heteroskedasticity (ARCH) model. His model assumed the variation of financial returns was not constant over time but are autocorrelated, or conditional to/dependent on each other. For instance, one can see this in stock returns where periods of volatility in returns tend to be clustered together. GARCH models were some of the first financial asset models to incorporate fast.

Since the original introduction, many variations of GARCH have emerged. These include Nonlinear (NGARCH), which addresses correlation and observed “volatility clustering” of returns, and Integrated GARCH (IGARCH) which restricts the volatility parameter. All the variations of GARCH models seek to incorporate the direction, positive or negative, of returns in addition to the magnitude (addressed in the original model).

Each derivation of GARCH can be used to accommodate the specific qualities of the stock, industry or economic data. In assessing risk, financial institutions incorporate GARCH models into their Value-at-Risk (VAR), maximum expected loss (whether for a single investment or trading position, portfolio or at a division or firm-wide level) over a specified time period projections. GARCH models are viewed to provide better gauges of risk than can be obtained through tracking standard deviation alone.

Various studies have been conducted on the reliability of various GARCH models during different market conditions, including during the periods leading up to and after the 2007 financial crisis.