时序数据的周期模式发现算法的递推改进

Recursive Improvement of Periodic Pattern Algorithm of Time Series Data

从时序数据中识别和提取出周期成分对掌握事物的内在发展规律有着重要的现实意义。在谐波分析法的基础上,提出了一种具有纳新机制的时序数据周期模式的递推发现算法。该算法通过对谐波分析法的傅里叶系数作Taylor级数的展开,得到了一系列相关的幂函数多项式,在此基础上,基于矩阵数量乘法的规则,将这些多项式解耦为可递推的表达式,进而推导出一种重复计算量极少的递推算法。数值实验验证了算法的有效性和稳定性,而且该算法在计算成本和计算精度之间还具有良好的伸缩性。

To identify and extract the periodic components from time series data has important practical significance for the inherent rule of things. Based on harmonic analysis method,a periodic pattern recursive algorithm of time series data with renewal mechanism was proposed. A series of power function polynomial is obtained by the expansion in Taylor series of Fourier transform coefficients. On this basis,an simple data algorithm is deduced by polynomial decomposition method on the account of rules of matrix multiplication. The numerical simulation shows that the proposed algorithm is efficient and stable. This algorithm also has good scalability between computing cost and calculation accuracy.