larch {gets}

Estimate a heterogeneous log-ARCH-X model

Description

The function larch() estimates a heterogeneous log-ARCH-X model, which is a generalisation of the dynamic log-variance model in Pretis, Reade and Sucarrat (2018). Internally, estimation is undertaken by a call to larchEstfun. The log-variance specification can contain log-ARCH terms, log-HARCH terms, asymmetry terms ('leverage'), the log of volatility proxies made up of past returns and other covariates ('X'), for example Realised Volatility (RV), volume or the range.

Usage

larch(e, vc=TRUE, arch = NULL, harch = NULL, asym = NULL, asymind = NULL,
  log.ewma = NULL, vxreg = NULL, zero.adj = NULL, 
  vcov.type = c("robust", "hac"), qstat.options = NULL,
  normality.JarqueB = FALSE, tol = 1e-07, singular.ok = TRUE,  plot = NULL)

Arguments

e

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

vc

logical. TRUE includes an intercept in the log-variance specification. Currently, vc cannot be set to any other value than TRUE

arch

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

harch

either NULL (default) or an integer vector, say, c(5,10). The (log of) heterogeneous ARCH terms (Muller et al. 1997) to include

asym

either NULL (default) or an integer vector, say, c(1) or 1:3. The asymmetry (i.e. 'leverage') terms to include in the log-variance specification

asymind

either NULL (default or an integer vector. The indicator asymmetry terms to include

log.ewma

either NULL (default) or a vector of the lengths of the volatility proxies, see leqwma. The terms serve as (log of) volatility proxies similar to RVs in the HAR-model of Corsi (2009). Here, the log.ewma terms are made up of past e's

vxreg

either NULL (default) or a numeric vector or matrix, say, a zoo object. If both e and vxreg are zoo objects, then their samples are chosen to match

zero.adj

NULL (default) or a strictly positive numeric scalar. If NULL, the zeros in the squared residuals are replaced by the 10 percent quantile of the non-zero squared residuals. If zero.adj is a strictly positive numeric scalar, then this value is used to replace the zeros of the squared e's

vcov.type

character. "robust" (default) or "hac" (partial matching is allowed). If "robust", the robust variance-covariance matrix of the White (1980) type is used. If "hac", the Newey and West (1987) heteroscedasticity and autocorrelation-robust matrix is used

qstat.options

NULL (default) or an integer vector of length two, say, c(1,1). The first value sets the lag-order of the AR diagnostic test of the standardised residuals, whereas the second value sets the lag-order of the ARCH diagnostic test of the standardised residuals. If NULL, then the two values of the vector are set automatically

normality.JarqueB

FALSE (default) or TRUE. If TRUE, then the results of the Jarque and Bera (1980) test for non-normality in the residuals are included in the estimation results

tol

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

singular.ok

logical. If TRUE (default), the regressors are checked for singularity, and the ones causing it are automatically removed. If FALSE, then the function returns an error

plot

NULL (default) or logical. If TRUE, the fitted values and the residuals are plotted. If NULL, then the value set by options determines whether a plot is produced or not

Details

No details for the moment

Value

A list of class 'larch'

Author(s)

Genaro Sucarrat: https://www.sucarrat.net/

References

G. Ljung and G. Box (1979): 'On a Measure of Lack of Fit in Time Series Models'. Biometrika 66, pp. 265-270

F. Corsi (2009): 'A Simple Approximate Long-Memory Model of Realized Volatility', Journal of Financial Econometrics 7, pp. 174-196

C. Jarque and A. Bera (1980): 'Efficient Tests for Normality, Homoscedasticity and Serial Independence'. Economics Letters 6, pp. 255-259. doi:10.1016/0165-1765(80)90024-5

U. Muller, M. Dacorogna, R. Dave, R. Olsen, O. Pictet and J. von Weizsacker (1997): 'Volatilities of different time resolutions - analyzing the dynamics of market components'. Journal of Empirical Finance 4, pp. 213-239

F. Pretis, J. Reade and G. Sucarrat (2018): 'Automated General-to-Specific (GETS) Regression Modeling and Indicator Saturation for Outliers and Structural Breaks'. Journal of Statistical Software 86, Number 3, pp. 1-44. doi:10.18637/jss.v086.i03

H. White (1980): 'A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity', Econometrica 48, pp. 817-838.

W.K. Newey and K.D. West (1987): 'A Simple, Positive Semi-Definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix', Econometrica 55, pp. 703-708.

See Also

Methods and extraction functions (mostly S3 methods): coef.larch, ES, fitted.larch, gets.larch,
logLik.larch, nobs.larch, plot.larch, predict.larch, print.larch,
residuals.larch, summary.larch, VaR, toLatex.larch and vcov.arx

regressorsVariance

Examples

##Simulate some data:
set.seed(123)
e <- rnorm(40)
x <- matrix(rnorm(40*2), 40, 2)

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

##estimate a log-variance specification with a log-ARCH(4)
##structure, a log-HARCH(5) term and a first-order asymmetry/leverage
##term:
larch(e, arch=1:4, harch=5, asym=1)

##estimate a log-variance specification with a log-ARCH(4)
##structure, an asymmetry/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:
larch(e, arch=1:4, asym=1, log.ewma=list(length=10), vxreg=log(x^2))