naginterfaces.library.rand.times_garch_asym2¶
- naginterfaces.library.rand.times_garch_asym2(dist, num, ip, iq, theta, gamma, df, fcall, comm, statecomm)[source]¶
times_garch_asym2
generates a given number of terms of a type II process (see Engle and Ng (1993)).For full information please refer to the NAG Library document for g05pe
https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/g05/g05pef.html
- Parameters
- diststr, length 1
The type of distribution to use for .
A Normal distribution is used.
A Student’s -distribution is used.
- numint
, the number of terms in the sequence.
- ipint
The number of coefficients, , for .
- iqint
The number of coefficients, , for .
- thetafloat, array-like, shape
The first element must contain the coefficient , the next elements must contain the coefficients , for . The remaining elements must contain the coefficients , for .
- gammafloat
The asymmetry parameter for the sequence.
- dfint
The number of degrees of freedom for the Student’s -distribution.
If , is not referenced.
- fcallbool
If , a new sequence is to be generated, otherwise a given sequence is to be continued using the information in [‘r’].
- commdict, communication object, modified in place
Communication structure for the reference vector.
If , this argument must have been initialized by a prior call to
times_garch_asym2
.- statecommdict, RNG communication object, modified in place
RNG communication structure.
This argument must have been initialized by a prior call to
init_repeat()
orinit_nonrepeat()
.
- Returns
- htfloat, ndarray, shape
The conditional variances , for , for the sequence.
- etfloat, ndarray, shape
The observations , for , for the sequence.
- Raises
- NagValueError
- (errno )
On entry, is not valid: .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
On entry, .
Constraint: .
- (errno )
or is not the same as when [‘r’] was set up in a previous call.
Previous value of and .
Previous value of and .
- (errno )
On entry, [‘state’] vector has been corrupted or not initialized.
- (errno )
On entry, sum of , for is : .
- Notes
A type II process can be represented by:
where or . Here is a standardized Student’s -distribution with degrees of freedom and variance , is the number of observations in the sequence, is the observed value of the process at time , is the conditional variance at time , and the set of all information up to time . Symmetric GARCH sequences are generated when is zero, otherwise asymmetric GARCH sequences are generated with specifying the amount by which positive (or negative) shocks are to be enhanced.
One of the initialization functions
init_repeat()
(for a repeatable sequence if computed sequentially) orinit_nonrepeat()
(for a non-repeatable sequence) must be called prior to the first call totimes_garch_asym2
.
- References
Bollerslev, T, 1986, Generalised autoregressive conditional heteroskedasticity, Journal of Econometrics (31), 307–327
Engle, R, 1982, Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation, Econometrica (50), 987–1008
Engle, R and Ng, V, 1993, Measuring and testing the impact of news on volatility, Journal of Finance (48), 1749–1777
Hamilton, J, 1994, Time Series Analysis, Princeton University Press