# midas_nlpr: Non-linear parametric MIDAS regression In midasr: Mixed Data Sampling Regression

## Description

Estimate restricted MIDAS regression using non-linear least squares.

## Usage

 `1` ```midas_nlpr(formula, data, start, 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 `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 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 = ∑_{j=1}^pα_jy_{t-j} +∑_{i=0}^{k}∑_{j=0}^{l_i}β_{j}^{(i)}x_{tm_i-j}^{(i)} + u_t,

estimate the parameters of the restriction

β_j^{(i)}=g^{(i)}(j,λ).

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. Model with no restrictions is called U-MIDAS model. The regressors x_τ^{(i)} must be of higher (or of the same) frequency as the dependent variable y_t.

## 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 `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

midasr documentation built on Feb. 23, 2021, 5:11 p.m.