Modified Nearest Neighbor Method for Multistep Ahead Time Series Forecasting

Abstract

Multistep ahead time series forecasting has become an important activity in various fields of science and technology due to its usefulness in future events management. Nearest neighbor search is a pattern matching algorithm for forecasting, and the accuracy of the method considerably depends on the similarity of the pattern found in the database with the reference pattern. Original time series is embedded into optimal dimension. The optimal dimension is determined by using autocorrelation function plot. The last vector in the embedded matrix is taken as the reference vector and all the previous vectors as candidate vectors. In nearest neighbor algorithm, the reference vector is matched with all the candidate vectors in terms of Euclidean distance and the best matched pattern is used for forecasting. In this paper, we have proposed a hybrid distance measure to improve the search of the nearest neighbor. The proposed method is based on cross-correlation and Euclidean distance. The candidate patterns are shortlisted by using cross-correlation and then Euclidean distance is used to select the best matched pattern. Moreover, in multistep ahead forecasting, standard nearest neighbor method introduces a bias in the search which results in higher forecasting errors. We have modified the search methodology to remove the bias by ignoring the latest forecasted value during the search of the nearest neighbor in the subsequent iteration. The proposed algorithm is evaluated on two benchmark time series as well as two real life time series.