GARCH_CALIBRATE - Optimal Values for Model's Parameters

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

Syntax

GARCH_CALIBRATE ([x], order, µ, [α], [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).
[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.
  5. For the input argument - ([α]) (parameters of the ARCH component):
    • The input argument is not optional.
    • The value in the first element must be positive.
    • The order of the parameters starts with the lowest lag.
    • One or more parameters may have missing values or error codes (i.e., #NUM!, #VALUE!, etc.).
    • In the case where alpha has one non-missing entry/element (first), no ARCH component is included.
    • The order of the ARCH component model is solely determined by the order (minus one) of the last value in the array with a numeric value (vs. missing or error).
  6. For the input argument - ([β]) (parameters of the GARCH component):
    • The input argument is optional and can be omitted, in which case no GARCH component is included.
    • The order of the parameters starts with the lowest lag.
    • One or more parameters may have missing values or error codes (i.e., #NUM!, #VALUE!, etc.).
    • The order of the GARCH component model is solely determined by the order of the last value in the array with a numeric value (vs. missing or error).
  7. The shape parameter (ν) is only used for non-Gaussian distributions and is otherwise ignored.
  8. For the student's t-distribution, the shape parameter’s value must be greater than four.
  9. For GED distribution, the shape parameter’s value must be greater than one.
  10. GARCH_CALIBRATE returns the values for the model's parameters in the following order:
    1. $\mu $.
    2. ${\alpha _o},{\phi _1},...,{\phi _p}$.
    3. ${\beta _1},{\beta _2},...,{\theta _q}$.
    4. $\nu $.

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