desla: Desparsified Lasso inference for Time Series

Installation

CRAN

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

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 depository directly by running:

devtools::install_github("RobertAdamek/desla")

Load Package

After installation, the package can be loaded in the standard way:

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

The desla() function provides inference on parameters of the linear regression model of y on X, using the desparsified lasso as detailed in Adamek et al. (2022a). First, we specify the indices of variables for which confidence intervals are required via the argument H. The desla() function then simply takes the response y, the predictor matrix X and the set of indices H as input. Its output is an object of class desla, that can be used to conduct inference on the desired set of parameters.

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

The function summary() provides a quick way to view the main 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 slot bhat or the coef() function. Confidence intervals can be accessed via the output slot intervals or the confint() function. For optional arguments and other details, see the function documentation with the command ?desla.

The function HDLP()

The second key function of the package is the HDLP() function which implements the high-dimensional local projections detailed in Adamek et al. (2022b). As an example, consider the response of y to a shock in the fourth predictor variable, and imagine that:

• We classify the first three predictor variables as “slow moving” and enter the equation contemporaneously (ordered before the fourth variable);

• The 5th up to 10th variables are classified as “fast moving” and only enter with a lag (thus ordered after the fourth variable). Then the following lines of code obtain the impulse responses with two lags included, up to a maximum horizon of 5. By applying the plot function to the output of the HDLP function, the corresponding impulse response function 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 of Ramey & Zubairy (2018) with the optional state_variables argument. State variables can be created in two ways:

• A matrix with dummy variables, where each column indicates a 1 (or TRUE) 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 state of the corresponding observation. This is particularly useful in the case of multiple state variables (which can be combined in a data frame), as the function then automatically creates the states as interactions between them.

# Factor corresponding to s_dummies above
s_factor <- factor(c(rep("A", 50), rep("B", 50)), levels = c("A","B"))
# A second state variable
a_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 in HDLP(). In case of doubt, a user can consult the function create_state_dummies() - which is also used internally in HDLP() - to check if the states are created as desired.

We show it here for the first option. Two separate impulse response functions are obtained for the response of y to a shock in the fourth predictor: one for state A and one for state B.

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 function documentation with the command ?HDLP.

References

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

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

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