midas.ardl {midasml}

MIDAS regression

Description

Fits MIDAS regression model with single high-frequency covariate. Options include linear-in-parameters polynomials (e.g. Legendre) or non-linear polynomials (e.g. exponential Almon). Nonlinear polynomial optimization routines are equipped with analytical gradients, which allows fast and accurate optimization.

Usage

midas.ardl(y, x, z = NULL, loss_choice = c("mse","logit"), 
           poly_choice = c("legendre","expalmon","beta"), 
           poly_spec = 0, legendre_degree = 3, nbtrials = 500)

Arguments

y

response variable. Continuous for loss_choice = "mse", binary for loss_choice = "logit".

x

high-frequency covariate lags.

z

other lower-frequency covariate(s) or AR lags (both can be supplied in an appended matrix). Either must be supplied.

loss_choice

which loss function to fit: loss_choice="mse" fits least squares MIDAS regression, loss_choice="logit" fits logit MIDAS regression.

poly_choice

which MIDAS lag polynomial function to use: poly_choice="expalmon" - exponential Almon polynomials, poly_choice="beta" - Beta density function (need to set poly_spec), poly_choice="legendre" - legendre polynomials (need to set legendre_degree). Default is set to poly_choice="expalmon".

poly_spec

which Beta density function specification to apply (applicable only for poly_choice="beta"). poly_spec = 0 - all three parameters are fitted, poly_spec = 1 (\theta_2,\theta_3) are fitted, poly_spec = 2 (\theta_1,\theta_2) are fitted, poly_spec = 3 (\theta_2) is fitted. Default is set to poly_spec = 0.

legendre_degree

the degree of legendre polynomials (applicable only for legendre="beta"). Default is set to 3.

nbtrials

number of initial values tried in multistart optimization. Default is set to poly_spec = 500.

Details

Several polynomial functional forms are available (poly_choice):

- beta: Beta polynomial
- expalmon: exponential Almon polynomial
- legendre: Legendre polynomials.

The ARDL-MIDAS model is:
y_t = μ + Σ_p ρ_p y_t-p + β Σ_j ω_j(θ)x_t-1
where μ, β, θ and ρ_p are model parameters, p is the number of low-frequency lags and ω is the weight function.

Value

midas.ardl object.

Author(s)

Jonas Striaukas

Examples

set.seed(1)
x = matrix(rnorm(100 * 20), 100, 20)
z = rnorm(100)
y = rnorm(100)
midas.ardl(y = y, x = x, z = z)