摘要：Most of the statistical tools are designed to model theconditional mean of a random variable. The tools describedin this article have a rather different purpose – tomodel the conditional variance, or volatility of a variable.There are several reasons to model and forecast volatility.First, we need to analyze the risk of holding an assetor the value of an option. Second, forecast confidence intervalsmay be time-varying, so that more accurate intervalscan be obtained by modeling the variance of the errors.Third, more efficient estimators can be obtained ifheteroskedasticity in the errors is handled properly.Autoregressive Conditional Heteroskedasticity (ARCH)models are specifically designed to model and forecastconditional variances. The variance of the dependentvariable is modeled as a function of past values of thedependent variable and independent, or exogenous variables.These models are widely used in various branches ofeconometrics, especially in financial time series analysis.This article analyses GARCH and ARCH models’ twomain characteristics: skewness and kurtosis.
其他摘要：Most of the statistical tools are designed to model theconditional mean of a random variable. The tools describedin this article have a rather different purpose – tomodel the conditional variance, or volatility of a variable.There are several reasons to model and forecast volatility.First, we need to analyze the risk of holding an assetor the value of an option. Second, forecast confidence intervalsmay be time-varying, so that more accurate intervalscan be obtained by modeling the variance of the errors.Third, more efficient estimators can be obtained ifheteroskedasticity in the errors is handled properly.Autoregressive Conditional Heteroskedasticity (ARCH)models are specifically designed to model and forecastconditional variances. The variance of the dependentvariable is modeled as a function of past values of thedependent variable and independent, or exogenous variables.These models are widely used in various branches ofeconometrics, especially in financial time series analysis.This article analyses GARCH and ARCH models’ twomain characteristics: skewness and kurtosis.
