General-to-Specific (GETS) Modelling of a heterogeneous log-ARCH-X model

The starting model, an object of the 'larch' class (see larch, is referred to as the General Unrestricted Model (GUM). The gets.larch() function undertakes multi-path GETS modelling of the log-variance specification. The diagnostic tests are undertaken on the standardised residuals, and the keep option enables regressors to be excluded from possible removal.

Usage

# S3 method for class 'larch'
gets(x, t.pval=0.05, wald.pval=t.pval, do.pet=TRUE, 
    ar.LjungB=NULL, arch.LjungB=NULL, normality.JarqueB=NULL, 
    user.diagnostics=NULL, info.method=c("sc", "aic", "aicc", "hq"),
    gof.function=NULL, gof.method=NULL, keep=c(1), include.gum=FALSE,
    include.1cut=TRUE, include.empty=FALSE, max.paths=NULL, tol=1e-07,
    turbo=FALSE, print.searchinfo=TRUE, plot=NULL, alarm=FALSE, ...)

Arguments

x: an object of class 'larch'
t.pval: numeric value between 0 and 1. The significance level used for the two-sided regressor significance t-tests
wald.pval: numeric value between 0 and 1. The significance level used for the Parsimonious Encompassing Tests (PETs). By default, wald.pval is equal to t.pval
do.pet: logical. If TRUE (default), then a Parsimonious Encompassing Test (PET) against the GUM is undertaken at each regressor removal for the joint significance of all the deleted regressors along the current path. If FALSE, then a PET is not undertaken at each regressor removal
ar.LjungB: NULL (default), or a list with named items lag and pval, or a two-element numeric vector where the first element contains the lag and the second the p-value. If NULL, then the standardised residuals are not checked for autocorrelation. If ar.LjungB is a list, then lag contains the order of the Ljung and Box (1979) test for serial correlation in the standardised residuals, and pval contains the significance level. If lag=NULL, then the order used is that of the estimated 'larch' object
arch.LjungB: NULL (default), or a list with named items lag and pval, or a two-element numeric vector where the first element contains the lag and the second the p-value. If NULL, then the standardised residuals are not checked for ARCH (autocorrelation in the squared standardised residuals). If ar.LjungB is a list, then lag contains the order of the test, and pval contains the significance level. If lag=NULL, then the order used is that of the estimated 'larch' object
normality.JarqueB: NULL (default) or a numeric value between 0 and 1. If NULL, then no test for non-normality is undertaken. If a numeric value between 0 and 1, then the Jarque and Bera (1980) test for non-normality is conducted using a significance level equal to the numeric value
user.diagnostics: NULL (default) or a list with two entries, name and pval, see the user.fun argument in diagnostics
info.method: character string, "sc" (default), "aic", "aicc" or "hq", which determines the information criterion to be used when selecting among terminal models. See infocrit for the details
gof.function: NULL (default) or a list, see getsFun. If NULL, then infocrit is used
gof.method: NULL (default) or a character, see getsFun. If NULL and gof.function is also NULL, then the best goodness-of-fit is characterised by a minimum value
keep: the regressors to be kept (i.e. excluded from removal) in the specification search. Currently, keep=c(1) is obligatory, which excludes the log-variance intercept from removal
include.gum: logical. If TRUE, the GUM (i.e. the starting model) is included among the terminal models. If FALSE (default), the GUM is not included
include.1cut: logical. If TRUE (default), then the 1-cut model is added to the list of terminal models. If FALSE, the 1-cut is not added, unless it is a terminal model in one of the paths
include.empty: logical. If TRUE, then an empty model is included among the terminal models, if it passes the diagnostic tests. If FALSE (default), then the empty model is not included
max.paths: NULL (default) or an integer equal to or greater than 0. If NULL, then there is no limit to the number of paths. If an integer (e.g. 1), then this integer constitutes the maximum number of paths searched (e.g. a single path)
tol: numeric value. The tolerance for detecting linear dependencies in the columns of the variance-covariance matrix when computing the Wald-statistic used in the Parsimonious Encompassing Tests (PETs), see the qr.solve function
turbo: logical. If TRUE, then paths are not searched twice (or more) unnecessarily, thus yielding a significant potential for speed-gain. However, the checking of whether the search has arrived at a point it has already been comes with a computational overhead. Accordingly, if turbo=TRUE, the total search time might in fact be higher than if turbo=FALSE. This is particularly likely to happen if estimation is very fast, say, less than a quarter of a second. Hence the default is FALSE
print.searchinfo: logical. If TRUE (default), then a print is returned whenever simiplification along a new path is started
plot: NULL or logical. If TRUE, then the fitted values and the standardised residuals of the final model are plotted after model selection. If FALSE, then they are not plotted. If NULL (default), then the value set by options determines whether a plot is produced or not
alarm: logical. If TRUE, then a sound or beep is emitted (in order to alert the user) when the model selection ends, see alarm
...: additional arguments

Details

See Pretis, Reade and Sucarrat (2018): doi:10.18637/jss.v086.i03 , and Sucarrat (2020): https://journal.r-project.org/archive/2021/RJ-2021-024/.

The arguments user.diagnostics and gof.function enable the specification of user-defined diagnostics and a user-defined goodness-of-fit function. For the former, see the documentation of diagnostics. For the latter, the principles of the same arguments in getsFun are followed, see its documentation under "Details", and Sucarrat (2020): https://journal.r-project.org/archive/2021/RJ-2021-024/.

Value

A list of class 'larch', see larch, with additional information about the GETS modelling

References

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

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

Felix Pretis, James Reade and Genaro 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

Genaro Sucarrat (2020): 'User-Specified General-to-Specific and Indicator Saturation Methods'. The R Journal 12:2, pages 388-401. https://journal.r-project.org/archive/2021/RJ-2021-024/

Author

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

Examples

##Simulate some data:
set.seed(123)
e <- rnorm(40)
x <- matrix(rnorm(4*40), 40, 4)

##estimate a log-ARCH(3) with asymmetry and log(x^2) as regressors:
gum <- larch(e, arch=1:3, asym=1, vxreg=log(x^2))

##GETS modelling of the log-variance:
simple <- gets(gum)
#> 
#> GUM log-variance equation:
#> 
#>        reg.no. keep      coef std.error  t-stat p-value  
#> vconst       1    1 -0.623183  0.561349 -1.1102 0.29571  
#> arch1        2    0  0.075856  0.206463  0.3674 0.72181  
#> arch2        3    0 -0.125252  0.147240 -0.8507 0.41701  
#> arch3        4    0  0.076151  0.163485  0.4658 0.65243  
#> asym1        5    0 -0.178412  0.237220 -0.7521 0.47120  
#> vxreg1       6    0  0.064916  0.116349  0.5579 0.59049  
#> vxreg2       7    0 -0.190337  0.129783 -1.4666 0.17654  
#> vxreg3       8    0  0.142136  0.137520  1.0336 0.32831  
#> vxreg4       9    0 -0.224855  0.121049 -1.8576 0.09619 .
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Diagnostics:
#> 
#>                     Chi-sq df p-value
#> Ljung-Box AR(1)   0.050748  1 0.82177
#> Ljung-Box ARCH(4) 4.228739  4 0.37593
#> 
#> 8 path(s) to search
#> Searching: 
#> 1 
#> 2 
#> 3 
#> 4 
#> 5 
#> 6 
#> 7 
#> 8 
#> 
#>   Path 1: 2 4 6 5 8 9 7 
#>   Path 2: 3 4 6 5 9 7 8 
#>   Path 3: 4 6 5 3 9 7 8 
#>   Path 4: 5 6 4 3 9 7 8 
#>   Path 5: 6 4 5 3 9 7 8 
#>   Path 6: 7 6 5 4 3 9 8 
#>   Path 7: 8 5 4 6 3 9 7 
#>   Path 8: 9 6 4 3 5 7 8 
#> 
#> Terminal models:
#> 
#>                 info(sc)      logl  n k
#> spec 1 (1-cut): 2.682133 -47.81400 37 1
#> spec 2:         2.769014 -47.61585 37 2
#> spec 3:         2.774207 -47.71192 37 2
#> 
#> Retained regressors (final model):
#>   vconst 

##GETS modelling with intercept and log-ARCH(1) terms
##excluded from removal:
simple <- gets(gum, keep=c(1,2))
#> 
#> GUM log-variance equation:
#> 
#>        reg.no. keep      coef std.error  t-stat p-value  
#> vconst       1    1 -0.623183  0.561349 -1.1102 0.29571  
#> arch1        2    1  0.075856  0.206463  0.3674 0.72181  
#> arch2        3    0 -0.125252  0.147240 -0.8507 0.41701  
#> arch3        4    0  0.076151  0.163485  0.4658 0.65243  
#> asym1        5    0 -0.178412  0.237220 -0.7521 0.47120  
#> vxreg1       6    0  0.064916  0.116349  0.5579 0.59049  
#> vxreg2       7    0 -0.190337  0.129783 -1.4666 0.17654  
#> vxreg3       8    0  0.142136  0.137520  1.0336 0.32831  
#> vxreg4       9    0 -0.224855  0.121049 -1.8576 0.09619 .
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Diagnostics:
#> 
#>                     Chi-sq df p-value
#> Ljung-Box AR(1)   0.050748  1 0.82177
#> Ljung-Box ARCH(4) 4.228739  4 0.37593
#> 
#> 7 path(s) to search
#> Searching: 
#> 1 
#> 2 
#> 3 
#> 4 
#> 5 
#> 6 
#> 7 
#> 
#>   Path 1: 3 6 5 7 9 8 
#>   Path 2: 4 6 5 8 9 7 
#>   Path 3: 5 6 4 8 9 7 
#>   Path 4: 6 4 5 8 9 7 
#>   Path 5: 7 6 5 4 9 8 
#>   Path 6: 8 5 4 6 9 7 
#>   Path 7: 9 6 4 5 7 8 
#> 
#> Terminal models:
#> 
#>                 info(sc)      logl  n k
#> spec 1 (1-cut): 2.774207 -47.71192 37 2
#> spec 2:         2.854352 -47.38913 37 3
#> spec 3:         2.860846 -47.50927 37 3
#> 
#> Retained regressors (final model):
#>   vconst   arch1 

##GETS modelling with non-default autocorrelation
##diagnostics settings:
simple <- gets(gum, ar.LjungB=list(pval=0.05))
#> 
#> GUM log-variance equation:
#> 
#>        reg.no. keep      coef std.error  t-stat p-value  
#> vconst       1    1 -0.623183  0.561349 -1.1102 0.29571  
#> arch1        2    0  0.075856  0.206463  0.3674 0.72181  
#> arch2        3    0 -0.125252  0.147240 -0.8507 0.41701  
#> arch3        4    0  0.076151  0.163485  0.4658 0.65243  
#> asym1        5    0 -0.178412  0.237220 -0.7521 0.47120  
#> vxreg1       6    0  0.064916  0.116349  0.5579 0.59049  
#> vxreg2       7    0 -0.190337  0.129783 -1.4666 0.17654  
#> vxreg3       8    0  0.142136  0.137520  1.0336 0.32831  
#> vxreg4       9    0 -0.224855  0.121049 -1.8576 0.09619 .
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Diagnostics:
#> 
#>                     Chi-sq df p-value
#> Ljung-Box AR(1)   0.050748  1 0.82177
#> Ljung-Box ARCH(4) 4.228739  4 0.37593
#> 
#> 8 path(s) to search
#> Searching: 
#> 1 
#> 2 
#> 3 
#> 4 
#> 5 
#> 6 
#> 7 
#> 8 
#> 
#>   Path 1: 2 4 6 5 8 9 7 
#>   Path 2: 3 4 6 5 9 7 8 
#>   Path 3: 4 6 5 3 9 7 8 
#>   Path 4: 5 6 4 3 9 7 8 
#>   Path 5: 6 4 5 3 9 7 8 
#>   Path 6: 7 6 5 4 3 9 8 
#>   Path 7: 8 5 4 6 3 9 7 
#>   Path 8: 9 6 4 3 5 7 8 
#> 
#> Terminal models:
#> 
#>                 info(sc)      logl  n k
#> spec 1 (1-cut): 2.682133 -47.81400 37 1
#> spec 2:         2.769014 -47.61585 37 2
#> spec 3:         2.774207 -47.71192 37 2
#> 
#> Retained regressors (final model):
#>   vconst 

##GETS modelling with very liberal (40%) significance level:
simple <- gets(gum, t.pval=0.4)
#> 
#> GUM log-variance equation:
#> 
#>        reg.no. keep      coef std.error  t-stat p-value  
#> vconst       1    1 -0.623183  0.561349 -1.1102 0.29571  
#> arch1        2    0  0.075856  0.206463  0.3674 0.72181  
#> arch2        3    0 -0.125252  0.147240 -0.8507 0.41701  
#> arch3        4    0  0.076151  0.163485  0.4658 0.65243  
#> asym1        5    0 -0.178412  0.237220 -0.7521 0.47120  
#> vxreg1       6    0  0.064916  0.116349  0.5579 0.59049  
#> vxreg2       7    0 -0.190337  0.129783 -1.4666 0.17654  
#> vxreg3       8    0  0.142136  0.137520  1.0336 0.32831  
#> vxreg4       9    0 -0.224855  0.121049 -1.8576 0.09619 .
#> ---
#> Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
#> 
#> Diagnostics:
#> 
#>                     Chi-sq df p-value
#> Ljung-Box AR(1)   0.050748  1 0.82177
#> Ljung-Box ARCH(4) 4.228739  4 0.37593
#> 
#> 5 path(s) to search
#> Searching: 
#> 1 
#> 2 
#> 3 
#> 4 
#> 5 
#> 
#>   Path 1: 2 4 6 5 
#>   Path 2: 3 4 6 5 
#>   Path 3: 4 6 5 
#>   Path 4: 5 6 4 
#>   Path 5: 6 4 5 
#> 
#> Terminal models:
#> 
#>                 info(sc)      logl  n k
#> spec 1 (1-cut): 2.975554 -47.82591 37 4
#> spec 2:         3.116885 -48.63508 37 5
#> spec 3:         3.075614 -47.87156 37 5
#> spec 4:         3.214387 -48.63341 37 6
#> 
#> Retained regressors (final model):
#>   vconst   vxreg2   vxreg3   vxreg4