论文总字数：25534字

摘 要

股票作为当今社会非常热门的一种投资理财方式，股票市场的波动能够体现一个公司甚至整个国家的经济变化、体系变化、制度变化。在经济发展的前提下，人们普遍拥有了更多可支配的收入，越来越多的人开始尝试各种理财方式。其中，股投资票就成为了最常见的一种投资选择。

本文介绍了关于ARIMA模型的相关知识，并收集了中石化股票2007年第一季度至2018年第四季度数据，以“每股净收益”作为观测值进行模型拟合。利用SAS软件编程，通过差分方式进行了序列平稳化的处理，接着通过平稳序列的自相关图以及偏自相关图结果确定了模型阶数并且选择拟合基于ARIMA模型的简单季节模型。经检验，所拟合的模型中，残差序列通过白噪声检验，即原观测值序列提取信息充分，各参数通过显著性检验，即模型拟合充分。根据所拟合模型完成了对数据的预测，预测值与观测值所绘制的图像结果显示，预测值的波动小于观测值，更接近均值，即预测值更加保守，并且预测值与观测值拥有相同的走势，即该模型能够根据预测值的历史数据，预测接下来一段时间的数据变化。根据预测数据最终给出了在2020年第一季度对该只股票持仓或不交易的操作建议。

关键词：时间序列分析；ARIMA模型；每股净收益；模型预测；投资建议

Sinopec stock data processing and time series model

Abstract

Stocks as a very popular way of investment in today's society, the fluctuation of the stock market can reflect the economic change and system change of a company or even the whole country. With the development of economy, people generally have more disposable income, more and more people are trying various ways to manage their money. stock has become the most common investment choice.

This article introduces the knowledge about ARIMA model. We collected the data of Sinopec’s stock from the first quarter of 2007 to the fourth quarter of 2018, the model was fitted with "net income per share" as the observed value. Through SAS programming method, sequence stabilization is carried out by differential method. The model is selected by autocorrelogram and partial autocorrelogram results. Finally, a simple seasonal model based on ARIMA model is fitted. The results show that in the fitted model, the residual sequence is verified by the white noise test, which indicates that the original observation sequence has sufficient extraction information. Each parameter passed the significance test, that is, the model fitting was fully completed and the prediction of data was completed according to the fitted model and the significance test of each parameter indicates that the model is fully fitted. The result of the graph drawn by the predicted value and the observed value shows that the fluctuation of the predicted value is smaller than the observed value and closer to the mean value, that is, the predicted value is more conservative and has the same trend with the observed value, that is, the model can predict the data change in the following period of time based on the historical data of the predicted value. Based on the forecast data, it finally gives a recommendation to hold or not trade the stock in the first quarter of 2020.

Key words: time series analysis; ARIMA model; net income per share; Model prediction; Investment advice

目 录

摘要…………………………………………………………………………………I

ABSTRACT…………………………………………………………………………II

第一章 引言………………………………………………………………………1

1.1 股票的研究意义以及背景…………………………………………………1

1.2 本文主要工作………………………………………………………………2

1.3 本文主要结构………………………………………………………………2

第二章 时间序列模型的理论综述……………………………………………3

2.1平稳时间序列………………………………………………………………3

2.1.1时间序列………………………………………………………………3

2.1.2平稳时间序列…………………………………………………………3

2.2 序列平稳性检验……………………………………………………………3

2.2.1 时序图检验…………………………………………………………4

2.2.2 自相关图检验………………………………………………………4

2.3 纯随机性检验………………………………………………………………4

2.3.1 纯随机序列的定义…………………………………………………4

2.3.2 纯随机序列的意义…………………………………………………5

2.4 本章小结……………………………………………………………………5

第三章 ARIMA模型……………………………………………………6

3.1 自回归（AR）模型………………………………………………………6

3.1.1 自回归（AR）模型的定义…………………………………………6

3.1.2 自回归（AR）模型平稳性判别方法………………………………6

3.2 移动平均（MA）模型……………………………………………………7

3.2.1 移动平均（MA）模型的定义………………………………………7

3.2.2 移动平均（MA）模型平稳性判别方法……………………………7

3.3 自回归移动平均（ARMA）模型…………………………………………8

3.3.1 自回归移动平均（ARMA）模型的定义……………………………8

3.3.2 自回归移动平均（ARMA）模型平稳性判别方法…………………8

3.4 求和移动自回归（ARIMA）模型…………………………………………8

3.4.1 求和移动自回归（ARIMA）模型定义……………………………8

3.4.2 ARIMA模型预测……………………………………………………9

3.5 ARIMA(p,d,q)模型建模步骤……………………………………………10

3.6 ARIMA模型用于股票预测………………………………………………11

3.7 本章小结…………………………………………………………………11

第四章 中石化股票数据拟合时间序列模型………………………13

4.1 中石化股票数据…………………………………………………………13

4.2 实验程序…………………………………………………………………14

4.3 实验结果…………………………………………………………………15

4.3.1 平稳性检验与平稳化………………………………………………15

4.3.2 模型识别……………………………………………………………18

4.3.3 模型检验……………………………………………………………19

4.3.4 模型预测……………………………………………………………21

4.4 本章小结…………………………………………………………………21

结论……………………………………………………………………23

参考文献…………………………………………………………………………24

致谢……………………………………………………………………26

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