Adaptive Forecasting after Classification for Functional Time Series with Application to High-Frequency Data
The high-frequency data recorded in real time demonstrate obvious character of continuous functions.Owing to the intrinsically complex characteristics such as infinite dimensional structure,tra-ditional classification and forecasting methods are limited in approaching functional data.Motivated by the need to identify distinct patterns and real-time dynamical forecasting of functional time series,in this study we propose a functional mixture forecasting method combining adaptive classification with functional forecasting,and provide the implementation algorithm in detail.(1)We reconstruct an ob-jectively weighted principal component distance based on subspace projected without core information loss.Then the initial clustering analysis is conducted by employing the weighted principal component distance to measure the dissimilarity between functions.(2)By comprehensively testing the significance of differences between the cluster mean functions and eigenfunctions,we propose the criteria for deter-mining the number of potential clusters and the iterative updating algorithm for optimizing the initial classification results.(3)We establish the discriminant function upon the optimal results of converged reclassification.(4)For a new and partly observed function,compute its posterior probability associated with each cluster and predict its future trajectory conditioning on each of the clusters.Then the func-tional mixture forecasting model is constructed via probabilistic weighting the sub-cluster forecasting values using posterior probabilities.Multiple simulation comparisons and empirical results of forecasting the high-frequency SSE indicate that,the proposed method not only assist in effectively indentifying patterns of intraday fluctuations,but also significantly improving the forecasting accuracy with robust comparative advantage.
functional time seriesadaptive classificationmixture predictioniterative updatinghigh-frequency data
万方数据
维普
