Description Usage Arguments Value Note Author(s) References See Also Examples
Fits a first order Beta-Skew-t-EGARCH model to a univariate time-series by exact Maximum Likelihood (ML) estimation. Estimation is via the nlminb
function
1 2 3 |
y |
numeric vector, typically a financial return series. |
asym |
logical. TRUE (default) includes leverage or volatility asymmetry in the log-scale specification |
skew |
logical. TRUE (default) enables and estimates the skewness in conditional density (epsilon). The skewness method is that of Fernandez and Steel (1998) |
components |
Numeric value, either 1 (default) or 2. The former estimates a 1-component model, the latter a 2-component model |
initial.values |
NULL (default) or a vector with the initial values. If NULL, then the values are automatically chosen according to model (with or without skewness, 1 or 2 components, etc.) |
lower |
NULL (default) or a vector with the lower bounds of the parameter space. If NULL, then the values are automatically chosen |
upper |
NULL (default) or a vector with the upper bounds of the parameter space. If NULL, then the values are automatically chosen |
hessian |
logical. If TRUE (default) then the Hessian is computed numerically via the optimHess function. Setting hessian=FALSE speeds up estimation, which might be particularly useful in simulation. However, it also slows down the extraction of the variance-covariance matrix by means of the vcov method. |
lambda.initial |
NULL (default) or a vector with the initial value(s) of the recursion for lambda and lambdadagger. If NULL then the values are chosen automatically |
c.code |
logical. TRUE (default) is faster since it makes use of compiled C-code |
logl.penalty |
NULL (default) or a numeric value. If NULL then the log-likelihood value associated with the initial values is used. Sometimes estimation can result in NA and/or +/-Inf values, which are fatal for simulations. The value logl.penalty is the value returned by the log-likelihood function in the presence of NA or +/-Inf values |
aux |
NULL (default) or a list, se code. Useful for simulations (speeds them up) |
... |
further arguments passed to the nlminb function |
Returns a list of class 'tegarch' with the following elements:
y |
the series used for estimation. |
date |
date and time of estimation. |
initial.values |
initial values used in estimation. |
lower |
lower bounds used in estimation. |
upper |
upper bounds used in estimation. |
lambda.initial |
initial values of lambda provided by the user, if any. |
model |
type of model estimated. |
hessian |
the numerically estimated Hessian. |
sic |
the value of the Schwarz (1978) information criterion. |
par |
parameter estimates. |
objective |
value of the log-likelihood at the maximum. |
convergence |
an integer code. 0 indicates successful convergence, see the documentation of nlminb. |
iterations |
number of iterations, see the documentation of nlminb. |
evaluations |
number of evaluations of the objective and gradient functions, see the documentation of nlminb. |
message |
a character string giving any additional information returned by the optimizer, or NULL. For details, see PORT documentation and the nlminb documentation. |
NOTE |
an additional message returned if one tries to estimate a 2-component model without leverage. |
Empty
Genaro Sucarrat, http://www.sucarrat.net/
Fernandez and Steel (1998), 'On Bayesian Modeling of Fat Tails and Skewness', Journal of the American Statistical Association 93, pp. 359-371.
Nelson, Daniel B. (1991): 'Conditional Heteroskedasticity in Asset Returns: A New Approach', Econometrica 59, pp. 347-370.
Harvey and Sucarrat (2014), 'EGARCH models with fat tails, skewness and leverage'. Computational Statistics and Data Analysis 76, pp. 320-338.
Schwarz (1978), 'Estimating the Dimension of a Model', The Annals of Statistics 6, pp. 461-464.
Sucarrat (2013), 'betategarch: Simulation, Estimation and Forecasting of First-Order Beta-Skew-t-EGARCH models'. The R Journal (Volume 5/2), pp. 137-147.
tegarchSim
, coef.tegarch
, fitted.tegarch
, logLik.tegarch
, predict.tegarch
, print.tegarch
, residuals.tegarch
, summary.tegarch
, vcov.tegarch
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ##simulate series with 500 observations:
set.seed(123)
y <- tegarchSim(500, omega=0.01, phi1=0.9, kappa1=0.1, kappastar=0.05,
df=10, skew=0.8)
##estimate a 1st. order Beta-t-EGARCH model and store the output in mymod:
mymod <- tegarch(y)
#print estimates and standard errors:
print(mymod)
#graph of fitted volatility (conditional standard deviation):
plot(fitted(mymod))
#graph of fitted volatility and more:
plot(fitted(mymod, verbose=TRUE))
#plot forecasts of volatility 1-step ahead up to 20-steps ahead:
plot(predict(mymod, n.ahead=20))
#full variance-covariance matrix:
vcov(mymod)
|
Loading required package: zoo
Attaching package: 'zoo'
The following objects are masked from 'package:base':
as.Date, as.Date.numeric
Date: Fri Oct 12 08:28:33 2018
Message (nlminb): relative convergence (4)
Coefficients:
omega phi1 kappa1 kappastar df skew
Estimate: 0.09851576 0.90227797 0.1222777 0.04601852 6.841971 0.83289703
Std. Error: 0.10152280 0.04901107 0.0273390 0.01826781 1.777501 0.04857256
Log-likelihood: -822.006027
BIC: 3.362599
omega phi1 kappa1 kappastar df
omega 1.030688e-02 5.141441e-04 4.008524e-05 3.215017e-04 0.0378532900
phi1 5.141441e-04 2.402085e-03 -6.478547e-04 6.971981e-05 -0.0105125169
kappa1 4.008524e-05 -6.478547e-04 7.474207e-04 9.901153e-05 -0.0162066060
kappastar 3.215017e-04 6.971981e-05 9.901153e-05 3.337129e-04 -0.0052085710
df 3.785329e-02 -1.051252e-02 -1.620661e-02 -5.208571e-03 3.1595088411
skew -4.513895e-04 -5.395232e-04 1.273991e-04 -3.590161e-04 0.0002487312
skew
omega -0.0004513895
phi1 -0.0005395232
kappa1 0.0001273991
kappastar -0.0003590161
df 0.0002487312
skew 0.0023592936
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