Movatterモバイル変換

desla:Desparsified Lasso inference for Time Series

Installation

CRAN

The easiest way to install the package from CRAN is with thecommand:

install.packages("desla")

GitHub

Working versions of updates to the package are available on GitHub.These can be installed easily with the devtools package:

install.packages("devtools")

You can then install the desla package from the GitHub depositorydirectly by running:

devtools::install_github("RobertAdamek/desla")

Load Package

After installation, the package can be loaded in the standardway:

library(desla)

Usage

The following toy example demonstrates how to use the functions.Let’s first simulate some data:

set.seed(312)X<-matrix(rnorm(100*100),nrow=100)y<-X[,1:4]%*%c(1,2,3,4)+rnorm(100)

The function`desla`

Thedesla() function provides inference on parameters ofthe linear regression model ofy onX, usingthe desparsified lasso as detailed in Adamek et al. (2022a). First, wespecify the indices of variables for which confidence intervals arerequired via the argumentH. Thedesla()function then simply takes the responsey, the predictormatrixX and the set of indicesH as input.Its output is an object of classdesla, that can be used toconduct inference on the desired set of parameters.

H<-1:3d<-desla(X=X,y=y,H=H)

The functionsummary() provides a quick way to view themain results:

summary(d)#>#> Call:#> desla(X = X, y = y, H = H)#>#>#> Coefficients:#>    Estimate Std. Error z value Pr(>|z|)#> X1   1.0788     0.1304   8.272   <2e-16 ***#> X2   1.9753     0.1386  14.247   <2e-16 ***#> X3   2.9455     0.1320  22.317   <2e-16 ***#> ---#> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#>#> Joint test of significance:#>#> Joint test statistic  6.232e+02#> p-value              9.436e-135#>#> Selected lambdas:#>#> Initial regression 0.06688#> X1                 0.28620#> X2                 0.28734#> X3                 0.28570#>#> Selected variables:#>#> Initial regression X1, X2, X3, X4#> X1                            X91#> X2                           none#> X3                           none

The point estimates are accessible via the output slotbhat or thecoef() function. Confidenceintervals can be accessed via the output slotintervals ortheconfint() function. For optional arguments and otherdetails, see the function documentation with the command?desla.

The function`HDLP()`

The second key function of the package is theHDLP()function which implements the high-dimensional local projectionsdetailed in Adamek et al. (2022b). As an example, consider the responseofy to a shock in the fourth predictor variable, andimagine that:

We classify the first three predictor variables as “slow moving”and enter the equation contemporaneously (ordered before the fourthvariable);
The 5th up to 10th variables are classified as “fast moving” andonly enter with a lag (thus ordered after the fourth variable). Then thefollowing lines of code obtain the impulse responses with two lagsincluded, up to a maximum horizon of 5. By applying the plot function tothe output of the HDLP function, the corresponding impulse responsefunction can be visualized.

h<-HDLP(x=X[,4],y=y,q=X[,1:3],r = X[,6:10],hmax=5,lags=2)plot(h)

The function also implements the state-based local projections ofRamey & Zubairy (2018) with the optionalstate_variables argument. State variables can be created intwo ways:

A matrix with dummy variables, where each column indicates a 1 (orTRUE) for the observations belongig to that state:

s_dummies<-matrix(c(rep(1,50),rep(0,100),rep(1,50)),ncol=2,dimnames =list(NULL,c("A","B")))

A categorical variable (factor) where each entry indicates the stateof the corresponding observation. This is particularly useful in thecase of multiple state variables (which can be combined in a dataframe), as the function then automatically creates the states asinteractions between them.

# Factor corresponding to s_dummies aboves_factor<-factor(c(rep("A",50),rep("B",50)),levels =c("A","B"))# A second state variablea_second_factor<-factor(c(rep("C",25),rep("D",50),rep("C",25)),levels =c("C","D"))s_twofactors<-data.frame(S1 = s_factor,S2 = a_second_factor)

Both options work with the same syntax inHDLP(). Incase of doubt, a user can consult the functioncreate_state_dummies() - which is also used internally inHDLP() - to check if the states are created as desired.

We show it here for the first option. Two separate impulse responsefunctions are obtained for the response ofy to a shock inthe fourth predictor: one for stateA and one for stateB.

h_s<-HDLP(x=X[,4],y=y,q=X[,1:3],r=X[,6:10],state_variables=s_dummies,hmax=5,lags=2)plot(h_s)

For other optional arguments and details, see the functiondocumentation with the command?HDLP.

References

Adamek, R., S. Smeekes, and I. Wilms (2022a). Lasso inference forhigh-dimensional time series.Journal of Econometrics,Forthcoming.

Adamek, R., S. Smeekes, and I. Wilms (2022b). Local Projectioninference in High Dimensions. arXiv e-print 2209.03218.

Ramey, V. A. and S. Zubairy (2018). Government spending multipliersin good times and in bad: evidence from US historical data.Journalof Political Economy 126, 850–901.

[8]ページ先頭