GARCH Process

The generalized autoregressive conditional heteroskedasticity (GARCH) process is an econometric term developed in 1982 by Robert F. Engle, an economist and 2003 winner of the Nobel Memorial Prize for Economics, to describe an approach to estimate volatility in financial markets. There are several forms of GARCH modeling. The GARCH process is often preferred by financial modeling professionals because it provides a more real-world context than other forms when trying to predict the prices and rates of financial instruments.

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. GARCH is a statistical model that can be used to analyze a number of different types of financial data, for instance, macroeconomic data. Financial institutions typically use this model 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.

The general process for a GARCH model involves three steps. The first is to estimate a best-fitting autoregressive model. The second is to compute autocorrelations of the error term. The third step is to test for significance. Two other widely used approaches to estimating and predicting financial volatility are the classic historical volatility (VolSD) method and the exponentially weighted moving average volatility (VolEWMA) method.

GARCH models help to describe financial markets in which volatility can change, becoming more volatile during periods of financial crises or world events and less volatile during periods of relative calm and steady economic growth. On a plot of returns, for example, stock returns may look relatively uniform for the years leading up to a financial crisis such as the one in 2007. In the time period following the onset of a crisis, however, returns may swing wildly from negative to positive territory. Moreover, the increased volatility may be predictive of volatility going forward. Volatility may then return to levels resembling that of pre-crisis levels or be more uniform going forward. A simple regression model does not account for this variation in volatility exhibited in financial markets and is not representative of the "black swan" events that occur more than one would predict.

GARCH processes differ from homoskedastic models, which assume constant volatility and are used in basic ordinary least squares (OLS) analysis. OLS aims to minimize the deviations between data points and a regression line to fit those points. With asset returns, volatility seems to vary during certain periods of time and depend on past variance, making a homoskedastic model not optimal.

GARCH processes, being autoregressive, depend on past squared observations and past variances to model for current variance. GARCH processes are widely used in finance due to their effectiveness in modeling asset returns and inflation. GARCH aims to minimize errors in forecasting by accounting for errors in prior forecasting and, thereby, enhancing the accuracy of ongoing predictions.