﻿ 基于函数型数据的上证指数预测 Prediction for the Shanghai Stock Index Based on the Functional Data

Vol.05 No.02(2016), Article ID:17696,7 pages
10.12677/AAM.2016.52037

Prediction for the Shanghai Stock Index Based on the Functional Data

Lijuan Cheng

School of Mathematics and Computation Science, Lingnan Normal University, Zhanjiang Guangdong

Received: May 6th, 2016; accepted: May 27th, 2016; published: May 30th, 2016

ABSTRACT

In the research of financial data, the functional data are often encountered. In this paper, the prediction model of functional principal components analysis is established to forecast the Shanghai Stock Index. Based on the principal component analysis theory and calculation method, the Shanghai Composite Index is forecasted by Matlab.

Keywords:Functional Data, Principal Component Analysis, Forecast

1. 引言

2. 函数型数据分析

(1)

2.1. 数据平滑

(2)

(3)

(4)

2.2. 函数型主成分分析

(5)

(6)

，则

2.3. 函数型主成分预测模型

(7)

(8)

(9)

(10)

3. 实证分析

Figure 1. Yield curve and smooth curve

Figure 2. First derivative curve

Figure 3. Principal component weighting function (the first interval)

Figure 4. Principal component weighting function (second interval)

Table 1. Principal component characteristic value and contribution rate

Table 2. Correlation coefficient

Table 3. Real value and predictive value

4. 结论

Prediction for the Shanghai Stock Index Based on the Functional Data[J]. 应用数学进展, 2016, 05(02): 291-297. http://dx.doi.org/10.12677/AAM.2016.52037

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