Cuckoo search-designated fractal interpolation functions with winner combination for estimating missing values in time series

Reliable data have always played a vital role in time series analysis and research. Nevertheless, missing data, which can bias the original properties of the time series if the pattern of missed data is systematic, is also a very common phenomenon in observed processes. Thus, how to address missing values is a very important challenge, especially in the upcoming big data era. This paper proposes the cuckoo search-designated fractal interpolation functions (CS-DFIFs) method and the CS-DFIFs-winners combining (CS-DFIFs-WC) method for estimating missing values. The former method skillfully transforms Fractal Interpolation Functions (FIFs) to make it possible to calculate a specified point's missing value, which is difficult to obtain with the traditional approach. Then, to optimize the parameters that transforming process generates, the cuckoo search algorithm (CS) and DFIFs are synthesized into a novel model, CS-DFIFs. Considering classical interpolation methods, such as Linear, Cubic Spline and Piecewise Cubic Hermite Interpolation Polynomial (PCHIP), having some born advantages, the inspiration of winners combining is sparked. CS algorithm is used to obtain the best weights of winners in this combined model, CS-DFIFs-WC. Two databases, electricity demands and prices, are chosen to be the numerical testing object at 7 missing levels in this paper. The results show that CS-DFIFs-WC overcomes the deficiency of FIFs that cannot calculate a specified point's missing value, and outperforms benchmarks at almost every level by four criteria.