English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We propose a two-stage estimation method of variance components in timeseries models known as FDSLRMs, whose observations can be described by a linearmixed model (LMM). We based estimating variances, fundamental quantities in atime 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 beused for any absolutely continuous probability distribution of time seriesdata. As a result of applying the convex optimization and the LMM methodology,we resolved two problems $-$ theoretical existence and equivalence betweenleast squares estimators, non-negative (M)DOOLSE, and maximum likelihoodestimators, (RE)MLE, as possible starting points of our method and a practicallack of computational implementation for FDSLRM. As for computing (RE)MLE inthe case of $ n $ observed time series values, we also discovered a newalgorithm 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(orR)-based computational packages, namely CVXPY, CVXR, nlme, sommer and mixed.  We illustrate our results on three real data sets $-$ electricityconsumption, tourism and cyber security $-$ which are easily available,reproducible, sharable and modifiable in the form of interactive Jupyternotebooks.

Estimating variances in time series linear regression models using empirical BLUPs and convex optimization