naginterfaces.library.tsa.uni_​garch_​exp_​forecast

naginterfaces.library.tsa.uni_garch_exp_forecast(nt, ip, iq, theta, ht, et)[source]

uni_garch_exp_forecast forecasts the conditional variances, from an exponential sequence, where is the forecast horizon and is the current time (see Engle and Ng (1993)).

For full information please refer to the NAG Library document for g13fh

https://www.nag.com/numeric/nl/nagdoc_27.1/flhtml/g13/g13fhf.html

Parameters
ntint

, the forecast horizon.

ipint

The number of coefficients, , for .

iqint

The number of coefficients, , for .

thetafloat, array-like, shape

The initial parameter estimates for the vector . The first element must contain the coefficient and the next elements must contain the autoregressive coefficients , for . The next elements must contain the coefficients , for . The next elements must contain the moving average coefficients , for .

htfloat, array-like, shape

The sequence of past conditional variances for the process, , for .

etfloat, array-like, shape

The sequence of past residuals for the process, , for .

Returns
fhtfloat, ndarray, shape

The forecast values of the conditional variance, , for .

Raises
NagValueError
(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

(errno )

On entry, .

Constraint: .

Notes

No equivalent traditional C interface for this routine exists in the NAG Library.

Assume the process represented by:

where or , and , denotes the expected value of , has been modelled by uni_garch_exp_estim(), and the estimated conditional variances and residuals are contained in the arrays and respectively.

uni_garch_exp_forecast will then use the last elements of the arrays and to estimate the conditional variance forecasts, , where and is the forecast horizon.

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

Glosten, L, Jagannathan, R and Runkle, D, 1993, Relationship between the expected value and the volatility of nominal excess return on stocks, Journal of Finance (48), 1779–1801

Hamilton, J, 1994, Time Series Analysis, Princeton University Press