Vector and recurrent singular spectrum analysis: which is better at forecasting?

Singular spectrum analysis (SSA) is an increasingly popular and widely adopted filtering and forecasting technique which is currently exploited in a variety of fields. Given its increasing application and superior performance in comparison to other methods, it is pertinent to study and distinguish between the two forecasting variations of SSA. These are referred to as Vector SSA (SSA-V) and Recurrent SSA (SSA-R). The general notion is that SSA-V is more robust and provides better forecasts than SSA-R. This is especially true when faced with time series which are non-stationary and asymmetric, or affected by unit root problems, outliers or structural breaks. However, currently there exists no empirical evidence for proving the above notions or suggesting that SSA-V is better than SSA-R. In this paper, we evaluate out-of-sample forecasting capabilities of the optimised SSA-V and SSA-R forecasting algorithms via a simulation study and an application to 100 real data sets with varying structures, to provide a statistically reliable answer to the question of which SSA algorithm is best for forecasting at both short and long run horizons based on several important criteria.     

Common singular spectrum analysis of several time series

Singular spectrum analysis (SSA) is a non-parametric time series modelling technique where an observed time series is unfolded into the column vectors of a Hankel structured matrix, known as a trajectory matrix. For noise-free signals the column vectors of the trajectory matrix lie on a single R-flat. Singular value decomposition (SVD) can be used to find the orthonormal base vectors of the linear subspace parallel to this R-flat. SSA can essentially handle functions that are governed by a linear recurrent formula (LRF) and include the broad class of functions that was proposed by Buchstaber [1994. Time series analysis and Grassmannians. Amer. Math. Soc. Transl. 162 (2), 1–17]. SSA is useful to model time series with complex cyclical patterns that increase over time.Various methods have been studied to extend SSA for application to several time series, see Golyandina et al. [2003. Variants of the Caterpillar SSA-method for analysis of multidimensional time series (in Russian) hhttp://www.gistatgroup.com/cat/i]. Prior to that Von Storch and Zwiers (1999) and Allen and Robertson (1996) (see Ghil et al. [2002. Advanced spectral methods for climatic time series. Rev. Geophys. 40 (1), 3.1–3.41]) used multi-channel SSA (M-SSA), to apply SSA to “grand” block matrices. Our approach is different from all of these by using the common principal components approaches introduced by Flury [1988. Common Principal Components and Related Multivariate Models. Wiley, New York]. In this paper SSA is extended to several time series which are similar in some respects, like cointegrated, i.e. sharing a common R-flat. By using the common principal component (CPC) approach of Flury [1988. Common Principal Components and Related Multivariate Models. Wiley, New York] the SSA method is extended to common singular spectrum analysis (CSSA) where common features of several time series can be studied. CSSA decomposes the different original time series into the sum of a common small number of components which are related to common trend and oscillatory components and noise. The determination of the most likely dimension of the supporting linear subspace is studied using a heuristic approach and a hierarchical selection procedure.     

直接数字频率合成器中的相位噪声分析

相位噪声和杂散性能是制约直接数字频率合成器（ＤＤＳ）用于高稳定频率源的关键指标。文中给出了一种全新思维,定量分析了ＤＤＳ中由相位截断引起的杂散谱及由相位截断、ＲＯＭ存储器有限字长和ＤＡＣ性能对其相位噪声性能的影响。     

基于应力强度干涉模型的疲劳损伤研究

基于Miner法则,分析了工程上常用的阶梯谱级数对疲劳寿命精度的影响．建立了变换的JS-N曲线与阶梯谱拟合曲线的应力强度干涉数学模型,采用参数求解的数值解析法得到参数,并推导出了疲劳损伤的积分公式．对铁路货车转向架侧架运行36万公里（一个段修期）内分阶段的多次载荷谱测试数据进行分析,得出随着各阶段阶梯谱离散级数的增大,损伤成收敛趋势,寿命预测精度高．采用本文的分析方法,建立了侧架一个段修期的载荷谱概率模型,预测了侧架的寿命及其可靠性．     

音乐声波对人体作用机理探讨——兼谈音乐逍遥气功的实践

本文介绍了作者在音乐与气功相结合方面所作的创造性实践和研究。在特制音乐声波激发下,能很收快到传统气功的功效,使练功者达到强身治病的目的。实践证明音乐逍遥气功对多种慢性病有很好疗效。文章从物理学、生物物理学的角度,以系统论的方法对音乐逍遥气功的机理进行探讨。认为这是自觉利用各种形式、以一定规律动态变化的能量流的一种新的尝试。     

蜂窝CDMA系统的功率控制

首先给出蜂窝ＣＤＭＡ系统中采用区内Ｃ／Ｉ平衡算法的几种方案；然后考虑路径损失的影响，分别采用Ｍｏｎｔｅ－Ｃａｒｌｏ模拟法和高斯近似法来估计系统的性能。     

无线电频谱管理模式比较研究

随着无线电技术与业务的迅速发展,无线电频谱资源的广泛应用与其稀缺特性形成的供需矛盾日益突出,亟需探寻有效的频谱管理模式。首先对国外无线电频谱的分配和收费管理模式进行总结,比较研究行政机制和市场机制两种频谱管理模式。其次,基于公共物品理论对频谱资源进行分类,并阐述每类频谱资源的管理特点。最后分析了我国频谱管理现状和问题,并借鉴国外无线电频谱管理经验,提出未来中国频谱管理参考建议。     

基于LD分解的空间谱估计技术

提出了一种基于对阵列协方差矩阵进行 LD 分解的空间谱估计算法。对一大类阵列来说,该算法对空间谱估计方法的工程实现问题具有十分重要的实际意义。文中证明了特殊Hernitian 矩阵 LD 分解的原理,给出了求分解因式的递推公式,然后,由 LD 分解找出的信号子空间,得出了估计信号源方向的空间谱计算公式。理论分析和模拟结果表明,LD 分解和原有的特征分解法相比,更易于用专用数字信号处理片实现,有更小的计算量,需更少的存储单元。     

碱卤晶体中电子型色心的吸收谱能态计算

本文采用多种近似方法,分别对碱卤晶体中的F、F_A(Ⅱ)、F_A(Ⅲ)、F_2~+、F_(2A)~+、F_(2H)~+、F_2、F_2~-等电子型色心的吸收谱能态作了系统的理论计算。理论计算值与本实验室获得的实验值相比,除了个别色心外,相对误差均小于10％,取得了满意的结果。