On the Generalized Autoregressive Conditional Heteroskedasticity Model
Abstract
The basic version of the least squares model assumes homoskedasticity,
the expected value of any given error term, squared, is equal to the
variance of all the error terms taken together. When this assumption
is violated; that is, where the error terms may reasonably be expected
to be larger for some points or ranges in the data than for others,
problems will then arise in the standard ordinary least squares analysis.
In practice, this issue often arises in financial applications where the
key issue is the variance of the error terms itself. The variance of the
returns on an asset or portfolio represents the risk level of those
returns. Empirical data will often show that some time periods are
riskier than others; that is, the expected value of error terms at some
times is greater than at others. Moreover, these risky times are not
scattered randomly across quarterly or annual data. Instead, there is
a degree of autocorrelation in the variance of financial returns. This
paper will explore the ARCH (autoregressive conditional heteroskedasticity)
and GARCH (generalized autoregressive conditional heteroskedasticity)
models which have become widely accepted tools for dealing with time series
heteroskedastic models. Similarly we will also discuss how these models
provide a volatility measure that can be used in financial decisions
concerning an analysis of risk, portfolio selection, or derivative pricing.
Table of Contents
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