00 Install fdslrm R package.ipynb

Kernel: R

Authors: Andrej Gajdoš, Jozef Hanč, Martina Hančová
Faculty of Science, P. J. Šafárik University in Košice, Slovakia
email: [email protected]

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Installation of fdslrm package

This installation has to be done once before the first run of any R-based Jupyter notebook.

fdslrm: Time series analysis and forecasting using LMM

• Purpose: The fdslrm package is an R package for modeling and prediction of time series using linear mixed models.

• Version: 0.1.0

• Depends: kableExtra, IRdisplay, MASS, Matrix, car, nlme, stats, forecast, fpp2, matrixcalc, sommer, gnm, pracma, CVXR

• Published: 2019

• Maintainer: Andrej Gajdoš

• URL: https://github.com/gajdosandrej/fdslrm

$1^{st}$ step - setting path to a repository

options(repos = 'http://cran.rstudio.com/')

$2^{nd}$ step - installation of devtools package

install.packages('devtools')

$3^{rd}$ step - installation of fdslrm package from GitHub

devtools::install_github("gajdosandrej/fdslrm")

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References

This notebook belongs to suplementary materials of the paper submitted to Statistical Papers and available at https://arxiv.org/abs/1905.07771.

• Hančová, M., Vozáriková, G., Gajdoš, A., Hanč, J. (2019). Estimating variance components in time series linear regression models using empirical BLUPs and convex optimization, https://arxiv.org/, 2019.

Abstract of the paper

We propose a two-stage estimation method of variance components in time series models known as FDSLRMs, whose observations can be described by a linear mixed model (LMM). We based estimating variances, fundamental quantities in a time series forecasting approach called kriging, on the empirical (plug-in) best linear unbiased predictions of unobservable random components in FDSLRM.

The method, providing invariant non-negative quadratic estimators, can be used for any absolutely continuous probability distribution of time series data. As a result of applying the convex optimization and the LMM methodology, we resolved two problems $-$ theoretical existence and equivalence between least squares estimators, non-negative (M)DOOLSE, and maximum likelihood estimators, (RE)MLE, as possible starting points of our method and a practical lack of computational implementation for FDSLRM. As for computing (RE)MLE in the case of $n$ observed time series values, we also discovered a new algorithm of order $\mathcal{O}(n)$, which at the default precision is $10^7$ times more accurate and $n^2$ times faster than the best current Python(or R)-based computational packages, namely CVXPY, CVXR, nlme, sommer and mixed.

We illustrate our results on three real data sets $-$ electricity consumption, tourism and cyber security $-$ which are easily available, reproducible, sharable and modifiable in the form of interactive Jupyter notebooks.

• Gajdoš A., Hanč J., and Hančová M. (2019). fdslrm package. P.J. Šafárik University in Košice, Slovakia. https://github.com/fdslrm/R-package.