函数型时间序列的自适应分类预测方法及其在高频数据中的应用

Adaptive Forecasting after Classification for Functional Time Series with Application to High-Frequency Data

实时记录的高频数据呈现出显著的连续函数特征,无穷维等复杂本征结构使得传统分类和预测方法凸现弊端。针对函数型时间序列的波动模式识别和实时动态预测,本文提出自适应分类基础上的混合期望预测方法,并给出具体算法流程。(1)基于无核心信息损失的空间映射重构客观赋权的加权主成分距离,并以此量化函数之间的疏密程度进行初始类别划分;(2)综合检验类别函数之间均值和特征展开空间的显著性差异,提出潜在类别数目的确定准则以及对初始分类结果进行迭代更新的优化算法;(3)基于收敛的优化再分类结果建立函数类别归属的判别准则;(4)对于部分观测的新函数,分别计算其类属的后验概率以及其在每一子类别的预测值,并以类属概率为权重加总新函数在所有类别的预测值,构建日内信息迭代更新的函数型混合预测模型。基于多种情形的数值模拟和高频的上证综指预测分析发现,函数型时间序列的自适应分类预测不仅可以有效识别日内波动的类别模式,而且能够显著提升预测准确率,并且其相对优势保持稳健。

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,traditional 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 objectively 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 determining 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 functional 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 fuctuations,but also significantly improving the forecasting accuracy with robust comparative advantage.