midasr (version 0.2)

midas_r: Restricted MIDAS regression

Description

Estimate restricted MIDAS regression using non-linear least squares.

Usage

midas_r(x, ...)
## S3 method for class 'default':
midas_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 appended with .gradi

...

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 MIDAS weights 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
• call
  the call to the function
• terms
  terms object
• gradient
  gradient of NLS objective function
• hessian
  hessian of NLS objective function
• Zenv
  the environment in which data is placed
• user.gradient
  the value of supplied argument user.gradient

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.

MIDAS regression involves times series with different frequencies.

MIDAS-AR* (a model with a common factor, see (Clements and Galvao, 2008)) can be estimated by specifying additional argument, see an example.

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

References

Clements, M. and Galvao, A., Macroeconomic Forecasting With Mixed-Frequency Data: Forecasting Output Growth in the United States, Journal of Business and Economic Statistics, Vol.26 (No.4), (2008) 546-554

See Also

midas_r.midas_r

Examples

##The parameter function
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)
}

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

##Plot the coefficients
plot(theta0)

##Generate the predictor variable
x <- simplearma.sim(list(ar=0.6),1500*12,1,12)

##Simulate the response variable
y <- midas.sim(500,theta0,x,1)

##Remove unnecessary history of x
x <- window(x,start=start(y))

##Fit restricted model
mr <- midas_r(y~fmls(x,4*12-1,12,theta.h0)-1,
              list(y=y,x=x),
              start=list(x=c(-0.1,10,-10,-10)))

##Include intercept and trend in regression
mr.it <- midas_r(y~fmls(x,4*12-1,12,theta.h0)+trend,
                 list(data.frame(y=y,trend=1:500),x=x),
                 start=list(x=c(-0.1,10,-10,-10)))

data("USrealgdp")
data("USunempr")

y.ar <- diff(log(USrealgdp))
xx <- window(diff(USunempr), start = 1949)
trend <- 1:length(y.ar)

##Fit AR(1) model
mr.ar <- midas_r(y.ar ~ trend + mls(y.ar, 1, 1) +
                 fmls(xx, 11, 12, nealmon),
                 start = list(xx = rep(0, 3)))

##First order MIDAS-AR* restricted model
mr.arstar <-  midas_r(y.ar ~ trend + mls(y.ar, 1, 1, "*")
                     + fmls(xx, 11, 12, nealmon),
                     start = list(xx = rep(0, 3)))