数学与统计学院知识库

随着近些年来科学技术的快速发展,函数型数据分析方法在数据分析方面也越来越凸显出它的重要性和便捷性.大数据时代的到来使得收集到的原始数据往往具有函数特征,表现形式上更多的展示为光滑的曲线或者是不间断的函数.对于这类函数型数据再运用传统数据分析方法是不适用的.运用传统方法建立模型会受太多的假设条件限制.因此,就需要寻找一种新的数据分析方法(即函数型数据分析).该方法是将观测到的数据看做一个整体,而不是单个的观测值,也不需要太多假设条件,这是函数型数据分析方法特有的特征.
运用该方法通过基函数将原始离散数据转化为光滑的拟合函数曲线.然后从函数的角度对其进行分析.在金融市场中,金融数据是具有函数型数据的特点. 本文运用十个银行股票的收开盘价数据,通过函数型数据分析方法探索了函数型数据的主成分分析理论.并基于函数型数据主成分建立了线性预测模型和非线性预测模型,进而预测十个银行股票的收盘价,并得到了较好的预测效果.

Over the past decade,with the rapid development of science and technology,FDA plays a more and more important role in modern scientific rescarch.In the big data time,the observed data will display an obvious functional feature.Most of them are smooth curves or continous functions.The traditional data analysis method is not applicable for this kind of functional data and it has its limitations to build models.A new solution to data analysis is introduced - Functional Data Analysis(FDA),which consider the observed functional data as a whole,not a series of numbers and with less assumptions.It is substantial of functional data analysis.
FDA selects a basis function system to linearly expand sample data and transform it into a smooth fitting function curve which can be analyzed in the context of function data.In the financial markets,the data can be regarded as a continuous function data.This thesis collectes ten banks shares of closeing and opening price data.According to the functional data analysis method to explore the functional theory of principal component analysis.Based functional data principal component bulid linear prediction model and nonlinear prediction model.In addition, the closing price of ten bank shares was predicted, and a good prediction effect was obtained.