| Type: | Package |
| Title: | Generalized Autoregressive Score Models |
| Version: | 0.3.4.1 |
| Description: | Simulate, estimate and forecast using univariate and multivariate GAS models as described in Ardia et al. (2019) <doi:10.18637/jss.v088.i06>. |
| License: | GPL-3 |
| BugReports: | https://github.com/LeopoldoCatania/GAS/issues |
| URL: | https://github.com/LeopoldoCatania/GAS |
| LazyData: | TRUE |
| Imports: | Rcpp (≥ 0.12.2), Rsolnp, MASS, xts, numDeriv, zoo, cubature |
| LinkingTo: | Rcpp, RcppArmadillo |
| Depends: | R (≥ 3.4.0), methods |
| Suggests: | testthat |
| NeedsCompilation: | yes |
| Packaged: | 2024-08-19 08:41:50 UTC; hornik |
| Repository: | CRAN |
| Date/Publication: | 2024-08-19 09:00:52 UTC |
| Author: | Leopoldo Catania |
| Maintainer: | Leopoldo Catania <leopoldo.catania@econ.au.dk> |
Generalized Autoregressive Score models in R
Description
The GAS package allows us to simulate, estimate and forecast using univariate and multivariate Generalized Autoregressive Score (GAS) models (also known as Dynamic Conditional Score (DCS) models), see e.g., Creal et. al. (2013) and Harvey (2013). A detailed implementation of the package functionalities are reported in Ardia et. al. (2018, 2019).
Details
The authors acknowledge Google for financial support via the Google Summer of
Code 2016 project "GAS"; see https://summerofcode.withgoogle.com/archive/2016/projects/4537082387103744/.
Current limitations:
The multivariate GAS model for N>4 does not report the exact update for the correlation parameters since the Jacobian of the hyperspherical coordinates transformation needs to be coded for the case N>4. The Jacobian for N>4 is replaced by the identity matrix.
Note
By using GAS you agree to the following rules:
You must cite Ardia et al. (2019) in working papers and published papers that use
GAS. Usecitation("GAS").You must place the following URL in a footnote to help others find
GAS: https://CRAN.R-project.org/package=GAS.You assume all risk for the use of
GAS.
Author(s)
Leopoldo Catania [aut,cre], Kris Boudt [ctb], David Ardia [ctb]
Maintainer: Leopoldo Catania <leopoldo.catania@econ.au.dk>
References
Ardia D, Boudt K and Catania L (2018).
"Downside Risk Evaluation with the R Package GAS."
R Journal, 10(2), 410-421.
doi:10.32614/RJ-2018-064.
Ardia D, Boudt K and Catania L (2019).
"Generalized Autoregressive Score Models in R: The GAS Package."
Journal of Statistical Software, 88(6), 1-28.
doi:10.18637/jss.v088.i06.
Creal D, Koopman SJ, Lucas A (2013).
"Generalized Autoregressive Score Models with Applications."
Journal of Applied Econometrics, 28(5), 777-795.
doi:10.1002/jae.1279.
Harvey AC (2013). Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series. Cambridge University Press.
Backtest a series of one-step ahead density predictions.
Description
The BacktestDensity() function accepts an object of the class uGASRoll, and returns a list with
two elements: (i) the averages Negative Log Score (NLS) and weighted Continuous Ranked Probability Score (wCRPS)
introduced by Gneiting and Ranjan (2012), and (ii) their values at each point in time. The wCRPS is
evaluated using 5 weight functions, see Details.
Usage
BacktestDensity(Roll, lower, upper, K = 1000, a = NULL, b = NULL)
Arguments
Roll |
an object of the class uGASRoll. |
lower |
|
upper |
|
K |
|
a |
|
b |
|
Details
The average Negative Log Score (NLS) is computed as the negative of the average of the log scores evaluated
during the out-of-sample period. The average weighted Continuous Ranked Probability Score (wCRPS) is computed as
the average of the wCRPS evaluated during the out-of-sample period, see Gneiting and Ranjan (2012).
The wCRPS is evaluated using Equation 16 of Gneiting and Ranjan (2012). The weights functions implemented are:
-
w(z) = 1: Uniform, -
w(z) = \phi_{a,b}(z): Center, -
w(z) = 1 - \phi_{a,b}(z): Tails, -
w(z) = \Phi_{a,b}(z): Right tail, -
w(z) = 1 - \Phi_{a,b}(z): Left tail,
where \phi_{a,b}(z) and \Phi_{a,b}(z) are the pdf and cdf of a Gaussian distribution with mean a
and standard deviation b, respectively. The label "Uniform" represents the case where equal
emphasis is given to all the parts of the distribution.
Value
A list with elements: average, series. The element "average" is a named vector
with the averages NLS and wCRSP. The element "series" is a list: the fist element, LS, contains
the out-of-sample Log Score (not with the negative sign), the second element, WCRPS, contains a matrix
with the wCRPS series. The columns of this matrix are named: "uniform", "center", "tails",
"tail_r", "tail_l", which are associated with the wCRSP with emphasis on: Uniform, Center, Tails,
Right tail and Left tail, respectively.
Author(s)
Leopoldo Catania
References
Gneiting T, Ranjan R (2011). "Comparing Density Forecasts using Threshold -and Quantile-Weighted Scoring Rules." Journal of Business & Economic Statistics, 29(3), 411-422. doi:10.1198/jbes.2010.08110.
Examples
## Not run:
data("cpichg")
GASSpec = UniGASSpec(Dist = "std", ScalingType = "Identity",
GASPar = list(location = TRUE, scale = TRUE,
shape = FALSE))
Roll = UniGASRoll(cpichg, GASSpec, ForecastLength = 50,
RefitEvery = 10, RefitWindow = c("moving"))
BackTest = BacktestDensity(Roll, lower = -100, upper = 100)
BackTest$average
## End(Not run)
Backtest Value at Risk (VaR)
Description
This function implements several backtesting procedures for the Value at Risk (VaR). These are: (i) The statistical tests of Kupiec (1995), Christoffesen (1998) and Engle and Manganelli (2004), (ii) The tick loss function detailed in Gonzalez-Rivera et al. (2004), the mean and max absolute loss used by McAleer and Da Veiga (2008) and the actual over expected exceedance ratio.
Usage
BacktestVaR(data, VaR, alpha, Lags = 4)
Arguments
data |
|
VaR |
|
alpha |
|
Lags |
|
Details
This function implements several backtesting procedure for the Value at Risk. The implemented statistical tests are:
-
LRucThe unconditional coverage test of Kupiec (1995). -
LRccThe conditional coverage test of Christoffesen (1998). -
DQThe Dynamic Quantile test of Engle and Manganelli (2004).
The implemented VaR backtesting quantities are:
-
ADmean and maximum absolute deviation between the observations and the quantiles as in McAleer and Da Veiga (2008). -
LossAverage quantile loss and quantile loss series as in Gonzalez-Rivera et al. (2004). -
AEActual over Expected exceedance ratio.
Value
A list with elements: LRuc, LRcc, DQ, AD, AE.
Author(s)
Leopoldo Catania
References
Christoffersen PF (1998).
"Evaluating Interval Rorecasts."
International Economic Review, 39(4), 841-862.
Engle RF and Manganelli S. (2004).
"CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles."
Journal of Business & Economic Statistics, 22(4), 367-381.
doi:10.1198/073500104000000370.
Gonzalez-Rivera G, Lee TH, and Mishra, S (2004).
"Forecasting Volatility: A Reality Check Based on Option Pricing, Utility Function, Value-at-Risk, and Predictive Likelihood."
International Journal of Forecasting, 20(4), 629-645.
doi:10.1016/j.ijforecast.2003.10.003.
Kupiec PH (1995).
"Techniques for Verifying the Accuracy of Risk Measurement Models."
The Journal of Derivatives, 3(2), 73-84.
doi:10.3905/jod.1995.407942
McAleer M and Da Veiga B (2008). "Forecasting Value-at-Risk with a Parsimonious Portfolio Spillover GARCH (PS-GARCH) Model." Journal of Forecasting, 27(1), 1-19. doi:10.1002/for.1049.
Examples
data("StockIndices")
GASSpec = UniGASSpec(Dist = "std", ScalingType = "Identity",
GASPar = list(location = FALSE, scale = TRUE,
shape = FALSE))
FTSEMIB = StockIndices[, "FTSEMIB"]
InSampleData = FTSEMIB[1:1500]
OutSampleData = FTSEMIB[1501:2404]
Fit = UniGASFit(GASSpec, InSampleData)
Forecast = UniGASFor(Fit, Roll = TRUE, out = OutSampleData)
alpha = 0.05
VaR = quantile(Forecast, alpha)
BackTest = BacktestVaR(OutSampleData, VaR, alpha)
Build confidence bands for the filtered parameters
Description
Build confidence bands for the filtered parameters sampling the coefficients from the asymptotic distribution as in Blasques et al. (2016).
Usage
ConfidenceBands(object, B = 10000, probs = c(0.01,0.1,0.9,0.99), ...)
Arguments
object |
|
B |
|
probs |
|
... |
Additional arguments. |
Details
This function implements the "In-Sample Simulation-Based Bands" Section 3.3 of Blasques et al. (2016).
Value
An object of the class array of dimension (T+1) x B x K, where T is the length of
the time series, K is the number of parameters and B the number of draws. The first slice reports
the estimated filtered parameters. The one step ahead prediction is also reported, this why T+1.
Author(s)
Leopoldo Catania
References
Blasques F, Koopman SJ, Lasak K, and Lucas, A (2016). "In-sample Confidence Bands and Out-of-Sample Forecast Bands for Time-Varying Parameters in Observation-Driven Models." International Journal of Forecasting, 32(3), 875-887. doi:10.1016/j.ijforecast.2016.04.002.
Examples
## Not run:
# show the information of all the supported distributions
library("GAS")
data("cpichg")
GASSpec = UniGASSpec(Dist = "std", ScalingType = "Identity",
GASPar = list(location = TRUE, scale = TRUE,
shape = FALSE))
Fit = UniGASFit(GASSpec, cpichg)
Bands = ConfidenceBands(Fit)
## End(Not run)
Information for the supported distributions
Description
Print the information regarding distributions supported in the GAS package.
Usage
DistInfo(DistLabel = NULL, N = 2, FULL = TRUE)
Arguments
DistLabel |
|
. Run DistLabels() to see
the labels of the currently implemented distributions.
N |
|
FULL |
|
Details
The information are printed in the console.
Author(s)
Leopoldo Catania
Examples
# show the information of all the supported distributions
library("GAS")
DistInfo()
Fissler and Ziegel (2016) (FZ) joint loss function for Value at Risk and Expected Shortfall.
Description
This function implements Fissler and Ziegel (2016) (FZ) joint loss function for Value at Risk and Expected Shortfall.
Usage
FZLoss(data, VaR, ES, alpha)
Arguments
data |
|
VaR |
|
ES |
|
alpha |
|
Details
This function implements Fissler and Ziegel (2016) (FZ) joint loss function for Value at Risk and Expected Shortfall. The parameterization used is that of Patton et al. (2017) and is given by:
\frac{1}{\alpha ES_t^\alpha}I_t^\alpha(y_t - VaR_t^\alpha) + \frac{VaR_t^\alpha}{ES_t^\alpha} + \log{-ES_t^\alpha} - 1.
See also Fissler et al. (2015).
Value
A numeric vector containing the joing VaR and ES loss values.
Author(s)
Leopoldo Catania
References
Fissler, T., Ziegel, J.F., (2016).
"Higher order elicitability and Osband's principle."
The Annals of Statistics 44, 1680-1707.
Fissler, T., Ziegel, J.F., Tilmann, G. (2015).
"Expected Shortfall is jointly elicitable with Value at Risk - Implications for backtesting."
arXiv preprint arXiv:1507.00244.
Patton, A. J., Ziegel, J.F., Chen, R. (2017).
"Dynamic semiparametric models for expected shortfall (and Value-at-Risk)."
arXiv preprint arXiv:1707.05108.
Examples
data("StockIndices")
GASSpec = UniGASSpec(Dist = "std", ScalingType = "Identity",
GASPar = list(location = FALSE, scale = TRUE,
shape = FALSE))
FTSEMIB = StockIndices[, "FTSEMIB"]
InSampleData = FTSEMIB[1:1500]
OutSampleData = FTSEMIB[1501:2404]
Fit = UniGASFit(GASSpec, InSampleData)
Forecast = UniGASFor(Fit, Roll = TRUE, out = OutSampleData)
alpha = 0.05
vVaR = quantile(Forecast, alpha)
vES = ES(Forecast, alpha)
FZ = FZLoss(OutSampleData, vVaR, vES, alpha)
data: Goals scored by England against Scotland in international football matches.
Description
Number of goals scored by England against Scotland in international football matches.
This is a 116 x 2 zoo object spanning the period 1872-1987 with a yearly frequency.
The first column reports the number of goals scored by England against Scotland. The second
column is a dummy variable equal 1 for matches played in England.
This data set is taken from the Harvey (1989) pg 524.
Usage
data("Goals")
Format
A zoo object containing 116 x 2 observations.
Source
Harvey (1989) pg. 524
References
Harvey, A. C. (1990). Forecasting, structural time series models and the Kalman filter. Cambridge university press. https://cran.r-project.org/package=rugarch.
Estimate multivariate GAS models
Description
Estimate multivariate GAS models by Maximum Likelihood.
Usage
MultiGASFit(GASSpec, data, fn.optimizer = fn.optim, Compute.SE = TRUE)
Arguments
GASSpec |
An object of the class mGASSpec created using the function MultiGASSpec |
data |
|
fn.optimizer |
|
Compute.SE |
|
Details
Maximum Likelihood estimation of GAS models is an on-going research topic.
General results are reported by Blasques et al. (2014b), Blasques et al. (2014a) and Harvey
(2013), while results for specific models have been derived by Blasques et al. (2014c) and
Andres (2014).
Starting values for the optimizer are chosen in the following way: (i) estimate the static
version of the model (i.e., with A = 0 and B = 0) and set the initial value of the
intercept parameter accordingly, and (ii) perform a grid search for the
coefficients contained in A and B. Further technical details are presented in Section 3.2 of Ardia et. al. (2016a).
The user is free to employ his/her own optimization routine via the fn.optimizer argument. fn.optimizer
accepts a function object. The user provided optimizer has to satisfy strict requirements. The arguments of the
fn.optimizer are : i) par0 a vector of starting values, ii) data the data provided, iii) GASSpec
an object of the class uGASSpec, and iv) FUN the likelihood function. The output of fn.optimizer has
to be an object of the class list with four named elements: i) pars: a numeric vector
where the estimated parameters are stored, ii) value: a numeric containing the value of the negative log likelihood
evaluated at its minimum, iii) hessian, a numeric matrix containing the Hessian matrix evaluated at
the minimum of the negative log likelihood, this is used for inferential purposes, and iv) convergence a numeric variable reporting information about the convergence of the optimization. This quantity is printed by the
show() and summary() methods. convergence = 0 has to indicates successful completion.
The user is allowed to not include the last two elements of the output of the fn.optimizer function, that is, the values
hessian = NULL and convergence = NULL are admissible. In the case of hessian = NULL, the Hessian matrix is
evaluated numerically using the hessian function in the numDeriv package of Gilbert and Varadhan (2016). If the provided hessian is not positive definite, a try with the hessian evaluation used by the BFGS quasi-Newton implementation in the function optim is made.
By default, the optim optimizer with method = "BFGS" is employed.
Value
An object of the class mGASFit.
Author(s)
Leopoldo Catania
References
Ardia D, Boudt K and Catania L (2016a).
"Generalized Autoregressive Score Models in R: The GAS Package."
https://www.ssrn.com/abstract=2825380.
Blasques F, Koopman SJ, Lucas A (2014a). "Maximum Likelihood Estimation for Correctly Specified Generalized Autoregressive Score Models: Feedback Effects, Contraction Conditions and Asymptotic Properties." techreport TI 14-074/III, Tinbergen Institute. https://www.tinbergen.nl/discussionpaper/?paper=2332.
Blasques F, Koopman SJ, Lucas A (2014b).
"Maximum Likelihood Estimation for Generalized Autoregressive Score Models."
techreport TI 2014-029/III, Tinbergen Institute.
https://www.tinbergen.nl/discussionpaper/?paper=2286.
Blasques F, Koopman SJ, Lucas A, Schaumburg J (2014c).
"Spillover Dynamics for Systemic Risk Measurement using Spatial Financial Time Series Models."
techreport TI 2014-103/III, Tinbergen Institute.
https://www.tinbergen.nl/discussionpaper/?paper=2369.
Creal D, Koopman SJ, Lucas A (2013).
"Generalized Autoregressive Score Models with Applications."
Journal of Applied Econometrics, 28(5), 777-795.
doi:10.1002/jae.1279.
Ghalanos A, Theussl S (2016).
"Rsolnp: General Non-Linear Optimization using Augmented Lagrange Multiplier Method."
https://cran.r-project.org/package=Rsolnp.
Gilbert P, Varadhan R (2016). numDeriv: Accurate Numerical Derivatives. R package 2016.8-1, https://CRAN.R-project.org/package=numDeriv.
Harvey AC (2013).
Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series.
Cambridge University Press.
Ye Y (1988). Interior Algorithms for Linear, Quadratic, and Linearly Constrained Convex Programming. Ph.D. thesis, Stanford University.
Examples
## Not run:
# Specify an GAS model with multivariate Student-t
# conditional distribution and time-varying scales and correlations
library("GAS")
data("StockIndices")
GASSpec = MultiGASSpec(Dist = "mvt", ScalingType = "Identity",
GASPar = list(scale = TRUE, correlation = TRUE))
Fit = MultiGASFit(GASSpec, StockIndices)
Fit
## End(Not run)
Forecast with multivariate GAS models
Description
Forecast with multivariate GAS models. One-step ahead prediction of the conditional density is available in closed form. Multistep ahead prediction are performed by simulation as detailed in Blasques et al. (2016).
Usage
MultiGASFor(mGASFit, H = NULL, Roll = FALSE, out = NULL, B = 10000,
Bands = c(0.1, 0.15, 0.85, 0.9), ReturnDraws = FALSE)
Arguments
mGASFit |
An object of the class mGASFit created using the function MultiGASFit |
H |
|
Roll |
|
out |
|
B |
|
Bands |
|
ReturnDraws |
|
Value
An object of the class mGASFor
Author(s)
Leopoldo Catania
References
Blasques F, Koopman SJ, Lasak K, and Lucas, A (2016). "In-sample Confidence Bands and Out-of-Sample Forecast Bands for Time-Varying Parameters in Observation-Driven Models." International Journal of Forecasting, 32(3), 875-887. doi:10.1016/j.ijforecast.2016.04.002.
Examples
## Not run:
# Specify a GAS model with multivatiate Student-t conditional
# distribution and time-varying scales and correlations.
# Stock returns forecast
set.seed(123)
data("StockIndices")
mY = StockIndices[, 1:2]
# Specification mvt
GASSpec = MultiGASSpec(Dist = "mvt", ScalingType = "Identity",
GASPar = list(location = FALSE, scale = TRUE,
correlation = TRUE, shape = FALSE))
# Perform H-step ahead forecast with confidence bands
# Estimation
Fit = MultiGASFit(GASSpec, mY)
# Forecast
Forecast = MultiGASFor(Fit, H = 50)
Forecast
# Perform 1-Step ahead rolling forecast
InSampleData = mY[1:1000, ]
OutSampleData = mY[1001:2404, ]
# Estimation
Fit = MultiGASFit(GASSpec, InSampleData)
Forecast = MultiGASFor(Fit, Roll = TRUE, out = OutSampleData)
Forecast
## End(Not run)
Rolling forecast with multivariate GAS models
Description
One-step ahead rolling forecasts with model re-estimation. The function also reports several quantity for backtesting for point and density forecasts.
Usage
MultiGASRoll(data, GASSpec, ForecastLength = 500, Nstart = NULL,
RefitEvery = 23, RefitWindow = c("moving", "recursive"),
cluster = NULL, Compute.SE = FALSE, ...)
Arguments
data |
|
GASSpec |
An object of the class mGASSpec created using the function MultiGASSpec |
ForecastLength |
|
Nstart |
|
RefitEvery |
|
RefitWindow |
|
cluster |
A |
Compute.SE |
|
... |
Additional arguments for MultiGASFit |
Value
An object of the class mGASRoll
Author(s)
Leopoldo Catania
Examples
## Not run:
# Specify a GAS model with Multivariate Student-t conditional
# distribution and time-varying scale and correlation parameters
# stock returns Forecast
data("StockIndices")
mY = StockIndices[, 1:2]
# Specification mvt
GASSpec = MultiGASSpec(Dist = "mvt", ScalingType = "Identity",
GASPar = list(location = FALSE, scale = TRUE,
correlation = TRUE, shape = FALSE))
# Perform 1-step ahead rolling forecast with refit
library(parallel)
Roll = MultiGASRoll(mY, GASSpec, ForecastLength = 250,
RefitEvery = 100, RefitWindow = c("moving"))
Roll
## End(Not run)
Simulate multivariate GAS processes
Description
Simulate multivariate GAS processes.
Usage
MultiGASSim(fit = NULL, T.sim = 1000, N = NULL,
kappa = NULL, A = NULL, B = NULL, Dist = NULL, ScalingType = NULL)
Arguments
fit |
An estimated object of the class mGASFit. By default |
T.sim |
|
N |
|
kappa |
|
A |
|
B |
|
Dist |
|
ScalingType |
|
Details
The function permits to simulate from an estimated mGASFit object. If fit is not provided, the user
can specify a GAS model via the additional arguments kappa, A, B, Dist and ScalingType.
All the information regarding the supported multivariate conditional distributions can be investigated using the DistInfo function. The model is specified as:
y_{t}\sim p(y|\theta_{t})
where \theta_{t} is the vector of parameters for the density p(y|.). Note that, \theta_{t}
includes also those parameters that are not time-varying. The GAS recursion
for \theta_{t} is:
\theta_{t} = \Lambda(\tilde{\theta}_{t})
\tilde{\theta}_{t}=\kappa + A*s_{t-1} + B*\tilde{\theta}_{t-1}
where h(.) is the mapping function (see MultiMapParameters) and \tilde{\theta}_{t} is
the vector of reparametrised parameters. The process is initialized at \theta_{1}=(I - B)^{-1}\kappa,
where \kappa is the Kappa vector. The vector s_{t} is the scaled score of p(y|.) with respect to \tilde{\theta}_{t}.
See Ardia et. al. (2016a) for further details.
Value
An object of the class mGASSim
Author(s)
Leopoldo Catania
References
Ardia D, Boudt K and Catania L (2016a).
"Generalized Autoregressive Score Models in R: The GAS Package."
https://www.ssrn.com/abstract=2825380.
Creal D, Koopman SJ, Lucas A (2013).
"Generalized Autoregressive Score Models with Applications."
Journal of Applied Econometrics, 28(5), 777-795.
doi:10.1002/jae.1279.
Harvey AC (2013). Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series. Cambridge University Press.
Examples
# Simulate from a GAS process with Multivariate Student-t conditional
# distribution, time-varying locations, scales, correlations
# and fixed shape parameter.
library("GAS")
set.seed(786)
T.sim = 1000 # Number of observations to simulate.
N = 3 # Trivariate series.
Dist = "mvt" # Conditional Multivariate Studen-t distribution.
# Build unconditional vector of reparametrised parameters.
Mu = c(0.1, 0.2, 0.3) # Vector of location parameters (this is not transformed).
Phi = c(1.0, 1.2, 0.3) # Vector of scale parameters for the firs, second and third variables.
Rho = c(0.1, 0.2, 0.3) # This represents vec(R), where R is the correlation matrix.
# Note that is up to the user to ensure that vec(R) implies a
# proper correlation matrix.
Theta = c(Mu, Phi, Rho, 7) # Vector of parameters such that the degrees of freedom are 7.
kappa = MultiUnmapParameters(Theta, Dist, N)
A = matrix(0, length(kappa), length(kappa))
# Update scales and correlations, do not update locations and shape parameters.
diag(A) = c(0, 0, 0, 0.05, 0.01, 0.09, 0.01, 0.04, 0.07, 0)
B = matrix(0, length(kappa), length(kappa))
# Update scales and correlations, do not update locations and shape parameters.
diag(B) = c(0, 0, 0, 0.7, 0.7, 0.5, 0.94, 0.97, 0.92, 0)
Sim = MultiGASSim(fit = NULL, T.sim, N, kappa, A, B, Dist, ScalingType = "Identity")
Sim
Multivariate GAS specification
Description
Specify the conditional distribution, scaling mechanism and time-varying parameters for multivariate GAS models.
Usage
MultiGASSpec(Dist = "mvnorm", ScalingType = "Identity",
GASPar = list(location = FALSE, scale = TRUE,
correlation = FALSE, shape = FALSE),
ScalarParameters = TRUE)
Arguments
Dist |
|
.
ScalingType |
|
GASPar |
|
ScalarParameters |
|
Details
All the information regarding the supported multivariate conditional distributions can be investigated using the DistInfo function.
Value
An object of the class mGASSpec
Author(s)
Leopoldo Catania
References
Creal D, Koopman SJ, Lucas A (2011).
"A Dynamic Multivariate Heavy-Tailed Model for Time-Varying Volatilities and Correlations."
Journal of Business & Economic Statistics, 29(4), 552-563.
doi:10.1198/jbes.2011.10070.
Creal D, Koopman SJ, Lucas A (2013).
"Generalized Autoregressive Score Models with Applications."
Journal of Applied Econometrics, 28(5), 777-795.
doi:10.1002/jae.1279.
Harvey AC (2013). Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series. Cambridge University Press.
Examples
# Specify a GAS model with multivariate Student-t
# conditional distribution and time-varying locations,
# scales and correlations parameters but constant shape parameter.
library("GAS")
GASSpec = MultiGASSpec(Dist = "mvt", ScalingType = "Identity",
GASPar = list(location = TRUE, scale = TRUE,
correlation = TRUE, shape = FALSE))
GASSpec
Mapping function for univariate distributions
Description
Map unrestricted vector of parameters into the proper space. This function transforms the parameters updated using the GAS recursion into their proper space.
Usage
MultiMapParameters(Theta_tilde, Dist, N)
Arguments
Theta_tilde |
|
Dist |
|
N |
|
Details
The order of the parameters is generally: locations, scales, correlations, shape. When the
distribution defined by Dist does not have, say, the shape parameter, this should be simply omitted.
See also DistInfo for specific distributions.
Value
A numeric vector of parameters.
Author(s)
Leopoldo Catania
Examples
# Map unrestricted parameters for the Multivariate Student-t distribution with N=3
library("GAS")
N = 3
Dist = "mvt"
# Vector of location parameters (this is not transformed).
Mu_tilde = c(0.1,0.2,0.3)
# Vector of unrestricted scales parameters such that
# the scales will be equal to 1.0, 1.2 and 0.3, for the first, second and
# third variables, respectively.
Phi_tilde = c(log(1.0), log(1.2), log(0.3))
# The vector c(0.1,0.2,0.3) represents vec(R),
# where R is the correlation matrix.
# Note that is up to the user to ensure that
# vec(R) implies a proper correlation matrix
# The function UnMapR_C transforms vec(R) in a vector of unrestricted parameters. It is
# the inverse of the hyperspherical coordinates transformration.
Rho_tilde = UnMapR_C(c(0.1,0.2,0.3), N)
# Vector of unconditional reparametrised parameters such that the
# degrees of freedom are 7.
#
# LowerNu() prints the lower bound numerical parameter for the degree
# of freedom, see help(LowerNu)
#
Theta_tilde = c(Mu_tilde, Phi_tilde , Rho_tilde, log(7 - LowerNu()))
Theta = MultiMapParameters(Theta_tilde, Dist, N)
Theta
Inverse of MultiMapParameters
Description
Transform distribution parameters into the unrestricted parameters. The unrestricted vector of parameters is updated using the GAS recursion.
Usage
MultiUnmapParameters(Theta, Dist, N)
Arguments
Theta |
|
Dist |
|
N |
|
Details
The order of the parameters is generally: locations, scales, correlations, shape. When the
distribution defined by Dist does not have, say, the shape parameter, this should be simply omitted.
See also DistInfo for specific distributions.
Value
A numeric vector of parameters.
Author(s)
Leopoldo Catania
Examples
# Unmap parameters for the Multivariate Student-t distribution with N=3
library(GAS)
N = 3
Dist = "mvt"
# Vector of location parameters (this is not transformed).
Mu = c(0.1, 0.2, 0.3)
# Vector of scales parameters for the firs, second and third variables.
Phi = c(1.0, 1.2, 0.3)
# This represents vec(R), where R is the correlation matrix.
# Note that is up to the user to ensure that vec(R) implies a proper correlation matrix
Rho = c(0.1, 0.2, 0.3)
# Vector of parameters such that the degrees of freedom are 7.
Theta = c(Mu, Phi, Rho, 7)
Theta_tilde = MultiUnmapParameters(Theta, Dist, N)
Theta_tilde
# It works
all(abs(MultiMapParameters(Theta_tilde, Dist, N) - Theta) < 1e-16)
Numerical bounds imposed in parameters transformation.
Description
Prints the numerical bounds.
Usage
UpperNu()
LowerNu()
UpperA()
LowerA()
UpperB()
LowerB()
Details
UpperNu() and LowerNu() print the numerical upper and lower bounds for the degree
of freedom parameter of the Student–t distribution, std. (including also sstd and mvt).
UpperA() and LowerA() print the numerical upper and lower bounds for the score parameter
in the GAS recursion. These bounds are applied to each diagonal element of the matrix A that premultiplies the scaled score.
UpperB() and LowerB() print the numerical upper and lower bounds for the autoregressive
parameter in the GAS recursion. These bounds are applied to each diagonal element
of the matrix B that premultiplies the past value of the parameters.
Value
Prints the numerical bounds.
Author(s)
Leopoldo Catania
Examples
UpperNu()
LowerNu()
UpperA()
LowerA()
UpperB()
LowerB()
Goodness of fit for conditional densities
Description
This function implements density goodness of fit procedure of Diebold et al. (1998).
Usage
PIT_test(U, G = 20, alpha = 0.05, plot = FALSE)
Arguments
U |
|
G |
|
alpha |
|
plot |
|
Details
This function implements density goodness of fit procedure of Diebold et al. (1998). The test relays on the result that, if the series of estimated conditional distributions is the true one, then the PIT series evaluated accordingly are iid Unif(0, 1) distributed. The test of the iid Uniform(0, 1) assumption consists of two parts. The first part concerns the independent assumption, and it tests if all the conditional moments of the data, up to the fourth one, have been accounted for by the model, while the second part checks if the conditional distribution assumption is reliable by testing if the PITs are Uniform over the interval (0, 1). See also Jondeau and Rockinger (2006) and Vlaar and Palm (1993).
Value
A list with elements: (i) Hist and (ii) IID. The fist element Hist concerns
the test of the unconditional assumption of uniformity of the PIT, it is a list with elements:
-
testStatistic test. -
critThe critical value of the test. -
pvalueThe pvalue of the test. -
histThe histogram, evaluated using the hist function. -
confidenceApproximated asymptotic confidence level.
The second element IID concerns the iid assumption, it is a list with elements:
-
testA namednumericvector with elements:test1,test2,test3,test4representing the Lagrange Multiplier test for the first four conditional moments of the PITs. -
critThe critical value of the test. -
pvalueA namednumericvector with elements:pvalue1,pvalue2,pvalue3,pvalue4representing the pvalues of the Lagrange Multiplier test for the first four conditional moments of the PITs.
Author(s)
Leopoldo Catania
References
Diebold FX, Gunther TA and Tay AS (1998).
"Evaluating Density Forecasts with Applications to Financial Risk Management."
International Economic Review, 39(4), 863-883.
Jondeau E and Rockinger M (2006).
"The Copula-Garch Model of Conditional Dependencies: An International Stock Market Application."
Journal of International Money and Finance, 25(5), 827-853.
doi:10.1016/j.jimonfin.2006.04.007.
Vlaar PJ and Palm FC (1993). "The Message in Weekly Exchange Rates in the European Monetary System: Mean Reversion, Conditional Heteroscedasticity, and Jumps." Journal of Business & Economic Statistics, 11(3), 351-360. doi:10.1080/07350015.1993.10509963.
Examples
data("StockIndices")
GASSpec = UniGASSpec(Dist = "std", ScalingType = "Identity",
GASPar = list(location = FALSE, scale = TRUE,
shape = FALSE))
FTSEMIB = StockIndices[, "FTSEMIB"]
Fit = UniGASFit(GASSpec, FTSEMIB)
U = pit(Fit)
Test = PIT_test(U, G = 20, alpha = 0.05, plot = TRUE)
Data: Daily logarithmic returns in percentage points of the DAX, FTSEMIB and CAC40 from 2007-01-03 to 2016-06-24
Description
Daily logarithmic returns in percentage points of the DAX, FTSEMIB and CAC40 from 2007-01-03 to 2016-06-24 obtained from Yahoo.
Usage
data("StockIndices")
Format
A matrix object of dimension 2,445 x 3 containing the daily logarithmic returns
in percentage points from 2007-01-03 to 2016-06-24. Missing values are simply removed.
References
Yahoo finance.
Estimate univariate GAS models
Description
Estimate univariate GAS models by Maximum Likelihood.
Usage
UniGASFit(GASSpec, data, fn.optimizer = fn.optim, Compute.SE = TRUE)
Arguments
GASSpec |
An object of the class uGASSpec created using the function UniGASSpec |
.
data |
|
fn.optimizer |
|
Compute.SE |
|
Details
Maximum Likelihood estimation of GAS models is an on-going research topic.
General results are reported by Blasques et al. (2014b), Blasques et al. (2014a) and Harvey
(2013), while results for specific models have been derived by Blasques et al. (2014c) and
Andres (2014).
Starting values for the optimizer are chosen in the following way: (i) estimate the static
version of the model (i.e., with A = 0 and B = 0) and set the initial value of the intercept parameter
accordingly, and (ii) perform a grid search for the coefficients contained in A and B.
Further technical details are presented in Section 3.2 of Ardia et. al. (2016a).
The user is free to employ his/her own optimization routine via the fn.optimizer argument. fn.optimizer
accepts a function object. The user provided optimizer has to satisfy strict requirements. The arguments of the
fn.optimizer are : i) par0 a vector of starting values, ii) data the data provided, iii) GASSpec
an object of the class uGASSpec, and iv) FUN the likelihood function. The output of fn.optimizer has
to be an object of the class list with four named elements: i) pars: a numeric vector
where the estimated parameters are stored, ii) value: a numeric containing the value of the negative log likelihood
evaluated at its minimum, iii) hessian, a numeric matrix containing the Hessian matrix evaluated at
the minimum of the negative log likelihood, this is used for inferential purposes, and iv) convergence a numeric variable reporting information about the convergence of the optimization. This quantity is printed by the
show() and summary() methods. convergence = 0 has to indicate successful completion.
The user is allowed to not include the last two elements of the output of the fn.optimizer function, that is, the values
hessian = NULL and convergence = NULL are admissible. In the case of hessian = NULL, the Hessian matrix is
evaluated numerically using the hessian function in the numDeriv package of Gilbert and Varadhan (2016). If the provided hessian is not positive definite, a try with the hessian evaluation used by the BFGS quasi-Newton implementation in the function optim is made.
By default, the optim optimizer with method = "BFGS" is employed.
Value
An object of the class uGASFit
Author(s)
Leopoldo Catania
References
Ardia D, Boudt K and Catania L (2016a).
"Generalized Autoregressive Score Models in R: The GAS Package."
https://www.ssrn.com/abstract=2825380.
Blasques F, Koopman SJ, Lucas A (2014a). "Maximum Likelihood Estimation for Correctly Specified Generalized Autoregressive Score Models: Feedback Effects, Contraction Conditions and Asymptotic Properties." techreport TI 14-074/III, Tinbergen Institute. https://www.tinbergen.nl/discussionpaper/?paper=2332.
Blasques F, Koopman SJ, Lucas A (2014b).
"Maximum Likelihood Estimation for Generalized Autoregressive Score Models."
techreport TI 2014-029/III, Tinbergen Institute.
https://www.tinbergen.nl/discussionpaper/?paper=2286.
Blasques F, Koopman SJ, Lucas A, Schaumburg J (2014c).
"Spillover Dynamics for Systemic Risk Measurement using Spatial Financial Time Series Models."
techreport TI 2014-103/III, Tinbergen Institute.
https://www.tinbergen.nl/discussionpaper/?paper=2369.
Creal D, Koopman SJ, Lucas A (2013).
"Generalized Autoregressive Score Models with Applications."
Journal of Applied Econometrics, 28(5), 777-795.
doi:10.1002/jae.1279.
Gilbert P, Varadhan R (2016). numDeriv: Accurate Numerical Derivatives. R package 2016.8-1, https://CRAN.R-project.org/package=numDeriv.
Ghalanos A, Theussl S (2016).
"Rsolnp: General Non-Linear Optimization using Augmented Lagrange Multiplier Method."
https://cran.r-project.org/package=Rsolnp.
Harvey AC (2013).
Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series.
Cambridge University Press.
Ye Y (1988). Interior Algorithms for Linear, Quadratic, and Linearly Constrained Convex Programming. Ph.D. thesis, Stanford University.
Examples
## Not run:
# Specify an univariate GAS model with Student-t
# conditional distribution and time-varying scale.
library("GAS")
data("sp500ret")
GASSpec = UniGASSpec(Dist = "std", ScalingType = "Identity",
GASPar = list(location = FALSE, scale = TRUE,
shape = FALSE))
Fit = UniGASFit(GASSpec, sp500ret)
Fit
# Estimate the model with a different optimizer.
# Assume we want to use the Nelder and Mead optimization provided by
# the optim() function, we create
# the wrapper fn.NM.optim in this way
fn.NM.optim <- function(par0, data, GASSpec, FUN) {
optimizer = optim(par0, FUN, data = data, GASSpec = GASSpec, method = "Nelder-Mead",
control = list(trace = 0), hessian = TRUE)
out = list(pars = optimizer$par,
value = optimizer$value,
hessian = optimizer$hessian,
convergence = optimizer$convergence)
return(out)
}
Fit.NM.optim = UniGASFit(GASSpec, sp500ret, fn.optimizer = fn.NM.optim )
Fit.NM.optim
# Estimate time-varying Negative Binomial distribution for the Goals dataset.
# Let's use the gosolnp() optimizer for the time-varying model estimation and
# the solnp() optimizer for estimation of the static model for the choice of
# the starting values. The logical is(GASSpec, "list") is TRUE when the function
# is evaluated for the choice of starting values, and FALSE when the function
# is evaluated for the time-varying model.
# We can also make use of parallel computation calling a cluster object defined
# in the Global environment.
library("Rsolnp")
fn.gosolnp <- function(par0, data, GASSpec, FUN) {
if (is(GASSpec, "list")) {
optimiser = suppressWarnings(solnp(par0, FUN, data = data,
GASSpec = GASSpec,
control = list(trace = 0)))
} else {
cluster = get("cluster", envir = globalenv())
optimiser = suppressWarnings(gosolnp(
pars = NULL,
fun = FUN, data = data, cluster = cluster,
GASSpec = GASSpec,
n.sim = 100000,
n.restarts = 10,
LB = c(-5, -2, -2, -2),
UB = c(5, 8, 3.0, 5.0))
)
}
out = list(pars = optimiser$pars,
value = tail(optimiser$values, 1),
hessian = optimiser$hessian,
convergence = optimiser$convergence)
return(out)
}
data("Goals")
library("parallel")
cluster = makeCluster(2)
GASSpec = UniGASSpec(Dist = "negbin", ScalingType = "Inv",
GASPar = list(location = TRUE, scale = FALSE))
vY = na.omit(Goals[, 1])
Fit = UniGASFit(GASSpec, vY, fn.optimizer = fn.gosolnp)
Fit
stopCluster(cluster)
rm("cluster")
## End(Not run)
Forecast with univariate GAS models
Description
Forecast with univariate GAS models. The one-step ahead prediction of the conditional density is available in closed form. The multi-step ahead prediction is performed by simulation as detailed in Blasques et al. (2016).
Usage
UniGASFor(uGASFit, H = NULL, Roll = FALSE, out = NULL, B = 10000,
Bands = c(0.1, 0.15, 0.85, 0.9), ReturnDraws = FALSE)
Arguments
uGASFit |
An object of the class uGASFit created using the function UniGASFit. |
H |
|
Roll |
|
out |
|
B |
|
Bands |
|
ReturnDraws |
|
Value
An object of the class uGASFor.
Author(s)
Leopoldo Catania
References
Blasques F, Koopman SJ, Lasak K, and Lucas, A (2016). "In-sample Confidence Bands and Out-of-Sample Forecast Bands for Time-Varying Parameters in Observation-Driven Models." International Journal of Forecasting, 32(3), 875-887. doi:10.1016/j.ijforecast.2016.04.002.
Examples
# Specify an univariate GAS model with Student-t
# conditional distribution and time-varying location, scale and shape parameter
# Inflation Forecast
set.seed(123)
data("cpichg")
GASSpec = UniGASSpec(Dist = "std", ScalingType = "Identity",
GASPar = list(location = TRUE, scale = TRUE, shape = FALSE))
# Perform H-step ahead forecast with confidence bands
Fit = UniGASFit(GASSpec, cpichg)
Forecast = UniGASFor(Fit, H = 12)
Forecast
# Perform 1-Step ahead rolling forecast
InsampleData = cpichg[1:250]
OutSampleData = cpichg[251:276]
Fit = UniGASFit(GASSpec, InsampleData)
Forecast = UniGASFor(Fit, Roll = TRUE, out = OutSampleData)
Forecast
Rolling forecast with univariate GAS models
Description
One-step ahead rolling forecasts with model re-estimation. The function also reports several quantity for backtesting for point and density forecasts.
Usage
UniGASRoll(data, GASSpec, ForecastLength = 500, Nstart = NULL,
RefitEvery = 23, RefitWindow = c("moving", "recursive"),
cluster = NULL, Compute.SE = FALSE, ...)
Arguments
data |
|
GASSpec |
An object of the class uGASSpec created using the function UniGASSpec. |
ForecastLength |
|
Nstart |
|
RefitEvery |
|
RefitWindow |
|
cluster |
A |
Compute.SE |
|
... |
Additional arguments for UniGASFit |
Value
An object of the class uGASRoll.
Author(s)
Leopoldo Catania
Examples
# Specify an univariate GAS model with Student-t
# conditional distribution and time-varying location, scale and shape parameter
# Inflation Forecast
data("cpichg")
help(cpichg)
GASSpec = UniGASSpec(Dist = "std", ScalingType = "Identity",
GASPar = list(location = TRUE, scale = TRUE, shape = FALSE))
# Perform 1-step ahead rolling forecast with refit
library("parallel")
Roll = UniGASRoll(cpichg, GASSpec, ForecastLength = 50,
RefitEvery = 12, RefitWindow = c("moving"))
Roll
Simulate Univariate GAS processes
Description
Simulate Univariate GAS processes.
Usage
UniGASSim(fit = NULL, T.sim = 1000,
kappa = NULL, A = NULL, B = NULL, Dist = NULL, ScalingType = NULL)
Arguments
fit |
An estimated object of the class uGASFit. By default |
T.sim |
|
kappa |
|
A |
|
B |
|
Dist |
|
ScalingType |
|
Details
The function permits to simulate from an estimated uGASFit object. If fit is not provided, the user
can specify a GAS model via the additional arguments kappa, A, B, Dist and ScalingType.
All the information regarding the supported univariate conditional distributions can be investigated using the DistInfo function. The model is specified as
y_{t}\sim p(y|\theta_{t})
,
where \theta_{t} is the vector of parameters for the density p(y|.). Note that, \theta_{t} includes
also those parameters that are not time-varying.
The GAS recursion for \theta_{t} is
\theta_{t} = \Lambda(\tilde{\theta}_{t})
,
\tilde{\theta}_{t}=\kappa + A*s_{t-1} + B*\tilde{\theta}_{t-1}
,
where \Lambda(.) is the mapping function (see UniMapParameters) and \tilde{\theta}_{t} is the vector of
reparametrised parameters. The process is initialized at \theta_{1}=(I - B)^{-1}\kappa, where \kappa is
the vKappa vector. The vector s_{t} is the scaled score of p(y|.) with respect to \tilde{\theta}_{t}.
See Ardia et. al. (2016a) for further details.
Value
An object of the class uGASSim.
Author(s)
Leopoldo Catania
References
Ardia D, Boudt K and Catania L (2016a).
"Generalized Autoregressive Score Models in R: The GAS Package."
https://www.ssrn.com/abstract=2825380.
Creal D, Koopman SJ, Lucas A (2013).
"Generalized Autoregressive Score Models with Applications."
Journal of Applied Econometrics, 28(5), 777-795.
doi:10.1002/jae.1279.
Harvey AC (2013). Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series. Cambridge University Press.
Examples
# Simulate from a GAS process with Student-t conditional
# distribution, time-varying location, scale and fixed shape parameter.
library(GAS)
set.seed(786)
T.sim = 1000 # number of observations to simulate
Dist = "std" # conditional Studen-t distribution
# vector of unconditional reparametrised parameters such that, the unconditional level of
# \eqn{\theta}_{t} is (0, 1.5 ,7), i.e. location = 0, scale = 1.5,
# degrees of freedom = 7.
kappa = c(0.0, log(1.5), log(7-2.01))
# in this way we specify that the shape parameter is constant while the score
# coefficients for the location and the scale
# parameters are 0.001 and 0.01, respectively.
A = matrix(c(0.001 , 0.0 , 0.0 ,
0.0 , 0.01 , 0.0 ,
0.0 , 0.0 , 0.0 ), 3, byrow = TRUE)
B = matrix(c(0.7 , 0.0 , 0.0 ,
0.0 , 0.98, 0.0 ,
0.0 , 0.0 , 0.0),3,byrow = TRUE) # Matrix of autoregressive parameters.
Sim = UniGASSim(fit = NULL, T.sim, kappa, A, B, Dist, ScalingType = "Identity")
Sim
Univariate GAS specification
Description
Specify the conditional distribution, scaling mechanism and time–varying parameters for univariate GAS models.
Usage
UniGASSpec(Dist = "norm", ScalingType = "Identity",
GASPar = list(location = FALSE, scale = TRUE,
skewness = FALSE, shape = FALSE, shape2 = FALSE))
Arguments
Dist |
|
ScalingType |
|
GASPar |
|
Details
All the information regarding the supported univariate conditional distributions can be investigated using the DistInfo function.
Value
An object of the class uGASSpec.
Author(s)
Leopoldo Catania
References
Ardia D, Boudt K and Catania L (2016).
"Generalized Autoregressive Score Models in R: The GAS Package."
https://www.ssrn.com/abstract=2825380.
Creal D, Koopman SJ, Lucas A (2013).
"Generalized Autoregressive Score Models with Applications."
Journal of Applied Econometrics, 28(5), 777-795.
doi:10.1002/jae.1279.
Harvey AC (2013). Dynamic Models for Volatility and Heavy Tails: With Applications to Financial and Economic Time Series. Cambridge University Press.
Examples
# Specify an univariate GAS model with Student-t
# conditional distribution and time-varying location, scale and shape parameter
library("GAS")
GASSpec = UniGASSpec(Dist = "std", ScalingType = "Identity",
GASPar = list(location = TRUE,
scale = TRUE, shape = TRUE))
GASSpec
Mapping function for univariate distributions
Description
Map unrestricted vector of parameters into the proper space. This function transforms the parameters updated using the GAS recursion into their proper space.
Usage
UniMapParameters(Theta_tilde, Dist)
Arguments
Theta_tilde |
|
Dist |
|
Details
The order of the parameters is generally: location, scale, skewness, shape, shape2.
When the distribution defined by Dist does not have, say, the shape parameter, this should be simply omitted.
See also DistInfo for specific distributions.
Value
A numeric vector of parameters.
Author(s)
Leopoldo Catania
Examples
# Map unrestricted parameters for the Student-t distribution.
library("GAS")
Dist = "std"
# Vector of unconditional reparametrised parameters such that,
# Theta = c(0, 1.5 ,7), i.e., location = 0, scale = 1.5,
# degrees of freedom = 7.
# LowerNu() prints the lower bound numerical parameter for the degree
# of freedom, see help(LowerNu).
Theta_tilde = c(0.1, log(1.5), log(7 - LowerNu()))
Theta = UniMapParameters(Theta_tilde, Dist)
Theta
Unmapping function for univariate distributions, i.e. inverse of UniMapParameters
Description
Transform distribution parameters into the unrestricted parameters. The unrestricted vector of parameters is updated using the GAS recursion.
Usage
UniUnmapParameters(Theta, Dist)
Arguments
Theta |
|
Dist |
|
Details
The order of the parameters is generally: location, scale, skewness, shape, shape2.
When the distribution defined by Dist does not have, say, the shape parameter, this should be simply omitted.
See also DistInfo for specific distributions.
Value
A numeric vector of parameters.
Author(s)
Leopoldo Catania
Examples
# Unmap parameters for the Student-t distribution
library("GAS")
Dist = "std"
# Vector of parameters such that,
# Theta = c(0, 1.5 ,7), i.e., location = 0, scale = 1.5,
# degrees of freedom = 7.
Theta = c(0.1, 1.5, 7)
Theta_tilde = UniUnmapParameters(Theta, Dist)
Theta_tilde
# It works.
all(abs(UniMapParameters(Theta_tilde, Dist) - Theta) < 1e-16)
Data: Quarterly logarithmic change in percentage points of the Consumer Price Index for All Urban Consumers: All Items (CPIAUCSL) from 1947-04-01 to 2016-05-01
Description
Quarterly logarithmic change in percentage points of the Consumer Price Index for All Urban Consumers: All Items (CPIAUCSL) from 1947-04-01 to 2016-05-01 available at https://fred.stlouisfed.org/series/CPIAUCSL.
Usage
data("cpichg")
Format
A xts object containing 276 observations from 1947-04-01 to 2016-05-01.
References
US. Bureau of Labor Statistics, Consumer Price Index for All Urban Consumers: All Items [CPIAUCSL], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/CPIAUCSL, June 24, 2016.
Distributions of the GAS package
Description
Density, distribution function, quantile function, random generator, moments, scores and information matrix of univariate and multivariate distributions of the GAS package.
Usage
ddist_Uni(y, Theta, Dist, log = FALSE)
pdist_Uni(q, Theta, Dist)
qdist_Uni(p, Theta, Dist)
rdist_Uni(Theta, Dist)
mdist_Uni(Theta, Dist)
Score_Uni(y, Theta, Dist)
IM_Uni(Theta, Dist)
ddist_Multi(y, Theta, Dist, log = FALSE)
rdist_Multi(Theta, N, Dist)
Score_Multi(y, Theta, Dist)
Arguments
y, q |
|
p |
|
Theta |
|
Dist |
|
log |
|
N |
|
Details
The function mdist_Uni returns a vector with four elements: mean, variance, skewness
and kurtosis coefficients. The functions Score_Uni and IM_Uni returns the score and the Fisher information matrix
for univariate distributions. The function Score_Multi returns the score for multivariate distributions.
See DistInfo for the lists of supported distributions.
These functions are not vectorized. ddist_Uni and ddist_Multi give the density, pdist_Uni gives
the distribution function, qdist_Uni gives the quantile function, and rdist_Uni and rdist_Multi generate random deviates.
Value
numericscalar for:ddist_Uni,pdist_Uni,qdist_Uni,rdist_Uni,numericvector for:Score_Uni,Score_Multiandrdist_Multi,matrixforIM_Uni.
Author(s)
Leopoldo Catania
Examples
# Skew Student-t distribution
# log density
Theta = c("location" = 0, "scales" = 1, "skewness" = 1.2, "shape" = 7)
ddist_Uni(y = 0.5, Theta, "sstd", TRUE)
# probability
pdist_Uni(q = -1.69, Theta, "sstd")
#quantile
qdist_Uni(p = 0.05, Theta, "sstd")
#random generator
rdist_Uni(Theta, "sstd")
#moments
mdist_Uni(Theta, "sstd")
data: Dow Jones 30 Constituents Closing Value Log Return in percentage points
Description
This dataset is taken from the rugarch package of Ghalanos (2015). Returns are in percentage points.
Dow Jones 30 Constituents closing value log returns from 1987-03-16 to 2009-02-03 from Yahoo Finance. Note that AIG was replaced by KFT (Kraft Foods) on September 22, 2008. This is not reflected in this data set as that would bring the starting date of the data to 2001.
Usage
data("dji30ret")
Format
A data.frame containing 5,521x30 observations.
Source
Yahoo Finance
References
Ghalanos A (2015). "rugarch: Univariate GARCH models." https://cran.r-project.org/package=rugarch.
A wrapper to the optim function.
Description
This function is a wrapper to the standard optim optimizer with method = "BFGS".
Usage
fn.optim(par0, data, GASSpec, FUN)
Arguments
par0 |
|
data |
|
GASSpec |
An object of the class uGASSpec or mGASSpec, created via the UniGASSpec and MultiGASSpec functions. |
FUN |
A function to optimize. |
Details
The following control parameters are used for control:
-
trace = 0 -
abstol = 1e-8
See the documentation of optim.
Value
It returns a named list with four elements: i) pars: a numeric vector
where the estimated parameters are stored, ii) value: a numeric containing the value of the negative log likelihood
evaluated at its minumum, iii) hessian, a numeric matrix containing the Hessian matrix evaluated at
the minimum of the negative log likelihood, iv) convergence a numeric element indicating the convergence results of
optim.
Author(s)
Leopoldo Catania
See Also
help(optim)
A wrapper to the solnp function of the Rsolnp package of Ghalanos and Theussl (2016).
Description
This function is a wrapper to the solnp function of the Rsolnp package of Ghalanos and Theussl (2016).
Usage
fn.solnp(par0, data, GASSpec, FUN)
Arguments
par0 |
|
data |
|
GASSpec |
An object of the class uGASSpec or mGASSpec, created via the UniGASSpec and MultiGASSpec functions. |
FUN |
A function to optimize. |
Details
The following control parameters are used: trace = 0, rho = 1, outer.iter = 400,
inner.iter = 1800, delta = 1e-08, tol = 1e-08. See the documentation of solnp.
Value
It returns a named list with four elements: i) pars: a numeric vector
where the estimated parameters are stored, ii) value: a numeric containing the value of the negative log likelihood
evaluated at its minumum, iii) hessian, a numeric matrix containing the Hessian matrix evaluated at
the minimum of the negative log likelihood, and iv) convergence a numeric element indicating the convergence results of
solnp.
Author(s)
Leopoldo Catania
References
Alexios Ghalanos and Stefan Theussl (2015).
"Rsolnp: General Non-linear Optimization Using Augmented Lagrange
Multiplier Method". R package version 1.16.
See Also
help(solnp)
Class for the Multivariate GAS fitted object
Description
Class for the multivariate GAS fitted object.
Objects from the Class
A virtual Class: No objects may be created from it.
Slots
Data:Object of class
list. Contains the user's data.Estimates:Object of class
list. Contains:lParListlist of estimated parameters,optimiserobject delivered from the optimization function,StaticFitML estimates for the constant model,Inferenceinferential results for the estimated parameters.GASDyn:Object of class
list. Contains: the series of filtered dynamic (GASDyn$mTheta) for the time–varying parameters, the series of scaled scores (GASDyn$mInnovation), the series of unrestricted filtered parameters (GASDyn$mTheta_tilde), the series of log densities (GASDyn$vLLK), the log likelihood evaluated at its optimum value (GASDyn$dLLK)ModelInfo:Object of class
list. Contains information about the GAS specification:-
SpecObject of the class uGASSpec containing the GAS specification. -
iTnumericNumber of observation. -
elapsedTimeNumericelapsed time in seconds.
-
Methods
-
showsignature(object = 'mGASFit'): print object information. -
summarysignature(object = 'mGASFit'): Show summary. plot
signature(x='mGASFit', y='missing'): Plot filtered dynamic and other estimated quantities.getFilteredParameters
signature(object = "mGASFit"): Extract filtered parameters.getObs
signature(object = "mGASFit"): Extract original observations.-
coefsignature(object = 'uGASFit'): Returns a named vector of estimated coefficients. Also accepts the additional logical argumentdo.list. Ifdo.list = TRUE, estimated coefficients are organized in a list with arguments:vKappathe intercept vector,mAthe A system matrix,mBthe B system matrix. By default,do.list = FALSE. getMoments
signature(object = "mGASFit"): Extract conditional moments.-
residualssignature(object = 'mGASFit'): Extract the residuals. Also accepts the additional logical argumentstandardize. Ifstandardize = TRUE, residuals are standardized by cholesky of the filtered covariance matrix. By defaultstandardize = FALSE. -
convergencesignature(object = 'mGASFit'): Extract convergence information.
Author(s)
Leopoldo Catania
Class for the Multivariate GAS Forecast object
Description
Class for the multivariate GAS forecast object.
Objects from the Class
A virtual Class: No objects may be created from it.
Slots
Forecast:Object of class
list. Contains forecasts:-
PointForecast:matrixwith parameters forecasts. -
Moments:listwith centered moments forecasts. The first element contains amatrixwith the predicted conditional means. The second element contains anarraywith the predicted conditional covariances. -
vLS:numericLog Score (Predictive Log Likelihood).
-
Bands:arraywith confidence bands parameters forecasts. Available only ifRoll = TRUE.Draws:If
ReturnsDraws = TRUEit is a iH x iBmatrixof draws from the predictive distribution.Info:listwith forecast information.Data:listwith original data.
Methods
-
showsignature(object = "uGASFor"): Show summary. -
plotsignature(x='uGASFor',y='missing'): Plot forecasted quantities. -
getForecastsignature(object = "uGASFor"): Extract parameters forecast. -
getObssignature(object = "uGASFor"): Extract original observations. -
getMomentssignature(object = "uGASFor"): Extract moments forecasts. -
LogScoresignature(object = "uGASFor"): Extract Log Scores.
Author(s)
Leopoldo Catania
Class for the Multivariate GAS Rolling object
Description
Class for the multivariate GAS rolling object.
Objects from the Class
A virtual Class: No objects may be created from it.
Slots
Forecast:Object of class
list. Contains forecasts:-
PointForecast:matrixwith parameters forecasts. -
Moments:listwith centered moments forecasts. The first element contains amatrixwith the predicted conditional means. The second element contains anarraywith the predicted conditional covariances. -
vLS:numericLog Score (Predictive Log Likelihood).
-
Info:listwith forecast information.Data:listwith original data.
Methods
-
showsignature(object = 'mGASRoll'): Show summary. -
plotsignature(x = 'mGASRoll',y = 'missing'): Plot forecasted quantities. -
getForecastsignature(object = 'mGASRoll'): Extract parameters forecast. -
getObssignature(object = 'mGASRoll'): Extract original observations. -
getMomentssignature(object = 'mGASRoll'): Extract moments forecasts. -
LogScoresignature(object = 'mGASRoll'): Extract Log Scores. -
residualssignature(object = 'mGASRoll'): Extract the forecast errors. Also accepts the additional logical argumentstandardize. Ifstandardize = TRUE, forecast errors are standardized by cholesky of the forecast covariance matrix. By defaultstandardize = FALSE. -
coefsignature(object = 'mGASFit'): Returns a matrix of estimated coefficients. Each row of the matrix corresponds to a refit of the model during the forecast period according to theRefitEveryargument provided in the MultiGASRoll function. Also accepts the additional logical argumentdo.list. Ifdo.list = TRUE, estimated coefficients are organized in a list of lists according according to theRefitEveryargument provided in the MultiGASRoll function. Each list is populated by three arguments:vKappathe intercept vector,mAthe A system matrix,mBthe B system matrix. By default,do.list = FALSE.
Author(s)
Leopoldo Catania
Class for Multivariate GAS Simulation
Description
Class for multivariate GAS model simulation.
Objects from the Class
A virtual Class: No objects may be created from it.
Slots
ModelInfo:Object of class
list. Contains information about the multivariate GAS specification:iT:
numericTime length of simulated observations.iN:
numericCross sectional dimension.iK :
numericnumber of (possibly) time–varying parameters implied by the distributional assumption.vKappa
numericvector of unconditional level for the reparametrized vector of parameters.mA
matrixof coefficients of dimension iK x iK that premultiply the conditional score in the GAS updating recursion.mB
matrixof autoregressive coefficients of dimension iK x iK.Dist
characterlabel of the conditional distribution, see DistInfoScalingType
characterrepresenting the scaling mechanism for the conditional score, see DistInfo
GASDyn:Object of class
list. Contains: the series of simulated parameters (GASDyn$mTheta), the series of scaled scores (GASDyn$mInnovation), the series of unrestricted simulated parameters (GASDyn$mTheta_tilde), the series of log densities (GASDyn$vLLK), the log likelihood evaluated at its optimum value (GASDyn$dLLK)Data:Object of class
matrix. Matrix of dimension iN x iT of simulated data
Methods
-
showsignature(object = 'mGASSim'): Show summary. -
plotsignature(x = 'mGASSim',y = 'missing'): Plot simulated data and parameters. -
getFilteredParameterssignature(object = 'mGASSim'): Extract simulated parameters. -
getObssignature(object = 'mGASSim'): Extract simulated observations -
coefsignature(object = 'mGASSim'): Extract delivered coefficients -
getMomentssignature(object = 'uGASFor'): Extract simulated moments.
Author(s)
Leopoldo Catania
Class for the Multivariate GAS model specification
Description
Class for the Multivariate GAS model specification.
Objects from the Class
A virtual Class: No objects may be created from it.
Slots
Spec:Object of class
list. Contains information abount the multivariate GAS specification:-
Dist:characterContaining the conditional distribution assumption. -
ScalingType:characterindicating the scaling mechanism for the conditional score. -
GASPar:listwith elements: location, scale, correlation, shape. -
ScalarParameters:logicalindicates if the parameters of the locations, scales and correlations dynamic have to be scalars or a diagonal matrices.
-
Methods
-
showsignature(object = 'mGASSpec'): Show summary.
Author(s)
Leopoldo Catania
Plot output from an object of the from the GAS package.
Description
This method provides plot functionalities for the uGASFit, mGASFit, uGASSim, mGASSim, uGASFor, mGASFor, uGASRoll and mGASRoll objects defined in the GAS package.
Usage
plot(x, y, ...)
PlotMenu(x)
Arguments
x, y |
objects of class uGASFit, mGASFit, uGASSim, mGASSim, uGASFor, mGASFor, uGASRoll, mGASRoll. |
... |
additional arguments, see Details |
Details
plot accepts the additional argument numeric argument which. By default which = NULL. If which is provided, plot() does not show the interactive menu and plot the corresponding option. The available options for each object class is printed by the function PlotMenu(x). By default which = NULL, that is, plot() display an interactive menu.
Value
Displays a plot of an object of class uGASFit, mGASFit, uGASSim, mGASSim, uGASFor, mGASFor, uGASRoll, mGASRoll.
Author(s)
Leopoldo Catania
Examples
## Not run:
## Plot filtered estimates of a GAS model estimated on the
## Quarterly logarithmic change in percentage points of the Consumer Price Index data set (cpichg)
library("GAS")
data("cpichg")
GASSpec = UniGASSpec(Dist = "std", ScalingType = "Identity",
GASPar = list(location = TRUE, scale = TRUE,
shape = FALSE))
Fit = UniGASFit(GASSpec, cpichg)
plot(Fit, which = 1)
## End(Not run)
Data: Daily logarithmic returns in percentage points of the S&P500 index from 1950-01-04 to 2016-06-24
Description
Daily logarithmic returns in percentage points of the S&P500 index from 1950-01-04 to 2016-06-24 obtained from yahoo finance.
Usage
data("sp500ret")
Format
A xts object of dimension 16,727 x 1 containing the daily logarithmic returns in percentage points from 1950-01-04 to 2016-06-24.
Source
Yahoo Finance
Data: SP500 Daily 5 minutes Realized Volatility from 2000-01-03 to 2000-01-10
Description
Oxford-Man Institute Daily 5 minutes Realized Volatility from 2000-01-03 to 2000-01-10 for the SP500 Index available at https://realized.oxford-man.ox.ac.uk/data.
Usage
data("sp500rv")
Format
A xts object containing 4,310 observations from 2000-01-03 to 2000-01-10.
References
https://realized.oxford-man.ox.ac.uk/data
Data from Bien et al (2011).
Description
From the readme.bnp.txt file in the JAE Data Archive available at http://qed.econ.queensu.ca/jae/2011-v26.4/bien-nolte-pohlmeier/:
The high-frequency data used in the paper come from the Trades and Quotation (TAQ) database. The data contains time-stamped quotations of Citicorp stock traded at the NYSE over the period from 20th February to 23rd February 2001.
In the study, 30-second bid and ask quote changes are constructed from the irregularly-spaced quote data. The study covers observations recorded from 9:35 EST until 16:00 EST.
The data contains 3080 rows and eight columns - in order:
1. year 2. month 3. day 4. time in number of seconds after the 9:35 EST 5. best ask quote 6. best bid quote 7. 30-second change of the ask quote in number of ticks 8. 30-second change of the bid quote in number of ticks.
Usage
data("tqdata")
Format
A data.frame object containing 3,080 observat. ions.
References
Bien K, Nolte, I, Pohlmeier W (2011). "An Inflated Multivariate Integer Count Hurdle Model: An Application to Bid and Ask Quote Dynamics". Journal of Applied Econometrics, 26(4), 669-707. doi:10.1002/jae.1122
Class for the univariate GAS fitted object
Description
Class for the univariate GAS fitted object.
Objects from the Class
A virtual Class: No objects may be created from it.
Slots
ModelInfo:Object of class
list. Contains information about the GAS specification:-
Spec: object of the class uGASSpec containing the GAS specification. -
iT:numericnumber of observation. -
elapsedTime:numericelapsed Time in seconds.
-
GASDyn:Object of class
list. Contains: the series of filtered dynamic (GASDyn$mTheta) for the time–varying parameters, the series of scaled scores (GASDyn$mInnovation), the series of unrestricted filtered parameters (GASDyn$mTheta_tilde), the series of log densities (GASDyn$vLLK), the log likelihood evaluated at its optimum value (GASDyn$dLLK)
.
Estimates:Object of class
list. Contains:lParListlist of estimated parameters,optimiserobject delivered from the optimization function,StaticFitML estimates for the constant model,Inferenceinferential results for the estimated parameters.Data:The user's data.
Testing:Statistical tests results.
Methods
-
showsignature(object = 'uGASFit'): print object information. -
summarysignature(object = 'uGASFit'): Show summary. -
plotsignature(x = 'uGASFit',y = 'missing'): Plot filtered dynamic and other estimated quantities. -
getFilteredParameterssignature(object = 'uGASFit'): Extract filtered parameters. -
getObssignature(object = 'uGASFit'): Extract original observations. -
coefsignature(object = 'uGASFit'): Returns a named vector of estimated coefficients. Also accepts the additional logical argumentdo.list. Ifdo.list = TRUE, estimated coefficients are organized in a list with arguments:vKappathe intercept vector,mAthe A system matrix,mBthe B system matrix. By default,do.list = FALSE. -
pitsignature(object = 'uGASFit'): Extract Probability Integral Transformation. -
getMomentssignature(object = 'uGASFit'): Extract conditional moments. -
residualssignature(object = 'uGASFit'): Extract the residuals. Also accepts the additional logical argumentstandardize. Ifstandardize = TRUE, residuals are standardized by the filtered standard deviation. By defaultstandardize = FALSE. -
convergencesignature(object = 'uGASFit'): Extract convergence information. -
quantilesignature(object = 'uGASSim'): Compute quantiles of the filtered estimated density at each point in time. It accepts the additional argumentprobsrepresenting the vector of probabilities. -
ESsignature(object = 'uGASSim'): Compute Expected Shortfall of the filtered estimated density at each point in time. It accepts the additional argumentprobsrepresenting the vector of probabilities.
Author(s)
Leopoldo Catania
Class for the univariate GAS forecast object
Description
Class for the univariate GAS forecast object.
Objects from the Class
A virtual Class: No objects may be created from it.
Slots
Forecast:Object of class
list. Contains forecasts:-
PointForecast:matrixwith parameters forecasts. -
Moments:matrixwith centered moments forecasts. -
vLS:numericLog Score (Predictive Log Likelihood). -
vU:numericOut-of-sample Probability Integral Transformation (PIT).
-
Bands:arraywith confidence bands parameters forecasts. Available only ifRoll = TRUE.Draws:If
ReturnsDraws = TRUEit is a iH x iBmatrixof draws from the predictive distribution.Info:listwith forecast information.Data:listwith original data.
Methods
-
showsignature(object = 'uGASFor'): Show summary. -
plotsignature(x = 'uGASFor', y = 'missing'): Plot forecasted quantities. -
getForecastsignature(object = 'uGASFor'): Extract parameters forecast. -
getObssignature(object = 'uGASFor'): Extract original observations. -
pitsignature(object = 'uGASFor'): Extract Probability Integral Transformation, only ifRoll = TRUE. -
quantilesignature(object = 'uGASFor'): Extract quantile forecasts. For multistep ahead prediction ES is computed by simulation andReturnsDraws = TRUEshould have been selected. It accepts the additional argumentprobsrepresenting the vector of probabilities. -
ESsignature(object = 'uGASFor'): Extract Expected Shortfall forecasts. For multistep ahead prediction ES is computed by simulation andReturnsDraws = TRUEshould have been selected. It accepts the additional argumentprobsrepresenting the vector of probabilities. -
getMomentssignature(object = 'uGASFor'): Extract moments forecasts. -
LogScoresignature(object = 'uGASFor'): Extract Log Scores.
Author(s)
Leopoldo Catania
Class for the univariate GAS rolling object
Description
Class for the univariate GAS rolling object.
Objects from the Class
A virtual Class: No objects may be created from it.
Slots
Forecast:Object of class
list. Contains forecasts:-
PointForecast:matrixwith parameters forecasts. -
Moments:matrixwith centered moments forecasts. -
vLS:numericLog Score (Predictive Log Likelihood). -
vU:numericOut-of-sample Probability Integral Transformation (PIT).
-
Info:listwith forecast information.Data:listwith original data.Testing:Statistical tests results.
Methods
-
showsignature(object = 'uGASRoll'): Show summary. -
plotsignature(x = 'uGASRoll', y = 'missing'): Plot forecasted quantities. -
getForecastsignature(object = 'uGASRoll'): Extract parameters forecast. -
getObssignature(object = 'uGASRoll'): Extract original observations. -
pitsignature(object = 'uGASRoll'): Extract Probability Integral Transformation, only ifRoll = TRUE -
quantilesignature(object = 'uGASRoll'): Extract quantile forecasts. It accepts the addional argumentprobsrepresenting the vector of probabilities. -
ESsignature(object = 'uGASRoll'): Extract Expected Shortfall forecasts. It accepts the addional argumentprobsrepresenting the vector of probabilities. -
getMomentssignature(object = 'uGASRoll'): Extract moments forecasts. -
LogScoresignature(object = 'uGASRoll'): Extract Log Scores. -
residualssignature(object = 'uGASRoll'): Extract the forecast errors. Also accepts the additional logical argumentstandardize. Ifstandardize = TRUE, forecast errors are standardized by the forecast standard deviation. By defaultstandardize = FALSE. -
coefsignature(object = 'uGASFit'): Returns a matrix of estimated coefficients. Each row of the matrix corresponds to a refit of the model during the forecast period according to theRefitEveryargument provided in the UniGASRoll function. Also accepts the additional logical argumentdo.list. Ifdo.list = TRUE, estimated coefficients are organized in a list of lists according according to theRefitEveryargument provided in the UniGASRoll function. Each list is populated by three arguments:vKappathe intercept vector,mAthe A system matrix,mBthe B system matrix. By default,do.list = FALSE.
Author(s)
Leopoldo Catania
Class for Univariate GAS Simulation
Description
Class for Univariate GAS model Simulation.
Objects from the Class
A virtual Class: No objects may be created from it.
Slots
ModelInfo:Object of class
list. Contains information about the univariate GAS specification:-
iTnumericTime length of simulated observations. -
iKnumericNumber of (possibly) time-varying parameters implied by the distributional assumption. -
vKappanumericVector of unconditional level for the reparametrised vector of parameters. -
mAmatrixOf coefficients of dimension iK x iK that premultiply the conditional score in the GAS updating recursion. -
mBmatrixOf autoregressive coefficients of dimension iK x iK. -
DistcharacterLabel of the conditional distribution, see DistInfo -
ScalingTypecharacterRepresenting the scaling mechanism for the conditional score, see DistInfo.
-
GASDyn:Object of class
list. Contains: the series of simulated parameters (GASDyn$mTheta), the series of scaled scores (GASDyn$mInnovation), the series of unrestricted simulated parameters (GASDyn$mTheta_tilde), the series of log densities (GASDyn$vLLK), the log likelihood evaluated at its optimum value (GASDyn$dLLK).Data:Object of class
numeric. Vector of lengthiTof simulated data.
Methods
-
showsignature(object = 'uGASSim'): Show summary. -
plotsignature(x = 'uGASSim', y = 'missing'): Plot simulated data and parameters. -
getFilteredParameterssignature(object = 'uGASSim'): Extract simulated parameters. -
getObssignature(object = 'uGASSim'): Extract simulated observations. -
coefsignature(object = 'uGASSim'): Extract delivered coefficients. -
quantilesignature(object = 'uGASSim'): Compute quantiles of the filtered simulated density at each point in time. It accepts the additional argumentprobsrepresenting the vector of probabilities. -
ESsignature(object = 'uGASSim'): Compute the Expected Shortfall of the filtered simulated density at each point in time. It accepts the additional argumentprobsrepresenting the vector of probabilities.
Author(s)
Leopoldo Catania
Class for the univariate GAS model specification
Description
Class for the univariate GAS model specification.
Objects from the Class
A virtual Class: No objects may be created from it.
Slots
Spec:Object of class
list. Contains information about the univariate GAS specification:-
Dist:charactercontaining the conditional distribution assumption. -
ScalingType:characterindicating the scaling mechanism for the conditional score. -
iK:numericrepresenting the number of (possibly) time-varying parameters implied by the distributional assumption. -
GASParlistwith elements:location,scale,skewness,shape,shape2.
-
Methods
-
showsignature(object = 'uGASSpec'): Show summary.
Author(s)
Leopoldo Catania
US Monthly Civilian Unemployment Rate (UNRATE) from 1948-01-01 to 2016-05-01
Description
From https://fred.stlouisfed.org/series/UNRATE: The unemployment rate represents the number of unemployed as a percentage of the labor force. Labor force data are restricted to people 16 years of age and older, who currently reside in 1 of the 50 states or the District of Columbia, who do not reside in institutions (e.g., penal and mental facilities, homes for the aged), and who are not on active duty in the Armed Forces.
Usage
data("usunp")
Format
A xts object containing 821 observations from 1948-01-01 to 2016-05-01.
References
US. Bureau of Labor Statistics, Civilian Unemployment Rate [UNRATE], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/UNRATE, July 2, 2016.