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Create EGARCH time series model
egarch creates model objects for EGARCH models. The EGARCH model is a conditional variance model that models the logged conditional variance (as opposed to the conditional variance directly). The EGARCH(P,Q) model includes P lagged log conditional variances, Q lagged standardized innovations, and Q leverage terms.
Create model objects with known or unknown coefficients. Estimate unknown coefficients from data using estimate.
model = egarch creates a conditional variance EGARCH model of degrees zero.
model = egarch(P,Q) creates a conditional variance EGARCH model with GARCH degree P and ARCH degree Q.
model = egarch(Name,Value) creates an EGARCH model with additional options specified by one or more Name,Value pair arguments. Name can also be a property name and Value is the corresponding value. Name must appear inside single quotes (''). You can specify several name-value pair arguments in any order as Name1,Value1,...,NameN,ValueN.
Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.
'Constant' |
Scalar constant in the EGARCH model. Default: NaN |
'GARCH' |
Cell vector of coefficients associated with the lagged log conditional variances. When specified without GARCHLags, GARCH is a P-element cell vector of coefficients at lags 1, 2,...,P. When specified with GARCHLags, GARCH is an equivalent-length cell vector of coefficients associated with the lags in GARCHLags. Default: Cell vector of NaNs. |
'ARCH' |
Cell vector of coefficients associated with the magnitude of lagged standardized innovations. When specified without ARCHLags, ARCH is a Q-element cell vector of coefficients at lags 1, 2,...,Q. When specified with ARCHLags, ARCH is an equivalent-length cell vector of coefficients associated with the lags in ARCHLags. Default: Cell vector of NaNs. |
'Leverage' |
Cell vector of coefficients associated with lagged standardized innovations. When specified without LeverageLags, Leverage is a Q-element cell vector of coefficients at lags 1, 2,...,Q. When specified with LeverageLags, Leverage is an equivalent-length cell vector of coefficients associated with the lags in LeverageLags. Default: Cell vector of NaNs. |
'Offset' |
Scalar offset, or additive constant, associated with an innovation mean model. Default: 0 |
'GARCHLags' |
Vector of positive integer lags associated with the GARCH coefficients. Default: Vector of integers 1, 2,...,P. |
'ARCHLags' |
Vector of positive integer lags associated with the ARCH coefficients. Default: Vector of integers 1, 2,...,Q. |
'LeverageLags' |
Vector of positive integer lags associated with the leverage coefficients. Default: Vector of integers 1, 2,...,Q. |
'Distribution' |
Conditional probability distribution of the innovation process. Distribution is a string you specify as 'Gaussian' or 't'. Alternatively, specify it as a data structure with the field Name to store the distribution 'Gaussian' or 't'. If the distribution is 't', then the structure also needs the field DoF to store the degrees of freedom. Default: 'Gaussian' |
Note: Each GARCH, ARCH and Leverage coefficient is associated with an underlying lag operator polynomial and is subject to a near-zero tolerance exclusion test. That is, each coefficient is compared to the default lag operator zero tolerance, 1e-12. A coefficient is only included in the model if its magnitude is greater than 1e-12. Otherwise, it is considered sufficiently close to zero and excluded from the model. See LagOp for additional details. |
estimate | Fit EGARCH conditional variance model to data |
filter | Filter disturbances with EGARCH model |
forecast | Forecast EGARCH process |
infer | Infer EGARCH model conditional variances |
Display parameter estimation results for EGARCH models | |
simulate | Monte Carlo simulation of EGARCH models |
Consider a time series y_{t} with a constant mean offset,
where The EGARCH(P,Q) conditional variance process, , is of the form
where
for a Gaussian innovation distribution, and
for a Student's t distribution with degrees of freedom
The additive constant μ corresponds to the name-value argument Offset.
The constant κ corresponds to the name-value argument Constant.
The coefficients correspond to the name-value argument GARCH.
The coefficients correspond to the name-value argument ARCH.
The coefficients correspond to the name-value argument Leverage.
The distribution of z_{t} (the innovation distribution) corresponds to the name-value argument Distribution, and can be Gaussian or Student's t.
egarch enforces stationarity by ensuring the roots of the P-degree polynomial
lie outside the unit circle.
Value. To learn how value classes affect copy operations, see Copying Objects in the MATLAB^{®} documentation.
estimate | filter | forecast | infer | print | simulate