What Is Generalized AutoRegressive Conඣditional Heteroskedasticity (GARCH)?

Generalized AutoRegressive Conditional Heteroskedasticity (GARCH) is used to help predict the volatility of returns on financial assets. The statistical model helps analyze time-series data where the variance error is believed to be serially autocorrelated. GARCH models assume that the variance of the error term follows an autoregressi🃏ve moving average process.

Understanding Generalize♈d AutoRegressive Conditional Heteroskedasticity (GAR𝔉CH)

Although GARCH models can be used in the analysis of a number of different types of financial data, such as macroeconomic data, financial institutions typically use them to estimate the 澳洲幸运5官方开奖结果体彩网: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 澳洲幸运5官方开奖结果体彩网:asset allocation, hedging, risk management, and portfolio optimization decisions.

GARCH models are used when the variance of the error term is not constant. That is, the error term is 澳洲幸运5官方开奖结果体彩网:heteroskedastic. Heteroskedasticity describes the irregular pattern of variation of an error term, or variable, in a statistical model.

Essenꩵtially, wherever there is heteroskedasticity, observations do not conform to a linear pattern. Instead, they tend to cluster. Therefore, if statistical models that assume constant variance are used on th🐷is data, then the conclusions and predictive value one can draw from the model will not be reliable.

The variance of the error term in GARCH models is assumed to vary systematically, conditional on the average size of the error terms in previous periods. In other words, it has conditional heteroskedasticity, and the reason for the heteroskedasticity is that the error term is following an autoregressive 澳洲幸运5官方开奖结果体彩网:moving average pattern. This means that it is a function of an average of its own past values.🧸

History of GARCH

GARCH was developed in 1986 by Dr. Tim Bollerslev, a doctoral student at the time, 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 Heteros🌟kedasticity (ARCH) model. His model assumed the variation of financial returns were not constant over time but autocorrelated, or conditional to/dependent on each other. One can see this exemplified in stock returns where periods of volatility in returns tend to be clustered together.

Since the original introduction, many variations of GARCH have emerged. These include Nonlinear (NGARCH), which addresses 澳洲幸运5官方开奖结果体彩网:correlation and obser𒅌ved "volatility clustering" of returns, and Integrated GARCH (IGARCH), which ꦜrestricts the volatility parameter. All the GARCH model variations 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. When assessing risk, financial institutions incorporate GARCH models into their 澳洲幸运5官方开奖结果体彩网: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. GARCH models are viewed to provide better gauges of risk than can be obtained through tracking 澳洲幸运5官方开奖结果体彩网: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 澳洲幸运5官方开奖结果体彩网:Great Recession.

The Bottom Line

A GARCH model, short for Generalized AutoRegressive🦂 Conditional Heteroskedasticity, is used in regressions where the erro🎃r terms appear to be linked with one another, or with other variables. In financial statistics, it is used to predict the volatility of stocks, bonds, and other securities in order to determine the likely risk and returns associated with those investments.