gets (version 0.1)

arx: Estimate an AR-X model with log-ARCH-X errors

Description

Estimation is by OLS in two steps. In the first the AR-X mean specification is estimated, whereas in the second step the residuals from the first are used to fit a log-ARCH-X model to the log-variance. The natural logarithm of the squared residuals constitutes the regressand in the second step. The AR-X mean specification can contain an intercept, AR-terms, lagged moving averages of the regressand and other conditioning covariates ('X'). The log-variance specification can contain log-ARCH terms, asymmetry or 'leverage' terms, log(EqWMA) where EqWMA is a lagged equally weighted moving average of past squared residuals (a volatility proxy) and other conditioning covariates ('X').

Usage

arx(y, mc = NULL, ar = NULL, ewma = NULL, mxreg = NULL, arch = NULL,
  asym = NULL, log.ewma = NULL, vxreg = NULL, zero.adj = 0.1, vc.adj = TRUE,
  vcov.type = c("ordinary", "white"), qstat.options = NULL, tol = 1e-07,
  LAPACK = FALSE, verbose = TRUE)

Arguments

y

numeric vector, time-series or zoo object. Missing values in the beginning and at the end of the series is allowed, as they are removed with the na.trim command

mc

logical or NULL (default). TRUE includes intercept in the mean specification, whereas any other value does not

ar

integer vector, say, c(2,4) or 1:4. The AR-lags to include in the mean specification

ewma

either NULL (default) or a list with arguments sent to the eqwma function. In the latter case a lagged moving average of y is included as a regressor

mxreg

numeric vector or matrix, say, a zoo object, of conditioning variables. Note that missing values in the beginning or at the end of the series is allowed, as they are removed with the

arch

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

asym

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

log.ewma

either NULL (default) or a list with arguments sent to the leqwma function. In the latter case (essentially the log of a volatility proxy) the log of a lagged moving average of the residuals e is included as

vxreg

numeric vector or matrix, say, a zoo object, of conditioning variables. Note that missing values in the beginning or at the end of the series is allowed, as they are removed with the

zero.adj

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

vc.adj

logical, TRUE (default) or FALSE. If true then the log-variance intercept is adjusted by the estimate of E[ln(z^2)]. This adjustment is needed for the conditional scale of e to be equal to the conditional standard deviation. If FALSE then the log-variance

vcov.type

character vector, "ordinary" (default) or "white". If "ordinary", then the ordinary variance-covariance matrix is used for inference. Otherwise the White (1980) heteroscedasticity robust matrix is used

qstat.options

NULL (default) or an integer vector of length two, say, c(2,5). The first value sets the order of the AR diagnostic test, whereas the second value sets the order of the ARCH diagnostic test. NULL sets the vector automatically

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 (default)

LAPACK

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

verbose

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

Value

• A list of class 'arx'

Details

See Sucarrat and Escribano (2012)

References

Genaro Sucarrat and Alvaro Escribano (2012): 'Automated Financial Model Selection: General-to-Specific Modelling of the Mean and Volatility Specifications', Oxford Bulletin of Economics and Statistics 74, Issue no. 5 (October), pp. 716-735 Halbert White (1980): 'A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity', Econometrica 48, pp. 817-838

See Also

Extraction functions (S3 methods): coef.arx, fitted.arx, print.arx, residuals.arx, summary.arx and vcov.arx Related functions: getsm, getsv, eqwma, leqwma

Examples

##Simulate from an AR(1):
set.seed(123)
y <- arima.sim(list(ar=0.4), 100)

##Simulate four independent Gaussian regressors:
xregs <- matrix(rnorm(4*100), 100, 4)

##estimate an AR(2) with intercept:
arx(y, mc=TRUE, ar=1:2)

##estimate an AR(2) with intercept and four conditioning
##regressors in the mean:
arx(y, mc=TRUE, ar=1:2, mxreg=xregs)

##estimate a log-variance specification with a log-ARCH(4)
##structure:
arx(y, arch=1:4)

##estimate a log-variance specification with a log-ARCH(4)
##structure and an asymmetry or leverage term:
arx(y, arch=1:4, asym=1)

##estimate a log-variance specification with a log-ARCH(4)
##structure, an asymmetry or leverage term, a 10-period log(EWMA) as
##volatility proxy, and the log of the squareds of the conditioning
##regressors in the log-variance specification:
arx(y, arch=1:4, asym=1, log.ewma=list(length=10), vxreg=log(xregs^2))

##estimate an AR(2) with intercept and four conditioning regressors
##in the mean, and a log-variance specification with a log-ARCH(4)
##structure, an asymmetry or leverage term, a 10-period log(EWMA) as
##volatility proxy, and the log of the squareds of the conditioning
##regressors in the log-variance specification:
arx(y, mc=TRUE, ar=1:2, mxreg=xregs, arch=1:4, asym=1,
  log.ewma=list(length=10), vxreg=log(xregs^2))