Spline based Hermite quasi-interpolation for univariate time series

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.