midasr (version 0.2)

imidas_r: Restricted MIDAS regression with I(1) regressors

Description

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

Usage

imidas_r(x, ...)
## S3 method for class 'default':
imidas_r(x, data, start, Ofunction = "optim",
  user.gradient = FALSE, ...)

Arguments

x

either formula for restricted MIDAS regression or midas_r object. 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.

user.gradient

the default value is FALSE, which means that the numeric approximation of weight function gradient is calculated. If TRUE it is assumed that the R function for weight function gradient has the name of the weight function

...

additional arguments supplied to optimisation function

Value

• a midas_r object which is the list with the following elements:
• coefficients
  the estimates of parameters of restrictions
• midas.coefficientas
  the estimates of restricted coefficients of MIDAS regression
• model
  model data
• weights
  the restriction function(s) used in estimation.
• unrestricted
  unrestricted regression estimated using midas_u
• param.map
  parameter map for optimisation function
• 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
• allcoef
  the function which evaluates the restricted 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

Details

Given MIDAS regression:

$$y_t=\sum_{j=0}^k\sum_{i=0}^{m-1}\theta_{jm+i} x_{(t-j)m-i}+\mathbf{z_t}\beta+u_t$$

estimate the parameters of the restriction

$$\theta_h=g(h,\lambda),$$ where $h=0,...,(k+1)m$, together with coefficients $\beta$ 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.

See Also

midas_r.midas_r

Examples

theta.h0 <- function(p, dk) {
  i <- (1:dk-1)/100
  pol <- p[3]*i + p[4]*i^2
 (p[1] + p[2]*i)*exp(pol)
}

theta0 <- theta.h0(c(-0.1,10,-10,-10),4*12)

xx <- simplearma.sim(list(ar=1),1500*12,1,12)
y <- midas.sim(500,theta0,xx,1)
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)))