Estimate semi-parametric MIDAS regression using non-linear least squares.
midas_sp(formula, data, bws, start, degree = 1, Ofunction = "optim", ...)a midas_sp object which is the list with the following elements:
the estimates of parameters of restrictions
the estimates of MIDAS coefficients of MIDAS regression
model data
unrestricted regression estimated using midas_u
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.
optimisation function for non-linear least squares problem solved in restricted MIDAS regression
the function which evaluates the right-hand side of the MIDAS regression
the function which generates the MIDAS coefficients of MIDAS regression
the output of optimisation procedure
the list containing the name of optimisation function together with arguments for optimisation function
the starting values used in optimisation
the starting values as a list
the call to the function
terms object
gradient of NLS objective function
hessian of NLS objective function
gradient function of MIDAS weight functions
the environment in which data is placed
the number of effective observations
the convergence message
the fitted values of MIDAS regression
the residuals of MIDAS regression
formula for restricted MIDAS regression or midas_r object. Formula must include fmls function
a named list containing data with mixed frequencies
a bandwith specification. Note you need to supply logarithm value of the bandwith.
the starting values for optimisation. Must be a list with named elements.
the degree of local polynomial. 0 corresponds to local-constant, 1 local-linear. For univariate models higher values can be provided.
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 optimx with arguments
method="Nelder-Mead" and control=list(maxit=5000). Other supported functions are nls, optimx.
additional arguments supplied to optimisation function
Virmantas Kvedaras, Vaidotas Zemlys-Balevičius
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 \(y_t\).