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gets.vol: General-to-Specific (GETS) model selection of a log-volatility specification

Description

The starting model is referred to as the General Unrestricted Model (GUM) log-volatility specification, and takes the residuals from a mean specification as its modelling objective. But the modelling or model selection is undertaken in terms of the log-volatility specification. The diagnostic tests are undertaken on the standardised residuals (this is not optional)

Usage

gets.vol(e, arch=NULL, asym=NULL, log.ewma=NULL, vx=NULL,
  p=2, keep=c(1), t.pval=0.05, wald.pval=0.05, do.pet=TRUE,
  ar.LjungB=c(1, 0.025), arch.LjungB=c(1, 0.025), tau=2,
  info.method=c("sc", "aic", "hq"),
  info.resids=c("standardised", "log-sigma"),
  include.empty=FALSE, zero.adj=0.1, vc.adj=TRUE, tol=1e-07,
  LAPACK=FALSE, max.regs=1000, verbose=TRUE, smpl=NULL)

Arguments

e

numeric vector, time-series or zoo object. Note that missing values in the beginning or at the end of the series is allowed, as they are removed with the na.trim command from the zoo package

arch

integer vector, say, c(1,3) or 2:5. The ARCH-lags to include in the log-volatility specification

asym

integer vector, say, c(1) or 1:3. The asymmetry or leverage terms to include in the log-volatility specification

log.ewma

NULL (default) or a list. If NULL then log(EWMA) is not included as volatility proxy. If a list, then log(EWMA) is included as a volatility proxy.

vx

numeric matrix, time-series or zoo object of conditioning covariates. Note that missing values in the beginning or at the end of the series is allowed, as they are removed with the na.trim command from the zoo package

p

numeric value greater than zero. The power of the log-volatility specification.

keep

NULL (default) or an integer vector. If keep = NULL, then no regressors are excluded from removal. Otherwise, the regressors associated with the numbers in keep are excluded from the removal space. For example, keep=c(1) excludes the constant from removal

t.pval

numeric value between 0 and 1. The significance level used for the regressor tests

wald.pval

numeric value between 0 and 1. The significance level used for the PETs

do.pet

logical, TRUE (default) or FALSE. If TRUE then a Parsimonious Encompassing Test (PET) against the GUM is undertaken at each regressor removal for the joint significance of all the deleted regressors along the current path

ar.LjungB

NULL or a two-element vector where the first element contains the order of a Ljung and Box (1979) test for serial correlation in the standardised residuals, and where the second element contains the significance level. If NULL, then the standardised resid

arch.LjungB

NULL or a two-element vector where the first element contains the order of a Ljung and Box (1979) test for ARCH (serial correlation in the squared standardised residuals), and where the second element contains the significance level. If NULL, then the sta

tau

NULL or a numeric value greater than 1. If NULL, then the shape parameter in a Generalised Error Distribution (GED) of the standardised residuals is estimated for the log-likelihood used in the calculation of the information criterion. If tau is iqual to

info.method

character string, "sc" (default), "aic" or "hq", which determines the information criterion used to select among terminal models. The abbreviations are short for the Schwarz or Bayesian information criterion (sc), the Akaike information criterion (aic) an

info.resids

character string, "mean" (default) or "standardised" which sets the residuals to be used in the computation of the information criterion

include.empty

logical, TRUE or FALSE (default). If TRUE then an empty model is included among the terminal models, if it passes the diagnostic tests, even if it is not equal to one of the terminals

zero.adj

numeric value between 0 and 1. The quantile adjustment for zero values. The default 0.1 means that the zero residuals are replaced by means of the 10 percent quantile of the absolute residuals before taking the logarithm

vc.adj

logical, TRUE (default) or FALSE. If true then the log-volatility constant is adjusted by means of the estimate of E[log(z^2)]. This adjustment is needed for the standardised residuals to have unit variance. If FALSE then the log-volatility constant is no

tol

numeric value (default = 1e-07). The tolerance for detecting linear dependencies in the columns of the regressors (see qr() function). Only used if LAPACK is FALSE

LAPACK

logical, TRUE or FALSE (default). If true use LAPACK otherwise use LINPACK (see qr() function)

max.regs

integer value, sets the maximum number of regressions along a deletion path. Default: max.regs=1000

verbose

logical, TRUE (default) or FALSE. FALSE returns less output and is therefore faster

smpl

Either NULL (default; the whole sample is used for estimation) or a two-element vector of dates with the start and end dates of the sample to be used in estimation. For example, smpl=c("2001-01-01", "2009-12-31")

Value

• Returns a list with the following elements:
• volatility.fit
  zoo-object with the fitted values of the volatility (sigma^p) of the final log-volatility specification
• resids.ustar
  zoo-object with the residuals of the AR-representation of the final log-volatility specification
• resids.std
  zoo-object with the standardised residuals of the final log-volatility specification
• Elogzp
  estimate of E[log(z^p)]
• call
  the function call
• gum.volatility
  a data frame with the estimation results of the log-volatility GUM
• gum.diagnostics
  data frame with selected diagnostics of the log-volatility GUM
• keep
  if any, the regressors that are excluded from deletion
• insigs.in.gum
  a numeric integer vector with the insignificant regressors of the log-volatility GUM
• paths
  a list containing the simplification paths, that is, the sequences of deleted regressors
• terminals
  the distinct terminal models
• terminals.results
  the value and type of the information criterion (info) used in selecting among terminal specifications, and the number of observations (T) and parameters (k) used in the calculation of the information criterion
• specific.volatility
  data frame with the estimation results of the final log-volatility specification
• specific.diagnostics
  data frame with selected diagnostics of the standardised residuals

Details

See Sucarrat and Escribano (2011)

References

Genaro Sucarrat and Alvaro Escribano: 'Automated Financial Model Selection: General-to-Specific Modelling of the Mean and Volatility Specifications', forthcoming in the Oxford Bulletin of Economics and Statistics Genaro Sucarrat and Alvaro Escribano: 'The Power Log-GARCH Model', working paper G. Ljung and G. Box (1979): 'On a Measure of Lack of Fit in Time Series Models'. Biometrika 66, pp. 265-270

See Also

sm, gets.mean, ewma

Examples

#Generate iid normal residuals and a matrix of independent
#normals:
set.seed(123)
e <- rnorm(200)
xregs <- matrix(rnorm(4*200), 200, 4)

#General-to-Specific model selection of log-volatility:
mymodel <- gets.vol(e, arch=1:5, vx=log(xregs^2))

#General-to-Specific model selection of log-volatility
#with the log-ARCH(1) term excluded from removal:
mymodel <- gets.vol(e, arch=1:5, vx=log(xregs^2), keep=2)

#General-to-Specific model selection of log-volatility
#with all the log-ARCH terms excluded from removal:
mymodel <- gets.vol(e, arch=1:5, vx=log(xregs^2), asym=1:2,
  keep=2:6, log.ewma=list(length=5))

#General-to-Specific model selection with (very) liberal
#significance levels:
mymodel <- gets.vol(e, arch=1:5, vx=log(xregs^2), t.pval=0.2,
  wald.pval=0.2)