基于函数型数据分析的证券投资收益研究

发布时间：2018-03-04 20:26

本文选题：函数型数据　切入点：基函数系统　出处：《首都经济贸易大学》2014年硕士论文　论文类型：学位论文

【摘要】：数据拟合是统计学中的一大重要和长久的课题，传统的统计分析方法如线性回归、多元统计，，我们的处理对象大都是离散数据，而我们常见的数据类型包括时间序列数据、横截面数据或二者的综合即面板数据。然而实际问题中，很多生成的统计数据事实上可以用一个近似函数表达式来描述，但传统的统计手段所获得的信息往往是片段的、离散的数列，这无疑损失了大量有用的信息，从而统计学家们设想可以将这些离散的观测数据拟合成函数，再从数学的角度利用函数对象的优良性质来深入研究，这无疑为统计分析领域打开了一个新的思路。我们将要在本文中大致介绍函数型数据分析方法，其拟合数据得到的函数大多是通过基函数系统来实现，并且具有很多优良的性质。传统的参数估计中用到的最小二乘法可能伴随着过拟合现象，因而我们将对其进行修正，并引入光滑参数和光滑矩阵的概念后将其应用到函数型数据分析的参数估计中。有了拟合函数后，我们分别将介绍经典多元统计理论中的方差分析、主成分分析及典型相关分析是如何经扩展后应用于函数型数据的分析中。此外在实证分析中,我们将通过一个具体的例子来说明函数型数据分析方法在金融领域尤其是证券投资中的应用。
[Abstract]:Data fitting is an important and long-term problem in statistics. Traditional statistical analysis methods such as linear regression, multivariate statistics, our processing objects are mostly discrete data, and our common data types include time series data. The cross-section data or the combination of the two is panel data. However, in practical problems, many of the generated statistics can in fact be described by an approximate functional expression, but the information obtained by traditional statistical methods is often segmented. Discrete sequence of numbers, which undoubtedly lost a lot of useful information, so statisticians imagine that these discrete observation data can be simulated as composite functions, and then from the point of view of mathematics, the excellent properties of function objects can be deeply studied. This undoubtedly opens a new way of thinking for the statistical analysis field. In this paper, we will introduce the method of functional data analysis. Most of the functions obtained from the fitting data are realized by the basis function system. And has many excellent properties. The least square method used in the traditional parameter estimation may be accompanied by the phenomenon of overfitting, so we will revise it. After introducing the concepts of smooth parameter and smooth matrix, we apply them to the parameter estimation of functional data analysis. With the fitting function, we will introduce the analysis of variance in classical multivariate statistical theory. How principal component analysis and canonical correlation analysis are extended to the analysis of functional data. We will illustrate the application of the functional data analysis method in the field of finance, especially in the field of securities investment through a concrete example.
【学位授予单位】：首都经济贸易大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F830.91

【引证文献】