midas_sp {midasr}

Semi-parametric MIDAS regression

Description

Estimate semi-parametric MIDAS regression using non-linear least squares.

Usage

midas_sp(formula, data, bws, start, degree = 1, Ofunction = "optim", ...)

Arguments

formula

formula for restricted MIDAS regression or midas_r object. Formula must include fmls function

data

a named list containing data with mixed frequencies

bws

a bandwith specification. Note you need to supply logarithm value of the bandwith.

start

the starting values for optimisation. Must be a list with named elements.

degree

the degree of local polynomial. 0 corresponds to local-constant, 1 local-linear. For univariate models higher values can be provided.

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 arguments method="Nelder-Mead" and control=list(maxit=5000). Other supported functions are nls, optimx.

...

additional arguments supplied to optimisation function

Details

Given MIDAS regression:

y_t = \sum_{j=1}^p\alpha_jy_{t-j} +\sum_{i=0}^{k}\sum_{j=0}^{l_i}\beta_{j}^{(i)}x_{tm_i-j}^{(i)} + u_t,

estimate the parameters of the restriction

\beta_j^{(i)}=g^{(i)}(j,\lambda).

Such model is a generalisation of so called ADL-MIDAS regression. It is not required that all the coefficients should be restricted, i.e the function g^{(i)} might be an identity function. The regressors x_\tau^{(i)} must be of higher (or of the same) frequency as the dependent variable y_t.

Value

a midas_sp 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

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-Balevičius