What Is Autoregressive Conditional Heteroskedasticity?

Autoregressive conditional heteroskedasticity (ARCH) is a time-series statistical model used to analyze effects left unexplained by econometric models. In these models, the error term is the residual result left unexplained by the model. The assumption of econometric models is that the variance of this term will be uniform. This is known as "homoskedasticity." However, in some circumstances, this variance is not uniform, but "heteroskedastic."

Understanding Autoregressive Conditional Heteroskedasticity

In fact, the variance of these error terms is not just non-uniform but is affected by variances preceding it. This is referred to as "autoregression." Similarly, in statistics, when the variance of a term is affected by the variance of one or more other variables, it is "conditional."

This is particularly true in time-series analyses of financial markets. For example, in securities markets, periods of low volatility are often followed by periods of high volatility. So the variance of the error term describing these markets would vary depending on the variance of previous periods.

The problem with heteroskedasticity is that it makes the confidence intervals too narrow, thus giving a greater sense of precision than is warranted by the econometric model. ARCH models attempt to model the variance of these error terms, and in the process correct for the problems resulting from heteroskedasticity. The goal of ARCH models is to provide a measure of volatility that can be used in financial decision-making.

In financial markets, analysts observe something called volatility clustering in which periods of low volatility are followed by periods of high volatility and vice versa. For example, volatility for the S&P 500 was unusually low for an extended period during the bull market from 2003 to 2007, before spiking to record levels during the market correction of 2008. ARCH models are able to correct for the statistical problems that arise from this type of pattern in the data. As a result, they have become mainstays in modeling financial markets that exhibit volatility. The ARCH concept was developed by economist Robert F. Engle, for which he won the 2003 Nobel Memorial Prize in Economic Sciences.