# imidas_r: Restricted MIDAS regression with I(1) regressors In midasr: Mixed Data Sampling Regression

## Description

Estimate restricted MIDAS regression using non-linear least squares, when the regressor is I(1)

## Usage

 1 2 3 4 5 6 7 8 imidas_r( formula, data, start, Ofunction = "optim", weight_gradients = NULL, ... ) 

## Arguments

 formula formula for restricted MIDAS regression. Formula must include fmls function data a named list containing data with mixed frequencies start the starting values for optimisation. Must be a list with named elements. Ofunction the list with information which R function to use for optimisation. The list must have element named Ofunction which contains character string of chosen R function. Other elements of the list are the arguments passed to this function. The default optimisation function is optim with argument method="BFGS". Other supported functions are nls weight_gradients a named list containing gradient functions of weights. The weight gradient function must return the matrix with dimensions d_k \times q, where d_k and q are the number of coefficients in unrestricted and restricted regressions correspondingly. The names of the list should coincide with the names of weights used in formula. The default value is NULL, which means that the numeric approximation of weight function gradient is calculated. If the argument is not NULL, but the name of the weight used in formula is not present, it is assumed that there exists an R function which has the name of the weight function appended with .gradient. ... additional arguments supplied to optimisation function

## Details

Given MIDAS regression:

y_t=∑_{j=0}^k∑_{i=0}^{m-1}θ_{jm+i} x_{(t-j)m-i}+\mathbf{z_t}β+u_t

estimate the parameters of the restriction

θ_h=g(h,λ),

where h=0,...,(k+1)m, together with coefficients β corresponding to additional low frequency regressors.

It is assumed that x is a I(1) process, hence the special transformation is made. After the transformation midas_r is used for estimation.

MIDAS regression involves times series with different frequencies.

The restriction function must return the restricted coefficients of the MIDAS regression.

## Value

a midas_r object which is the list with the following elements:

 coefficients the estimates of parameters of restrictions midas_coefficients the estimates of MIDAS coefficients of MIDAS regression model model data unrestricted unrestricted regression estimated using midas_u term_info the named list. Each element is a list with the information about the term, such as its frequency, function for weights, gradient function of weights, etc. fn0 optimisation function for non-linear least squares problem solved in restricted MIDAS regression rhs the function which evaluates the right-hand side of the MIDAS regression gen_midas_coef the function which generates the MIDAS coefficients of MIDAS regression opt the output of optimisation procedure argmap_opt the list containing the name of optimisation function together with arguments for optimisation function start_opt the starting values used in optimisation start_list the starting values as a list call the call to the function terms terms object gradient gradient of NLS objective function hessian hessian of NLS objective function gradD gradient function of MIDAS weight functions Zenv the environment in which data is placed use_gradient TRUE if user supplied gradient is used, FALSE otherwise nobs the number of effective observations convergence the convergence message fitted.values the fitted values of MIDAS regression residuals the residuals of MIDAS regression

## Author(s)

Virmantas Kvedaras, Vaidotas Zemlys

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 theta.h0 <- function(p, dk) { i <- (1:dk-1)/100 pol <- p*i + p*i^2 (p + p*i)*exp(pol) } theta0 <- theta.h0(c(-0.1,10,-10,-10),4*12) xx <- ts(cumsum(rnorm(600*12)), frequency = 12) ##Simulate the response variable y <- midas_sim(500, xx, theta0) x <- window(xx, start=start(y)) imr <- imidas_r(y~fmls(x,4*12-1,12,theta.h0)-1,start=list(x=c(-0.1,10,-10,-10)))