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Create the regressors of the variance equation

regressorsVariance.Rd

The function generates the regressors of the log-variance equation in an arx model. The returned value is a matrix with the regressors and, by default, the regressand in column one. 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, asym = NULL,
  log.ewma = NULL, vxreg = NULL, zero.adj = 0.1, 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

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

log.ewma

either NULL (default) or a vector of the lengths of the volatility proxies, see leqwma

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

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 log-variance intercept is adjusted by the estimate of E[ln(z^2)], where z is the standardised error. This adjustment is needed for the conditional scale to be equal to the conditional standard deviation. If FALSE, then the log-variance intercept is not adjusted

return.regressand

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

return.as.zoo

TRUE, the default, returns the matrix as a zoo object.

na.trim

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

na.omit

TRUE, the non-default, removes observations with NA-values, not necessarily in the beginning or in the end, with na.omit.

Value

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

References

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     vxreg5
#> 1  -0.1634702      1 -1.1696153  0.05621485  1.61554532  0.1467085 -0.5272343
#> 2   0.3786650      1 -1.4420346  0.29908690 -0.02969397  1.6236212  1.6659909
#> 3   0.4123792      1  1.0543223 -0.75939812  0.56226735  0.9112097 -1.1392006
#> 4  -0.5960116      1 -0.5973301  2.68485900 -0.09741250  0.1424584  0.1436232
#> 5  -4.9797594      1  0.7894599 -0.45839014  1.01645522 -1.3894835 -1.0995509
#> 6  -0.4719057      1  1.5164906  0.06424356 -1.15616739 -0.8660377  0.9035164
#> 7  -2.6357287      1 -0.1917748  0.64979187  2.32086022 -0.1632849  1.4837795
#> 8  -1.0488618      1  0.2838789 -0.02601863 -0.60353125  2.5530261  1.9507210
#> 9  -1.9974294      1 -1.7510675 -0.64356739 -1.45884941 -1.8602276  0.7976007
#> 10  1.2331983      1 -0.8186698  1.04530566 -0.35091783  1.1310547  1.8432663
regressorsVariance(eps, vxreg=x, return.regressand=FALSE)
#>    vconst     vxreg1      vxreg2      vxreg3     vxreg4     vxreg5
#> 1       1 -1.1696153  0.05621485  1.61554532  0.1467085 -0.5272343
#> 2       1 -1.4420346  0.29908690 -0.02969397  1.6236212  1.6659909
#> 3       1  1.0543223 -0.75939812  0.56226735  0.9112097 -1.1392006
#> 4       1 -0.5973301  2.68485900 -0.09741250  0.1424584  0.1436232
#> 5       1  0.7894599 -0.45839014  1.01645522 -1.3894835 -1.0995509
#> 6       1  1.5164906  0.06424356 -1.15616739 -0.8660377  0.9035164
#> 7       1 -0.1917748  0.64979187  2.32086022 -0.1632849  1.4837795
#> 8       1  0.2838789 -0.02601863 -0.60353125  2.5530261  1.9507210
#> 9       1 -1.7510675 -0.64356739 -1.45884941 -1.8602276  0.7976007
#> 10      1 -0.8186698  1.04530566 -0.35091783  1.1310547  1.8432663
regressorsVariance(eps, arch=1:3, vxreg=x)
#>         loge2 vconst      arch1      arch2      arch3     vxreg1      vxreg2
#> 4  -0.5960116      1  0.4123792  0.3786650 -0.1634702 -0.5973301  2.68485900
#> 5  -4.9797594      1 -0.5960116  0.4123792  0.3786650  0.7894599 -0.45839014
#> 6  -0.4719057      1 -4.9797594 -0.5960116  0.4123792  1.5164906  0.06424356
#> 7  -2.6357287      1 -0.4719057 -4.9797594 -0.5960116 -0.1917748  0.64979187
#> 8  -1.0488618      1 -2.6357287 -0.4719057 -4.9797594  0.2838789 -0.02601863
#> 9  -1.9974294      1 -1.0488618 -2.6357287 -0.4719057 -1.7510675 -0.64356739
#> 10  1.2331983      1 -1.9974294 -1.0488618 -2.6357287 -0.8186698  1.04530566
#>        vxreg3     vxreg4     vxreg5
#> 4  -0.0974125  0.1424584  0.1436232
#> 5   1.0164552 -1.3894835 -1.0995509
#> 6  -1.1561674 -0.8660377  0.9035164
#> 7   2.3208602 -0.1632849  1.4837795
#> 8  -0.6035312  2.5530261  1.9507210
#> 9  -1.4588494 -1.8602276  0.7976007
#> 10 -0.3509178  1.1310547  1.8432663
regressorsVariance(eps, arch=1:2, asym=1, vxreg=x)
#>         loge2 vconst      arch1      arch2      asym1     vxreg1      vxreg2
#> 3   0.4123792      1  0.3786650 -0.1634702  0.3786650  1.0543223 -0.75939812
#> 4  -0.5960116      1  0.4123792  0.3786650  0.4123792 -0.5973301  2.68485900
#> 5  -4.9797594      1 -0.5960116  0.4123792  0.0000000  0.7894599 -0.45839014
#> 6  -0.4719057      1 -4.9797594 -0.5960116 -4.9797594  1.5164906  0.06424356
#> 7  -2.6357287      1 -0.4719057 -4.9797594  0.0000000 -0.1917748  0.64979187
#> 8  -1.0488618      1 -2.6357287 -0.4719057 -2.6357287  0.2838789 -0.02601863
#> 9  -1.9974294      1 -1.0488618 -2.6357287 -1.0488618 -1.7510675 -0.64356739
#> 10  1.2331983      1 -1.9974294 -1.0488618 -1.9974294 -0.8186698  1.04530566
#>        vxreg3     vxreg4     vxreg5
#> 3   0.5622673  0.9112097 -1.1392006
#> 4  -0.0974125  0.1424584  0.1436232
#> 5   1.0164552 -1.3894835 -1.0995509
#> 6  -1.1561674 -0.8660377  0.9035164
#> 7   2.3208602 -0.1632849  1.4837795
#> 8  -0.6035312  2.5530261  1.9507210
#> 9  -1.4588494 -1.8602276  0.7976007
#> 10 -0.3509178  1.1310547  1.8432663
regressorsVariance(eps, arch=1:2, asym=1, log.ewma=5)
#>         loge2 vconst      arch1      arch2     asym1 logEqWMA(5)
#> 6  -0.4719057      1 -4.9797594 -0.5960116 -4.979759  -0.1328886
#> 7  -2.6357287      1 -0.4719057 -4.9797594  0.000000  -0.1857433
#> 8  -1.0488618      1 -2.6357287 -0.4719057 -2.635729  -0.5928434
#> 9  -1.9974294      1 -1.0488618 -2.6357287 -1.048862  -1.1371270
#> 10  1.2331983      1 -1.9974294 -1.0488618 -1.997429  -1.4368514

##let eps and x be 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 -0.1634702      1 -1.1696153  0.05621485  1.61554532  0.1467085
#> 2016 Q4  0.3786650      1 -1.4420346  0.29908690 -0.02969397  1.6236212
#> 2017 Q1  0.4123792      1  1.0543223 -0.75939812  0.56226735  0.9112097
#> 2017 Q2 -0.5960116      1 -0.5973301  2.68485900 -0.09741250  0.1424584
#> 2017 Q3 -4.9797594      1  0.7894599 -0.45839014  1.01645522 -1.3894835
#> 2017 Q4 -0.4719057      1  1.5164906  0.06424356 -1.15616739 -0.8660377
#> 2018 Q1 -2.6357287      1 -0.1917748  0.64979187  2.32086022 -0.1632849
#> 2018 Q2 -1.0488618      1  0.2838789 -0.02601863 -0.60353125  2.5530261
#> 2018 Q3 -1.9974294      1 -1.7510675 -0.64356739 -1.45884941 -1.8602276
#> 2018 Q4  1.2331983      1 -0.8186698  1.04530566 -0.35091783  1.1310547
#>           Series 5
#> 2016 Q3 -0.5272343
#> 2016 Q4  1.6659909
#> 2017 Q1 -1.1392006
#> 2017 Q2  0.1436232
#> 2017 Q3 -1.0995509
#> 2017 Q4  0.9035164
#> 2018 Q1  1.4837795
#> 2018 Q2  1.9507210
#> 2018 Q3  0.7976007
#> 2018 Q4  1.8432663
regressorsVariance(eps, arch=1:3, vxreg=x)
#>              loge2 vconst      arch1      arch2      arch3   Series 1
#> 2017 Q2 -0.5960116      1  0.4123792  0.3786650 -0.1634702 -0.5973301
#> 2017 Q3 -4.9797594      1 -0.5960116  0.4123792  0.3786650  0.7894599
#> 2017 Q4 -0.4719057      1 -4.9797594 -0.5960116  0.4123792  1.5164906
#> 2018 Q1 -2.6357287      1 -0.4719057 -4.9797594 -0.5960116 -0.1917748
#> 2018 Q2 -1.0488618      1 -2.6357287 -0.4719057 -4.9797594  0.2838789
#> 2018 Q3 -1.9974294      1 -1.0488618 -2.6357287 -0.4719057 -1.7510675
#> 2018 Q4  1.2331983      1 -1.9974294 -1.0488618 -2.6357287 -0.8186698
#>            Series 2   Series 3   Series 4   Series 5
#> 2017 Q2  2.68485900 -0.0974125  0.1424584  0.1436232
#> 2017 Q3 -0.45839014  1.0164552 -1.3894835 -1.0995509
#> 2017 Q4  0.06424356 -1.1561674 -0.8660377  0.9035164
#> 2018 Q1  0.64979187  2.3208602 -0.1632849  1.4837795
#> 2018 Q2 -0.02601863 -0.6035312  2.5530261  1.9507210
#> 2018 Q3 -0.64356739 -1.4588494 -1.8602276  0.7976007
#> 2018 Q4  1.04530566 -0.3509178  1.1310547  1.8432663
regressorsVariance(eps, arch=1:2, asym=1, vxreg=x)
#>              loge2 vconst      arch1      arch2      asym1   Series 1
#> 2017 Q1  0.4123792      1  0.3786650 -0.1634702  0.3786650  1.0543223
#> 2017 Q2 -0.5960116      1  0.4123792  0.3786650  0.4123792 -0.5973301
#> 2017 Q3 -4.9797594      1 -0.5960116  0.4123792  0.0000000  0.7894599
#> 2017 Q4 -0.4719057      1 -4.9797594 -0.5960116 -4.9797594  1.5164906
#> 2018 Q1 -2.6357287      1 -0.4719057 -4.9797594  0.0000000 -0.1917748
#> 2018 Q2 -1.0488618      1 -2.6357287 -0.4719057 -2.6357287  0.2838789
#> 2018 Q3 -1.9974294      1 -1.0488618 -2.6357287 -1.0488618 -1.7510675
#> 2018 Q4  1.2331983      1 -1.9974294 -1.0488618 -1.9974294 -0.8186698
#>            Series 2   Series 3   Series 4   Series 5
#> 2017 Q1 -0.75939812  0.5622673  0.9112097 -1.1392006
#> 2017 Q2  2.68485900 -0.0974125  0.1424584  0.1436232
#> 2017 Q3 -0.45839014  1.0164552 -1.3894835 -1.0995509
#> 2017 Q4  0.06424356 -1.1561674 -0.8660377  0.9035164
#> 2018 Q1  0.64979187  2.3208602 -0.1632849  1.4837795
#> 2018 Q2 -0.02601863 -0.6035312  2.5530261  1.9507210
#> 2018 Q3 -0.64356739 -1.4588494 -1.8602276  0.7976007
#> 2018 Q4  1.04530566 -0.3509178  1.1310547  1.8432663
regressorsVariance(eps, arch=1:2, asym=1, log.ewma=5)
#>              loge2 vconst      arch1      arch2     asym1 logEqWMA(5)
#> 2017 Q4 -0.4719057      1 -4.9797594 -0.5960116 -4.979759  -0.1328886
#> 2018 Q1 -2.6357287      1 -0.4719057 -4.9797594  0.000000  -0.1857433
#> 2018 Q2 -1.0488618      1 -2.6357287 -0.4719057 -2.635729  -0.5928434
#> 2018 Q3 -1.9974294      1 -1.0488618 -2.6357287 -1.048862  -1.1371270
#> 2018 Q4  1.2331983      1 -1.9974294 -1.0488618 -1.997429  -1.4368514