esemifar {esemifar}

esemifar: A package for data-driven nonparametric estimation of the trend and its derivatives in equidistant time series.

Description

The esemifar package provides different applicable functions for the estimation of the trend or its derivatives in equidistant time series. The main functions include an automated bandwidth selection method for time series with long-memory errors.

An alternative method to create an ESEMIFAR estimation object stitched together from a nonparametric and a parametric part.

Usage

esemifar(nonpar_model, par_model)

Arguments

nonpar_model

an estimation object returned by gsmooth.

par_model

an estimation object returned by fracdiff fitted to the residuals of nonpar_model.

Details

The main function tsmoothlm already returns a fully estimated ESEMIFAR model. In some instances, alternative specifications of the nonparametric and parametric model parts are needed, for which tsmoothlm with its automated estimation algorithm does not provide sufficient flexibility. Therefore, this function allows to stitch together a nonparametric model part returned by gsmooth and a FARIMA part for the residuals obtained via fracdiff. The resulting object can then be used for forecasting.

Value

The function returns a list of class "esemifar" with elements nonpar_model and par_model.

Functions (version 1.0.0)

The esemifar functions are either meant for calculating nonparametric estimates of the trend of a time series or its derivatives.

dsmoothlm is a function that calculates the derivatives of the trend after obtaining the optimal bandwidth by an iterative plug-in algorithm.

tsmoothlm is the central function of the package. It allows the user to conduct a local polynomial regression of the trend based on an optimal bandwidth that is obtained by an iterative plug-in algorithm. Inflation rate (and other factors) can be manually and individually adjusted as arguments in the function (see also: tsmoothlm).

critMatlm is a quick tool for the calculation of information criteria for FARIMA(p,d,q) models with different order combinations p and q. The function returns a matrix with the obtained values of the selected criterion for the different combinations of p and q (see also: critMatlm).

Datasets

The package includes two datasets: airLDN (see also: airLDN) with daily observations of individual air pollutants from 2014 to 2020 and gdpG7 (see also: gdpG7) that has data concerning the quarterly G7 GDP between Q1 1962 and Q4 2019.

License

The package is distributed under the General Public License v3 ([GPL-3](https://tldrlegal.com/license/gnu-general-public-license-v3-(gpl-3))).

Author(s)

• Yuanhua Feng (Department of Economics, Paderborn University),
  Author of the Algorithms
  Website: https://wiwi.uni-paderborn.de/en/dep4/feng/

• Sebastian Letmathe,
  Author (and Original Package Creator and Maintainer)

• Dominik Schulz,
  Author and Current Package Creator and Maintainer

• Dominik Schulz (Scientific Employee) (Department of Economics, Paderborn University),
  Author

References

Beran, J. and Y. Feng (2002a). Iterative plug-in algorithms for SEMIFAR models - definition, convergence, and asymptotic properties. Journal of Computational and Graphical Statistics 11(3), 690-713.

Beran, J. and Feng, Y. (2002b). Local polynomial fitting with long-memory, short-memory and antipersistent errors. Annals of the Institute of Statistical Mathematics, 54(2), 291-311.

Beran, J. and Feng, Y. (2002c). SEMIFAR models - a semiparametric approach to modelling trends, longrange dependence and nonstationarity. Computational Statistics & Data Analysis 40(2), 393-419.

Letmathe, S., Beran, J. and Feng, Y. (2023). An extended exponential SEMIFAR model with application in R. Communications in Statistics - Theory and Methods: 1-13.

Examples

lgdp <- log(esemifar::gdpG7$gdp)
nonpar <- gsmooth(lgdp, b = 0.15)
res <- nonpar$res
par <- fracdiff::fracdiff(res, nar = 1, nma = 1)
model <- esemifar(nonpar_model = nonpar, par_model = par)
model