Estimation is by OLS in two steps. In the first the mean specification (ARX) is estimated, whereas in the second step the logvariance specification (logARCHX) is estimated.
The ARX mean specification can contain an intercept, ARterms, lagged moving averages of the regressand and other conditioning covariates ('X'). The logvariance specification can contain logARCH 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').
1 2 3 4 5 
y 
numeric vector, timeseries or 
mc 
logical. TRUE includes an intercept in the mean specification, whereas FALSE (default) does not 
ar 
integer vector, say, c(2,4) or 1:4. The ARlags to include in the mean specification 
ewma 
either NULL (default) or a list with arguments sent to the 
mxreg 
numeric vector or matrix, say, a 
vc 
logical. TRUE includes an intercept in the logvariance specification, whereas FALSE (default) does not. If the logvariance specification contains any other item but the logvariance intercept, then vc is set to TRUE 
arch 
integer vector, say, c(1,3) or 2:5. The logARCH lags to include in the logvariance specification 
asym 
integer vector, say, c(1) or 1:3. The asymmetry (i.e. 'leverage') terms to include in the logvariance specification 
log.ewma 
either NULL (default) or a vector of the lengths of the volatility proxies, see 
vxreg 
numeric vector or matrix, say, a 
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. If TRUE (default), then the logvariance 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 logvariance intercept is not adjusted 
vcov.type 
character vector, "ordinary" (default), "white" or "neweywest". If "ordinary", then the ordinary variancecovariance matrix is used for inference. If "white", then the White (1980) heteroscedasticityrobust matrix is used. If "neweywest", then the Newey and West (1987) heteroscedasticity and autocorrelationrobust matrix is used 
qstat.options 
NULL (default) or an integer vector of length two, say, c(1,1). The first value sets the order of the AR diagnostic test, whereas the second value sets the order of the ARCH diagnostic test. If NULL, then the two values of the vector are set automatically 
user.estimator 

user.diagnostics 

tol 
numeric value (default = 1e07). The tolerance for detecting linear dependencies in the columns of the regressors (see 
LAPACK 
logical. If TRUE, then use LAPACK. If FALSE (default), then use LINPACK (see 
plot 
NULL or logical. If TRUE, then the fitted values and the residuals are plotted. If NULL (default), then the value set by 
See Sucarrat and Escribano (2012)
A list of class 'arx'
Genaro Sucarrat, http://www.sucarrat.net/
Genaro Sucarrat and Alvaro Escribano (2012): 'Automated Financial Model Selection: GeneraltoSpecific Modelling of the Mean and Volatility Specifications', Oxford Bulletin of Economics and Statistics 74, Issue no. 5 (October), pp. 716735
Halbert White (1980): 'A HeteroskedasticityConsistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity', Econometrica 48, pp. 817838
Whitney K. Newey and Kenned D. West (1987): 'A Simple, Positive SemiDefinite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix', Econometrica 55, pp. 703708
Extraction functions (S3 methods): coef.arx
, fitted.arx
, plot.arx
, print.arx
,
residuals.arx
, sigma.arx
, summary.arx
and vcov.arx
Related functions: getsm
, getsv
, eqwma
, leqwma
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35  ##Simulate from an AR(1):
set.seed(123)
y < arima.sim(list(ar=0.4), 70)
##estimate an AR(2) with intercept:
arx(y, mc=TRUE, ar=1:2)
##Simulate four independent Gaussian regressors:
xregs < matrix(rnorm(4*70), 70, 4)
##estimate an AR(2) with intercept and four conditioning
##regressors in the mean:
arx(y, mc=TRUE, ar=1:2, mxreg=xregs)
##estimate a logvariance specification with a logARCH(4)
##structure:
arx(y, arch=1:4)
##estimate a logvariance specification with a logARCH(4)
##structure and an asymmetry/leverage term:
arx(y, arch=1:4, asym=1)
##estimate a logvariance specification with a logARCH(4)
##structure, an asymmetry or leverage term, a 10period log(EWMA) as
##volatility proxy, and the log of the squareds of the conditioning
##regressors in the logvariance 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 logvariance specification with a logARCH(4)
##structure, an asymmetry or leverage term, a 10period log(EWMA) as
##volatility proxy, and the log of the squareds of the conditioning
##regressors in the logvariance specification:
arx(y, mc=TRUE, ar=1:2, mxreg=xregs, arch=1:4, asym=1,
log.ewma=list(length=10), vxreg=log(xregs^2))

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