Open AccessSpline based Hermite quasi-interpolation for univariate time series
Author(s) -
Antonella Falini,
Francesca Mazzia,
Cristiano Tamborrino
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series s
Language(s) - English
Resource type - Journals
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2022039
Subject(s) - univariate , spline interpolation , hermite spline , cluster analysis , smoothing spline , algorithm , hermite polynomials , computer science , cubic hermite spline , series (stratigraphy) , mathematics , spline (mechanical) , hermite interpolation , interpolation (computer graphics) , artificial intelligence , statistics , bilinear interpolation , mathematical analysis , engineering , multivariate statistics , motion (physics) , paleontology , structural engineering , biology
In this article the authors introduce a spline Hermite quasi-interpolation technique for the preprocessing operations of imputation and smoothing of univariate time series. The constructed model is then applied for the forecast and for the anomaly detection. In particular, for the latter case, algorithms based on the combination of quasi-interpolation, dynamic copulas and clustering have been proposed. Some numerical results are included showing the effectiveness of the presented techniques.