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Univariate GARCH(P,Q) parameter estimation with Gaussian innovations
Syntax
Arguments
Description
[Kappa, Alpha, Beta] = ugarch(U, P, Q)
computes estimated univariate GARCH(P,Q) parameters with Gaussian innovations.
Kappa
is the estimated scalar constant term () of the GARCH process.
Alpha
is a P
-by-1 vector of estimated coefficients, where P
is the number of lags of the conditional variance included in the GARCH process.
Beta
is a Q
-by-1 vector of estimated coefficients, where Q
is the number of lags of the squared innovations included in the GARCH process.
The time-conditional variance, t2, of a GARCH(P,Q) process is modeled as
where represents the argument
Alpha
, represents
Beta
, and the GARCH(P, Q) coefficients {,
,
} are subject to the following constraints.
Note that U
is a vector of residuals or innovations (t) of an econometric model, representing a mean-zero, discrete-time stochastic process.
Although t2 is generated using the equation above,
t and
t2 are related as
where {vt} is an independent, identically distributed (i.i.d.) sequence ~ N(0,1).
Note
ugarch corresponds generally to the GARCH Toolbox function garchfit . The GARCH Toolbox provides a comprehensive and integrated computing environment for the analysis of volatility in time series. For information, see the GARCH Toolbox User's Guide or the financial products Web page at http://www.mathworks.com/products/finprod/.
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Examples
See ugarchsim
for an example of a GARCH(P,Q) process.
See Also
ugarchpred
, ugarchsim
, and the GARCH Toolbox function garchfit
References
James D. Hamilton, Time Series Analysis, Princeton University Press, 1994
![]() | tr2bonds | ugarchllf | ![]() |