midas_sp function

Semi-parametric MIDAS regression

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

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

Returns

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

Details

Given MIDAS regression:

estimate the parameters of the restriction

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 $y_t$.

Author(s)

Virmantas Kvedaras, Vaidotas Zemlys-Balevičius