Skip to contents

Create regressors for a log-variance model

regressorsVariance.Rd

The function creates the regressors of a log-variance model, e.g. in a arx model. The returned value is a matrix with the regressors and, by default, the regressand in the first column. By default, observations (rows) with missing values are removed in the beginning and the end with na.trim, and the returned matrix is a zoo object.

Usage

regressorsVariance(e, vc = TRUE, arch = NULL, harch = NULL, asym = NULL,
  asymind = NULL, log.ewma = NULL, vxreg = NULL, prefix = "v", zero.adj = NULL,
  vc.adj = TRUE, return.regressand = TRUE, return.as.zoo = TRUE, na.trim = TRUE,
  na.omit = FALSE)

Arguments

e

numeric vector, time-series or zoo object.

vc

logical. TRUE includes an intercept in the log-variance specification, whereas FALSE (default) does not. If the log-variance specification contains any other item but the log-variance intercept, then vc is set to 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(5,20). The log of heterogenous ARCH-terms as proposed by Muller et al. (1997).

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, say, c(1) or 1:3. The indicator ('binary') asymmetry terms to include in the log-variance specification.

log.ewma

either NULL (default) or a vector of the lengths of the volatility proxies, see leqwma. The log of heterogenous volatility proxies similar to those of Corsi (2009).

vxreg

either NULL (default) or a numeric vector or matrix, say, a zoo object, of conditioning variables. If both y and mxreg are zoo objects, then their samples are chosen to match.

prefix

a character used as prefix in the labelling of the variables in vxreg and of the intercept.

zero.adj

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

vc.adj

deprecated and ignored.

return.regressand

logical. TRUE (default) includes the regressand as column one in the returned matrix.

return.as.zoo

logical. TRUE (default) returns the matrix as a zoo object.

na.trim

logical. TRUE (default) removes observations with NA-values in the beginning and the end with na.trim.

na.omit

logical. FALSE (default) means NA-observations that are not in the beginning or at the end are kept (i.e. not omitted). TRUE removes with na.omit.

Value

A matrix, by default of class zoo, with the regressand as column one (the default).

References

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

Muller, Ulrich A., Dacorogna, Michel M., Dave, Rakhal D., Olsen, Richard B, Pictet, Olivier, Weizsaker, Jacob E. (1997): 'Volatilities of different time resolutions - Analyzing the dynamics of market components'. Journal of Empirical Finance 4, pp. 213-239

Pretis, Felix, Reade, James and Sucarrat, Genaro (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: https://www.jstatsoft.org/article/view/v086i03

Sucarrat, Genaro and Escribano, Alvaro (2012): 'Automated Financial Model Selection: General-to-Specific Modelling of the Mean and Volatility Specifications', Oxford Bulletin of Economics and Statistics 74, Issue 5 (October), pp. 716-735

Author

Genaro Sucarrat, http://www.sucarrat.net/

See also

regressorsMean, arx, zoo, leqwma, na.trim and na.omit.

Examples


##generate some data:
eps <- rnorm(10) #error term
x <- matrix(rnorm(10*5), 10, 5) #regressors

##create regressors (examples):
regressorsVariance(eps, vxreg=x)
#>           loge2 vconst     vxreg1      vxreg2        vxreg3      vxreg4
#> 1   -1.81358320      1 -0.6688047 -0.36611661 -1.4664402136 -1.90744533
#> 2  -10.83053327      1  0.3430061  0.50644120  0.5132418443  0.48435318
#> 3    0.03604845      1  1.2668281 -0.57849893  1.2300639371 -1.01534253
#> 4   -1.04171751      1 -0.5358369 -0.01510772  0.0003588142  0.05616500
#> 5    0.86050185      1 -0.5206941 -0.70741163 -0.4171432908  1.26706961
#> 6   -0.67502714      1  0.4855969  1.18353451 -0.5300941211 -0.21457269
#> 7   -1.66462185      1 -0.6016140 -0.42845570  0.7221536300  0.73344466
#> 8    0.82681302      1 -0.5872741 -1.98554270  2.5598198662 -0.05893913
#> 9   -4.35101692      1  0.7789016 -1.00981190 -0.5577840830  1.13043653
#> 10  -0.68979645      1  1.8546588 -0.12814534 -0.0823527423  0.76247928
#>         vxreg5
#> 1  -0.35578297
#> 2   1.38183780
#> 3   0.53277462
#> 4  -0.32518627
#> 5  -1.32926819
#> 6  -0.52779093
#> 7   1.49037243
#> 8  -0.02900963
#> 9   0.01237915
#> 10  1.73204559
regressorsVariance(eps, vxreg=x, return.regressand=FALSE)
#>    vconst     vxreg1      vxreg2        vxreg3      vxreg4      vxreg5
#> 1       1 -0.6688047 -0.36611661 -1.4664402136 -1.90744533 -0.35578297
#> 2       1  0.3430061  0.50644120  0.5132418443  0.48435318  1.38183780
#> 3       1  1.2668281 -0.57849893  1.2300639371 -1.01534253  0.53277462
#> 4       1 -0.5358369 -0.01510772  0.0003588142  0.05616500 -0.32518627
#> 5       1 -0.5206941 -0.70741163 -0.4171432908  1.26706961 -1.32926819
#> 6       1  0.4855969  1.18353451 -0.5300941211 -0.21457269 -0.52779093
#> 7       1 -0.6016140 -0.42845570  0.7221536300  0.73344466  1.49037243
#> 8       1 -0.5872741 -1.98554270  2.5598198662 -0.05893913 -0.02900963
#> 9       1  0.7789016 -1.00981190 -0.5577840830  1.13043653  0.01237915
#> 10      1  1.8546588 -0.12814534 -0.0823527423  0.76247928  1.73204559
regressorsVariance(eps, arch=1:3, vxreg=x)
#>         loge2 vconst       arch1        arch2        arch3     vxreg1
#> 4  -1.0417175      1  0.03604845 -10.83053327  -1.81358320 -0.5358369
#> 5   0.8605019      1 -1.04171751   0.03604845 -10.83053327 -0.5206941
#> 6  -0.6750271      1  0.86050185  -1.04171751   0.03604845  0.4855969
#> 7  -1.6646218      1 -0.67502714   0.86050185  -1.04171751 -0.6016140
#> 8   0.8268130      1 -1.66462185  -0.67502714   0.86050185 -0.5872741
#> 9  -4.3510169      1  0.82681302  -1.66462185  -0.67502714  0.7789016
#> 10 -0.6897965      1 -4.35101692   0.82681302  -1.66462185  1.8546588
#>         vxreg2        vxreg3      vxreg4      vxreg5
#> 4  -0.01510772  0.0003588142  0.05616500 -0.32518627
#> 5  -0.70741163 -0.4171432908  1.26706961 -1.32926819
#> 6   1.18353451 -0.5300941211 -0.21457269 -0.52779093
#> 7  -0.42845570  0.7221536300  0.73344466  1.49037243
#> 8  -1.98554270  2.5598198662 -0.05893913 -0.02900963
#> 9  -1.00981190 -0.5577840830  1.13043653  0.01237915
#> 10 -0.12814534 -0.0823527423  0.76247928  1.73204559
regressorsVariance(eps, arch=1:2, asym=1, vxreg=x)
#>          loge2 vconst        arch1        arch2      asym1     vxreg1
#> 3   0.03604845      1 -10.83053327  -1.81358320  0.0000000  1.2668281
#> 4  -1.04171751      1   0.03604845 -10.83053327  0.0000000 -0.5358369
#> 5   0.86050185      1  -1.04171751   0.03604845  0.0000000 -0.5206941
#> 6  -0.67502714      1   0.86050185  -1.04171751  0.8605019  0.4855969
#> 7  -1.66462185      1  -0.67502714   0.86050185  0.0000000 -0.6016140
#> 8   0.82681302      1  -1.66462185  -0.67502714 -1.6646218 -0.5872741
#> 9  -4.35101692      1   0.82681302  -1.66462185  0.0000000  0.7789016
#> 10 -0.68979645      1  -4.35101692   0.82681302 -4.3510169  1.8546588
#>         vxreg2        vxreg3      vxreg4      vxreg5
#> 3  -0.57849893  1.2300639371 -1.01534253  0.53277462
#> 4  -0.01510772  0.0003588142  0.05616500 -0.32518627
#> 5  -0.70741163 -0.4171432908  1.26706961 -1.32926819
#> 6   1.18353451 -0.5300941211 -0.21457269 -0.52779093
#> 7  -0.42845570  0.7221536300  0.73344466  1.49037243
#> 8  -1.98554270  2.5598198662 -0.05893913 -0.02900963
#> 9  -1.00981190 -0.5577840830  1.13043653  0.01237915
#> 10 -0.12814534 -0.0823527423  0.76247928  1.73204559
regressorsVariance(eps, arch=1:2, asym=1, log.ewma=5)
#>         loge2 vconst      arch1      arch2      asym1 logEqWMA(5)
#> 6  -0.6750271      1  0.8605019 -1.0417175  0.8605019 -0.24411448
#> 7  -1.6646218      1 -0.6750271  0.8605019  0.0000000 -0.15944987
#> 8   0.8268130      1 -1.6646218 -0.6750271 -1.6646218 -0.11601575
#> 9  -4.3510169      1  0.8268130 -1.6646218  0.0000000  0.13131270
#> 10 -0.6897965      1 -4.3510169  0.8268130 -4.3510169  0.06983704

##example where eps and x are time-series:
eps <- ts(eps, frequency=4, end=c(2018,4))
x <- ts(x, frequency=4, end=c(2018,4))
regressorsVariance(eps, vxreg=x)
#>                loge2 vconst   Series 1    Series 2      Series 3    Series 4
#> 2016 Q3  -1.81358320      1 -0.6688047 -0.36611661 -1.4664402136 -1.90744533
#> 2016 Q4 -10.83053327      1  0.3430061  0.50644120  0.5132418443  0.48435318
#> 2017 Q1   0.03604845      1  1.2668281 -0.57849893  1.2300639371 -1.01534253
#> 2017 Q2  -1.04171751      1 -0.5358369 -0.01510772  0.0003588142  0.05616500
#> 2017 Q3   0.86050185      1 -0.5206941 -0.70741163 -0.4171432908  1.26706961
#> 2017 Q4  -0.67502714      1  0.4855969  1.18353451 -0.5300941211 -0.21457269
#> 2018 Q1  -1.66462185      1 -0.6016140 -0.42845570  0.7221536300  0.73344466
#> 2018 Q2   0.82681302      1 -0.5872741 -1.98554270  2.5598198662 -0.05893913
#> 2018 Q3  -4.35101692      1  0.7789016 -1.00981190 -0.5577840830  1.13043653
#> 2018 Q4  -0.68979645      1  1.8546588 -0.12814534 -0.0823527423  0.76247928
#>            Series 5
#> 2016 Q3 -0.35578297
#> 2016 Q4  1.38183780
#> 2017 Q1  0.53277462
#> 2017 Q2 -0.32518627
#> 2017 Q3 -1.32926819
#> 2017 Q4 -0.52779093
#> 2018 Q1  1.49037243
#> 2018 Q2 -0.02900963
#> 2018 Q3  0.01237915
#> 2018 Q4  1.73204559
regressorsVariance(eps, arch=1:3, vxreg=x)
#>              loge2 vconst       arch1        arch2        arch3   Series 1
#> 2017 Q2 -1.0417175      1  0.03604845 -10.83053327  -1.81358320 -0.5358369
#> 2017 Q3  0.8605019      1 -1.04171751   0.03604845 -10.83053327 -0.5206941
#> 2017 Q4 -0.6750271      1  0.86050185  -1.04171751   0.03604845  0.4855969
#> 2018 Q1 -1.6646218      1 -0.67502714   0.86050185  -1.04171751 -0.6016140
#> 2018 Q2  0.8268130      1 -1.66462185  -0.67502714   0.86050185 -0.5872741
#> 2018 Q3 -4.3510169      1  0.82681302  -1.66462185  -0.67502714  0.7789016
#> 2018 Q4 -0.6897965      1 -4.35101692   0.82681302  -1.66462185  1.8546588
#>            Series 2      Series 3    Series 4    Series 5
#> 2017 Q2 -0.01510772  0.0003588142  0.05616500 -0.32518627
#> 2017 Q3 -0.70741163 -0.4171432908  1.26706961 -1.32926819
#> 2017 Q4  1.18353451 -0.5300941211 -0.21457269 -0.52779093
#> 2018 Q1 -0.42845570  0.7221536300  0.73344466  1.49037243
#> 2018 Q2 -1.98554270  2.5598198662 -0.05893913 -0.02900963
#> 2018 Q3 -1.00981190 -0.5577840830  1.13043653  0.01237915
#> 2018 Q4 -0.12814534 -0.0823527423  0.76247928  1.73204559
regressorsVariance(eps, arch=1:2, asym=1, vxreg=x)
#>               loge2 vconst        arch1        arch2      asym1   Series 1
#> 2017 Q1  0.03604845      1 -10.83053327  -1.81358320  0.0000000  1.2668281
#> 2017 Q2 -1.04171751      1   0.03604845 -10.83053327  0.0000000 -0.5358369
#> 2017 Q3  0.86050185      1  -1.04171751   0.03604845  0.0000000 -0.5206941
#> 2017 Q4 -0.67502714      1   0.86050185  -1.04171751  0.8605019  0.4855969
#> 2018 Q1 -1.66462185      1  -0.67502714   0.86050185  0.0000000 -0.6016140
#> 2018 Q2  0.82681302      1  -1.66462185  -0.67502714 -1.6646218 -0.5872741
#> 2018 Q3 -4.35101692      1   0.82681302  -1.66462185  0.0000000  0.7789016
#> 2018 Q4 -0.68979645      1  -4.35101692   0.82681302 -4.3510169  1.8546588
#>            Series 2      Series 3    Series 4    Series 5
#> 2017 Q1 -0.57849893  1.2300639371 -1.01534253  0.53277462
#> 2017 Q2 -0.01510772  0.0003588142  0.05616500 -0.32518627
#> 2017 Q3 -0.70741163 -0.4171432908  1.26706961 -1.32926819
#> 2017 Q4  1.18353451 -0.5300941211 -0.21457269 -0.52779093
#> 2018 Q1 -0.42845570  0.7221536300  0.73344466  1.49037243
#> 2018 Q2 -1.98554270  2.5598198662 -0.05893913 -0.02900963
#> 2018 Q3 -1.00981190 -0.5577840830  1.13043653  0.01237915
#> 2018 Q4 -0.12814534 -0.0823527423  0.76247928  1.73204559
regressorsVariance(eps, arch=1:2, asym=1, log.ewma=5)
#>              loge2 vconst      arch1      arch2      asym1 logEqWMA(5)
#> 2017 Q4 -0.6750271      1  0.8605019 -1.0417175  0.8605019 -0.24411448
#> 2018 Q1 -1.6646218      1 -0.6750271  0.8605019  0.0000000 -0.15944987
#> 2018 Q2  0.8268130      1 -1.6646218 -0.6750271 -1.6646218 -0.11601575
#> 2018 Q3 -4.3510169      1  0.8268130 -1.6646218  0.0000000  0.13131270
#> 2018 Q4 -0.6897965      1 -4.3510169  0.8268130 -4.3510169  0.06983704