EGARCH_CALIBRATE - Optimal Values for Model's Parameters

Computes the maximum likelihood estimated (MLE) model's parameters.

Syntax

EGARCH_CALIBRATE ([x], order, µ, [α], [γ], [β], f, ν, [mask], method, maxiter)

[X]

Required. Is the univariate time series data (a one-dimensional array of cells (e.g., rows or columns)).

Order

Optional. Is the time order in the data series (i.e., the first data point's corresponding date (earliest date = 1 (default), latest date = 0)).

Value	Order
1	Ascending (the first data point corresponds to the earliest date) (default).
0	Descending (the first data point corresponds to the latest date).

µ

Optional. Is the GARCH model long-run mean (i.e., mu). If missing, the process mean is assumed to be zero.

[α]

Required. Are the parameters of the ARCH(p) component model: [αo α1, α2 … αp] (starting with the lowest lag).

[γ]

Optional. Are the leverage parameters: [γ1, γ2 … γp] (starting with the lowest lag).

[β]

Optional. Are the parameters of the GARCH(q) component model: [β1, β2 … βq] (starting with the lowest lag).

F

Optional. Is the probability distribution function of the innovations/residuals (1 = Gaussian (default), 2 = t-Distribution, 3 = GED).

Value	Probability Distribution
1	Gaussian or Normal Distribution (default).
2	Student's t-Distribution.
3	Generalized Error Distribution (GED).

ν

Optional. Is the shape parameter (or degrees of freedom) of the innovations/residuals’ probability distribution function.

[Mask]

Optional. Is an array of 0's and 1's to specify which parameters to calibrate for. If missing, all parameters are included in the calibration.

Method

Optional. Is the calibration/fitting method (1 = MLE, 2 = Bayesian). If missing, a Maximum Likelihood Estimate (MLE) is assumed.

Value	Method
1	Maximum Likelihood Estimate (MLE) (default).
2	Bayesian.

MaxIter

Optional. Is the maximum number of iterations used to calibrate the model. If missing, the default maximum of 100 is assumed.

Remarks

1. The underlying model is described here.
2. The time series is homogeneous or equally spaced.
3. The time series may include missing values (e.g., #N/A) at either end.
4. The maximum likelihood estimation (MLE) is a statistical method for fitting a model to the data and provides estimates for the model's parameters.

Files Examples

Related Links

• Wikipedia - Autoregressive conditional heteroskedasticity.

References

• James Douglas Hamilton; Time Series Analysis, Princeton University Press; 1st edition(Jan 11, 1994), ISBN: 691042896.
• Tsay, Ruey S.; Analysis of Financial Time Series, John Wiley & SONS; 2nd edition(Aug 30, 2005), ISBN: 0-471-690740.