多周期时序数据的傅氏级数拟合算法

摘要

一般地说，时序数据通常是由趋势项、随机项及季节周期项三种成分组成的。通过对已有的时序数据进行分析与建模，便可以找出事物所蕴含的变化规律。针对多周期时序数据，设计实现了一种高精度的数据拟合算法。该算法首先对被拟合时序数据的趋势成分进行消除，然后应用自相关函数理论从剩余成分中析出多个两两互质的基本周期，最后基于最小二乘原理，用多组傅氏级数对多周期时序数据进行了拟合。实际应用验证了算法的有效性及先进性。%Generally speaking, time-series data can be divided into three ingredients such as trend, random and season. Analyzing and modeling through the available time-series data, change law can find things contained. A kind of high precision data fitting method was designed for multiple periodic time-series data. Firstly, the algorithm eliminated random component of fitted time-series data. Secondly, several co-primed basic cycles were analyzed by the application of the theory of autocorrelation function. Finally, multiple periodic time-series data was fitting by using multiple sets of Fourier series based on the least squares principle. Practical application proved the effectiveness and progressiveness of the algorithm.