midasr (version 0.5)

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(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 def

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 n

...

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_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

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 <- 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)))