specs {specs}

SPECS

Description

This function estimates the Single-equation Penalized Error Correction Selector as described in Smeekes and Wijler (2020). The function takes a dependent variable y and a matrix of independent variables x as input, and transforms it to a conditional error correction model. This model is estimated by means of penalized regression, involving L1-penalty on individual coefficients and a potential L2-penalty on the coefficients of the lagged levels in the model, see Smeekes and Wijler (2020) for details.

Usage

specs(
  y,
  x,
  p = 1,
  deterministics = c("constant", "trend", "both", "none"),
  ADL = FALSE,
  weights = c("ridge", "ols", "none"),
  k_delta = 1,
  k_pi = 1,
  lambda_g = NULL,
  lambda_i = NULL,
  thresh = 1e-04,
  max_iter_delta = 1e+05,
  max_iter_pi = 1e+05,
  max_iter_gamma = 1e+05
)

Arguments

y

A vector containing the dependent variable in levels.

x

A matrix containing the independent variables in levels.

p

Integer indicating the desired number of lagged differences to include. Default is 1.

deterministics

A character object indicating which deterministic variables should be added ("none","constant","trend","both"). Default is "constant".

ADL

Logical object indicating whether an ADL model without error-correction term should be estimated. Default is FALSE.

weights

Choice of penalty weights. The weights can be automatically generated by ridge regression (default) or ols. Alternatively, a conformable vector of non-negative weights can be supplied or no weights can be applied.

k_delta

The power to which the weights for delta should be raised, if weights are set to "ridge" or "ols".

k_pi

The power to which the weights for pi should be raised, if weights are set to "ridge" or "ols".

lambda_g

An optional user-specified grid for the group penalty may be supplied. If left empty, a 10-dimensional grid containing 0 as the minimum value is generated.

lambda_i

An optional user-specified grid for the individual penalty may be supplied. If left empty, a 10-dimensional grid containing 0 as the minimum value is generated.

thresh

The treshold for convergence.

max_iter_delta

Maximum number of updates for delta. Default is 10^5.

max_iter_pi

Maximum number of updates for pi. Default is 10^5.

max_iter_gamma

Maximum number of updates for gamma. Default is 10^5.

Details

The function can generate an automated sequence of penalty parameters and offers the option to compute and include adaptive penalty weights. In addition, it is possible to estimate a penalized ADL model in differences by excluding the lagged levels from the model. For automated selection of an optimal penalty value, see the function specs_opt(...).

Value

D

A matrix containing the deterministic variables included in the model.

gammas

A matrix containing the estimated coefficients of the stochastic variables in the conditional error-correction model.

lambda_g

The grid of group penalties.

lambda_i

The grid of individual penalties.

Mv

A matrix containing the independent variables, after regressing out the deterministic components.

My_d

A vector containing the dependent variable, after regressing out the deterministic components.

theta

The estimated coefficients for the constant and trend. If a deterministic component is excluded, its coefficient is set to zero.

v

A matrix containing the independent variables (excluding deterministic components).

weights

The vector of penalty weights.

y_d

A vector containing the dependent variable, i.e. the differences of y.

Examples

#Estimate a model for unemployment and ten google trends

#Organize data
y <- Unempl_GT[,1]
index_GT <- sample(c(2:ncol(Unempl_GT)),10)
x <- Unempl_GT[,index_GT]

#Estimate a CECM with 1 lagged differences
my_specs <- specs(y,x,p=1)

#Estimate a CECM with 1 lagged differences and no group penalty
my_specs2 <- specs(y,x,p=1,lambda_g=0)

#Estimate an autoregressive distributed lag model with 2 lagged differences
my_specs3 <- specs(y,x,ADL=TRUE,p=2)