主成分和因子分析在保险市场分析中的应用--乌鲁木齐保险市场影响困素分析

本文运用主成分和因子分析等统计方法分析了乌鲁木齐保险市场调查数据.各种分析表明,不同职业的居民对保险产品的需求是有差异的.社会环境、生活习惯、收入水平是影响居民保险的重要因素.中高收入人群对保险产品的认同感较其它职业高.低收入人群偏好生死合险,而高收入人群对偏好除生死舍险外的其余保险产品.整体上可将保险产品分成三类,职业分为四类.这对保险业务员对不同职业居民推荐保险产品及附加险时有一定的参考价值.     

我国普通高等教育发展水平的全局主成分分析

本文根据 1995年、1997年和 1999年共同构成的关于我国普通高等教育发展水平的时序立体数据表 ,通过全局主成分分析得到公共主成分子空间L(F1,F2 ,… ,Fm) ,并在该子空间对我国高等教育发展背景和现状进行统计分析 ,给出了排名和变化趋势。     

主成分分析法在内蒙古自治区乡镇企业综合评价中的应用

运用多元统计分析中的主成分分析法对内蒙古地区一九九九年的 12个盟市的乡镇企业进行了综合评价 ,通过编程、计算机试算取得了较为满意的结果     

变量聚类—全局主成分分析在我国普通高等教育发展水平评价中的应用

本文根据1997年~2003年共同构成的关于我国普通高等教育发展水平的时序立体数据表,对各地区高等教育发展整体状况的各项指标进行变量聚类,以区分对我国高教发展背景与现状分别产生影响的各项指标,然后对每一类作主成分分析,选出能够代表该类的主成分。在此基础上,计算出各地区各年度主成分的增长度;再对各年度主成分的增长度作主成分分析,以期对我国高教发展背景与现状的总体变化趋势做出综合评价。     

对台湾工农业产品产量的主成分分析

主成分析分析法是一种将多个指标化为少数几个不相关的综合指标 (即主成分 )的多元统计分析方法 .本文通过运用主成分方法对我国台湾地区 1 989 1 996工农业主要指标的原始数据的处理分析 ,表明主成分分析确是在实用中很可行的一种常用的统计方法 .     

主成分分析法在学生成绩评价中的应用

简述了主成分的定义,给出了求解主成分的重要定理及性质的证明、对主要的性质进行了解释,归纳总结出求解主成分的步骤.在应用到评价学生成绩的例子中,借助统计软件SAS计算出每一个学生在各主成分的得分和综合得分,根据各主成分的得分对学生在学科中的优势与劣势进行了说明,为教师有针对性的进行因材施教提供了一个依据.     

长沙经济发展的动态分析

本文根据1997~2004年的长沙经济主要指标的时序立体数据表,进行时序全局主成分分析,得到一条动态轨迹并表明和客观实际能较好的吻合,为促进经济的快速发展提供一定的参考依据.     

主成分分析法在分析江苏经济发展状况中的应用

用多元统计分析中的主成分分析的基本原理和方法,透过2005年江苏省内13个省辖市的14项国民经济主要指标,从整体和区域经济的两个角度,分析江苏经济发展的现状.     

主成分分析法在工业企业经济效益综合评价中的应用

本文运用多元统计中的主成分分析原理，结合延边通用机械厂几年来生产经营中的经济效益变化状况进行了综合评价     

西部大开发中的各省区区位优势的多层次的主成分分析

本文利用多层次主成分分析法 ,对我国西部大开发中的八个省区综合实力的五个要素及多层指标体系 ,找出具有代表性的两个主成分 ,通过多层次分析综合及排序 ,用以描述各省的综合实力。结果说明 ,该法对多层次多指标研究社会经济问题是一可行的方法     

A nonparametric procedure to detect periods in time series

Suppose that for a given time series the experimenter knows that it has a certain periodic property and that he wishes to find out the length of the period. For this problem a nonparametric procedure is proposed. It consists of a new smoothing technique based on Kendall's Tau and a specific counting method. The procedure is studied under a simple model of periodic time series which are composed of periodic (deterministic) functions, a linear trend and exchangeable (stochastic) sequences. The performance of the procedure is illustrated by a simple example.     

Multivariate time series analysis

Some key theorems in the asymptotic theory for multivariate time series, using spectrl methods, are established. These theorems relate to various estimation situations including multiple systems of regressions, the determination of the frequency of a periodic signal and the determination of the velocity of a signal propagated through a dispersive medium and received with noise at a number of recorders. The theorems are of a general kind and relate to the almost sure convergence of averages of the periodogram and to the limiting covariance properties and the central limit theorem for such averages. Some brief indications are given concerning extensions of the results to cases where processes are observed that are stationary in time and homogenous with respect to spatial translation.     

A note on the time series which is the product of two stationary time series

The time series […,x_-1y_-1,x₀y₀,x₁y₁,…]> which is the product of two stationary time series x_t and y_t is studied. Such sequences arise in the study of nonlinear time series, censored time series, amplitude modulated time series, time series with random parameters, and time series with missing observations. The mean and autocovariance function of the product sequence are derived.     

Topological analysis of chaotic time series data from the Belousov-Zhabotinskii reaction

Summary We have applied topological methods to analyze chaotic time series data from the Belousov-Zhabotinskii reaction. First, the periodic orbits shadowed by the data set were identified. Next, a three-dimensional embedding without self-intersections was constructed from the data set. The topological structure of that flow was visualized by constructing a branched manifold such that every periodic orbit in the flow could be held by the branched manifold. The branched manifold, or induced template, was computed using the three lowest-period orbits. The organization of the higher-period orbits predicted by this induced template was compared with the organization of the orbits reconstructed from the data set with excellent results. The consequences of the presence of certain knots found in the data are discussed.     

Detecting high-dimensional determinism in time series with application to human movement data

We numerically investigate the ability of a statistic to detect determinism in time series generated by high-dimensional continuous chaotic systems. This recently introduced statistic (denoted V_E2) is derived from the averaged false nearest neighbors method for analyzing data. Using surrogate data tests, we show that the proposed statistic is able to discriminate high-dimensional chaotic data from their stochastic counterparts. By analyzing the effect of the length of the available data, we show that the proposed criterion is efficient for relatively short time series. Finally, we apply the method to real-world data from biomechanics, namely postural sway time series. In this case, the results led us to exclude the hypothesis of nonlinear deterministic underlying dynamics for the observed phenomena.     

The information matrices of the parameters of multiple mixed time series

Closed form matrix equations are given for the information matrix of the parameters of the vector mixed autoregressive moving average time series model.     

The problem of processing time series: Extending possibilities of the local approximation method using singular spectrum analysis

We present algorithms for singular spectrum analysis and local approximation methods used to extrapolate time series. We analyze the advantages and disadvantages of these methods and consider the peculiarities of applying them to various systems. Based on this analysis, we propose a generalization of the local approximation method that makes it suitable for forecasting very noisy time series. We present the results of numerical simulations illustrating the possibilities of the proposed method.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 148–159, January, 2005.     

The application of time series analysis to describe the dynamic movements of suspension bridges

Operational safety and the operational status of engineering structures depend on the specifications given during the design stage of the structure, on the observations made during the construction and which continue when the structure is in use. Furthermore, it is important that comprehensive emergency situation plans exist in case irregular movements occur. The Istanbul Bosphorus Bridge was completed in 1973 and connects Asia to Europe. To determine the current operational safety of the bridge, its movements were observed under different stress factors such as wind speed, temperature change and traffic load. The observed lateral, longitudinal and vertical movements of bridge’s deck and towers were studied and described using time series analyses. As a result of the analysis of the short-term observations, the linear trend components in the series originating from long-term periodical movements of the bridge were determined. In the analysis of the periodic components of the series, high-pass and low-pass filtering processes were applied to the series to determine the low and high frequencies of the bridge. The transformation of the series from the time domain to the frequency domain was ensured by Fast Fourier Transform (FFT), and power spectrums of the series were calculated. It was found that low and high frequencies obtained from power spectrums reflected the expected movements of the bridge. It was determined that the bridge deck had many significant periodical movements resulting from wind forces and traffic load. The calculated high frequency values for vertical movements of the bridge deck were found to be in harmony with natural frequency and periodic values of the first 6 modes of the Bosphorus Bridge at the 0.127–0.463 Hz interval. Finally, stochastic components of the time series were determined by the use of Autoregressive (AR) and Autoregressive Moving Average (ARMA) models. In terms of the operational safety and operational status of the Bosphorus Bridge, there were no unexpected results determined by the time series analysis in the observed movements of the bridge.     

Canonical correlation and reduction of multiple time series

It is shown that a degenerate rankd-variate stationary time series can be reduced to a full rank time series of lower dimension via an orthogonal transformationT provided that , the canonical correlation between past and future of the time series is strictly less than one. Procedures for estimation of rank of the multiple time series,T and testing =1 are outlined, the latter is related to testing the unit root hypothesis in ARMA models.