Heteroskedasticity

Explained: conditional heteroskedasticity conditional homoskedasticity heteroskedasticity homoskedasticity regime switching model unconditional heteroskedasticity unconditional homoskedasticity

A univariate stochastic process X is said to be homoskedastic if standard deviations of terms are constant for all times t. Otherwise, it is said to be heteroskedastic. This is illustrated with realizations of two stochastic processes in Exhibit 1.

Homoskedastic vs. Heteroskedastic Exhibit 1

Realizations of two processes are indicated. The first exhibits homoskedasticity. The second exhibits heteroskedasticity.

Heteroskedasticity is an important concept in finance because asset returns in the capital, commodity and energy markets often exhibit heteroskedasticity.

Heteroskedasticity can take two forms. A process is unconditionally heteroskedastic if unconditional standard deviations are not constant. It is conditionally heteroskedastic if conditional standard deviations are not constant (see the notation conventions documentation).

For example, stock or bond returns tend to be conditionally heteroskedastic. The prices exhibit non-constant volatility, but periods of low or high volatility are generally not known in advance. New England electricity prices, on the other hand, exhibit unconditional heteroskedasticity. The prices tend to have higher volatilities during the Summer than during other seasons. This is predictable, so the electricity prices exhibit unconditional heteroskedasticity.

If a process is unconditionally heteroskedastic, then it is necessarily conditionally heteroskedastic. The converse is not true. If a process is not unconditionally heteroskedastic or not conditionally heteroskedastic, it is said to be unconditionally homoskedastic or conditionally homoskedastic, respectively.

All these notions extend to higher dimensions, A multivariate stochastic process X is said to be homoskedastic if its covariance matrix is constant for all times t, etc.

In finance, a variety of models are used for conditionally heteroskedastic processes. These include

autoregressive conditional heteroskedastic (ARCH) models;

generalized ARCH (GARCH) models

regime-switching models; and

stochastic volatility models.

Related Internal Links
ARCH A category of conditionally heteroskedastic stochastic processes. kurtosis A parameter describing the peakedness and tails of a probability distribution. random walk A discrete stochastic process whose increments form a white noise. stochastic volatility model A category of conditionally heteroskedastic stochastic processes. time series and stochastic processes An introductory article. volatility A metric of  variability in a stochastic process. volatility skew A condition where implied volatilities vary by strike. white noise A simple form of stochastic process.
Sponsored Links
	Ads by Contingency Analysis
Related Books
Franses (1998) is an excellent introductions to time series analysis. Alexander (2001) discusses GARCH models in the context of financial applications. Hamilton (1994) is the authoritative reference on time series analysis. Time Series Models for Business and Economic Forecasting Philip Hans Franses quality   technical   1998   Market Models Carol Alexander quality   technical   2001   Time Series Analysis James Hamilton quality   technical   1994
Related Forum Discussions
HeterosCedacity vs. HeterosKedacity 03 Mar 2005 Which spelling is correct?
Sponsored Links
Disclaimer website: http://www.contingencyanalysis.com glossary direct link: http://www.riskglossary.com copyright © Contingency Analysis, 2004