中文摘要：

时间序列的频域分析并不如时域分析应用广泛,但其弥补了时域分析的不足：能够把时间序列分解为具有不同振幅,相位和频率的周期分量的叠加,找出原序列中隐含的主要周期分量,并从周期波动的角度对序列进行解释.针对非平稳时间序列进行研究,利用B样条函数为基底并引入惩罚项,提取序列中的趋势项之后,再根据样本谱密度理论得到时序数据中的潜周期,最终将原始时间序列分解为趋势项,周期项和随机扰动项.数据模拟部分验证了通过B样条估计并提取的趋势项具有较高的精确度,并会对周期项的提取产生积极的影响.实际数据部分使用了黄金价格的月度数据,得到了长,中,短三个波动周期这一有意义的结论,验证了本方法的可行性和有效性.

英文摘要：

Spectral analysis of time series can decompose the series into several cycles with different amplitude,phase and frequency.This paper mainly studies non-stationary time series.The implicit cycles in non-stationary time series are obtained by the theory of spectral analysis,after subtracting the trend using penalized B-spline functions.This way the initial time series data is decomposed into trend term,seasonal term and random term.Simulations prove that the extracted trend term using B-spline function is more accurate than other methods,and therefore has positive effect on the extract of seasonal terms.Also we use the series of monthly gold price,and end up with an interesting result which shows three different cycles,verifying the feasibility and effectiveness of the proposed method.