[TOC]python
程序简介
<font size=3>调用statsmodels模块对上证指数的收盘价进行ARIMA模型动态建模，ARIMA适合短时间预测，所以输入为15个数据，输出为1个数据 程序输入：原序列，须要日后预测的个数 程序输出：预测序列，模型结构(白噪声检验、单根检验、一阶差分自相关图、一阶差分偏自相关图)api
<b>差分整合移动平均自回归模型(ARIMA)</b>，ARIMA(p，d，q)中，AR是”自回归”，p为自回归项数；MA为”滑动平均”，q为滑动平均项数，d为使之成为平稳序列所作的差分次数（阶数）。</font>app
程序/数据集下载
<font size=3>点击进入下载地址</font>函数
代码分析
<font size=3>导入模块、路径<br></font>测试
# -*- coding: utf-8 -*- from Module.BuildModel import ARIMA from sklearn.metrics import mean_absolute_error import pandas as pd import numpy as np import matplotlib.pyplot as plt import os #路径目录 baseDir = ''#当前目录 staticDir = os.path.join(baseDir,'Static')#静态文件目录 resultDir = os.path.join(baseDir,'Result')#结果文件目录
<font size=3>读取数据、分红训练集和测试集，查看前5行<br></font>ui
#读取数据 data = pd.read_csv(staticDir+'/000001.csv',encoding='gbk') train = data['收盘价'].values[-20:-10]#训练数据 test = data['收盘价'].values[-10:]#测试数据 data.head()
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</style> <table border="1" class="dataframe"> <thead> <tr style="text-align: right;"> <th></th> <th>日期</th> <th>股票代码</th> <th>名称</th> <th>收盘价</th> <th>最高价</th> <th>最低价</th> <th>开盘价</th> <th>前收盘</th> <th>涨跌额</th> <th>涨跌幅</th> <th>成交量</th> <th>成交金额</th> </tr> </thead> <tbody> <tr> <th>0</th> <td>2020-02-18</td> <td>'000001</td> <td>上证指数</td> <td>2984.9716</td> <td>2990.6003</td> <td>2960.7751</td> <td>2981.4097</td> <td>2983.6224</td> <td>1.3492</td> <td>0.0452</td> <td>311665913</td> <td>3.74998562648e+11</td> </tr> <tr> <th>1</th> <td>2020-02-17</td> <td>'000001</td> <td>上证指数</td> <td>2983.6224</td> <td>2983.6371</td> <td>2924.9913</td> <td>2924.9913</td> <td>2917.0077</td> <td>66.6147</td> <td>2.2837</td> <td>313198007</td> <td>3.67014340129e+11</td> </tr> <tr> <th>2</th> <td>2020-02-14</td> <td>'000001</td> <td>上证指数</td> <td>2917.0077</td> <td>2926.9427</td> <td>2899.5739</td> <td>2899.8659</td> <td>2906.0735</td> <td>10.9342</td> <td>0.3763</td> <td>250650627</td> <td>3.08080368726e+11</td> </tr> <tr> <th>3</th> <td>2020-02-13</td> <td>'000001</td> <td>上证指数</td> <td>2906.0735</td> <td>2935.4060</td> <td>2901.2425</td> <td>2927.1443</td> <td>2926.8991</td> <td>-20.8256</td> <td>-0.7115</td> <td>274804844</td> <td>3.34526327364e+11</td> </tr> <tr> <th>4</th> <td>2020-02-12</td> <td>'000001</td> <td>上证指数</td> <td>2926.8991</td> <td>2926.8991</td> <td>2892.4240</td> <td>2895.5561</td> <td>2901.6744</td> <td>25.2247</td> <td>0.8693</td> <td>248733429</td> <td>2.97534420493e+11</td> </tr> </tbody> </table> </div>spa
<font size=3>调用ARIMA函数进行动态建模，函数自动绘制一阶差分自相关图和一阶差分偏自相关图，即每次预测1个值，持续屡次，计算并打印MAE.net
其中ARIMA函数位置在Module/BuildModel.py，代码会在下文给出 </font>code
#ARIMA动态建模
yPre = []
for i in range(test.shape[0]):
#只预测1个数
result = ARIMA(train,1)
yPre.append(result['predict']['value'][0])
#更新训练集
train = train.tolist()[:-1]
train.append(test[i])
train = np.array(train).reshape(-1)
#计算MAE
MAE = mean_absolute_error(test,yPre)
print('偏差MAE',MAE)
<font size=3>这里给出上文用到的ARIMA函数，直接运行是直接验证代码有效性的另外一个简单实验，程序会保留白噪声检验、单根检验、一阶差分自相关图、一阶差分偏自相图</font>
# -*- coding: utf-8 -*-
import os
import pandas as pd
import numpy as np
import statsmodels.api as sm
from statsmodels.graphics.tsaplots import plot_acf, plot_pacf
from statsmodels.tsa.stattools import adfuller
from statsmodels.tsa import arima_model
from statsmodels.stats.diagnostic import acorr_ljungbox
import warnings
warnings.filterwarnings("ignore")
def ARIMA(series,n):
'''
只讨论一阶差分的ARIMA模型，预测，数字索引从1开始
series:时间序列
n:须要日后预测的个数
'''
series = np.array(series)
series = pd.Series(series.reshape(-1))
currentDir = os.getcwd()#当前工做路径
#一阶差分数据
fd = series.diff(1)[1:]
plot_acf(fd).savefig(currentDir+'/一阶差分自相关图.png')
plot_pacf(fd).savefig(currentDir+'/一阶差分偏自相关图.png')
#一阶差分单位根检验
unitP = adfuller(fd)[1]
if unitP>0.05:
unitAssess = '单位根检验中p值为%.2f，大于0.05，该一阶差分序列可能为非平稳序列'%(unitP)
#print('单位根检验中p值为%.2f，大于0.05，认为该一阶差分序列判断为非平稳序列'%(unitP))
else:
unitAssess = '单位根检验中p值为%.2f，小于0.05，认为该一阶差分序列为平稳序列'%(unitP)
#print('单位根检验中p值为%.2f，小于0.05，认为该一阶差分序列判断为平稳序列'%(unitP))
#白噪声检验
noiseP = acorr_ljungbox(fd, lags=1)[-1]
if noiseP<=0.05:
noiseAssess = '白噪声检验中p值为%.2f，小于0.05，认为该一阶差分序列为非白噪声'%noiseP
#print('白噪声检验中p值为%.2f，小于0.05，认为该一阶差分序列为非白噪声'%noiseP)
else:
noiseAssess = '白噪声检验中p值%.2f，大于0.05，该一阶差分序列可能为白噪声'%noiseP
#print('白噪声检验中%.2f，大于0.05，认为该一阶差分序列为白噪声'%noiseP)
#BIC准则肯定p、q值
pMax = int(series.shape[0]/10)# 通常阶数不超过length/10
qMax = pMax# 通常阶数不超过length/10
bics = list()
for p in range(pMax + 1):
tmp = list()
for q in range(qMax + 1):
try:
tmp.append(arima_model.ARIMA(series, (p, 1, q)).fit().bic)
except Exception as e:
#print(str(e))
tmp.append(1e+10)#加入一个很大的数
bics.append(tmp)
bics = pd.DataFrame(bics)
p, q = bics.stack().idxmin()
#print('BIC准则下肯定p,q为%s,%s'%(p,q))
#建模
model = arima_model.ARIMA(series,order=(p, 1, q)).fit()
predict = model.forecast(n)[0]
return {
'model':{'value':model,'desc':'模型'},
'unitP':{'value':unitP,'desc':unitAssess},
'noiseP':{'value':noiseP[0],'desc':noiseAssess},
'p':{'value':p,'desc':'AR模型阶数'},
'q':{'value':q,'desc':'MA模型阶数'},
'params':{'value':model.params,'desc':'模型系数'},
'predict':{'value':predict,'desc':'日后预测%d个的序列'%(n)}
}
if __name__ == "__main__":
data = data = np.array([1.2,2.2,3.1,4.5,5.6,6.7,7.1,8.2,9.6,10.6,11,12.4,13.5,14.7,15.2])
x = data[0:10]#输入数据
y = data[10:]#须要预测的数据
result = ARIMA(x,len(y))#预测结果,一阶差分偏自相关图,一阶差分自相关图
predict = result['predict']['value']
predict = np.round(predict,1)
print('真实值:',y)
print('预测值:',predict)
print(result)
<font size=3>打印创建的股票模型假设检验结论，能够看到序列可能为白噪声，可是仍然能够强行建模</font>
#打印模型结构 print(result['noiseP']['desc']) print(result['unitP']['desc'])
白噪声检验中p值0.98，大于0.05，该一阶差分序列可能为白噪声 单位根检验中p值为0.99，大于0.05，该一阶差分序列可能为非平稳序列
<font size=3>观测值预测值对比可视化</font>
#可视化
plt.clf()#清理历史绘图
#用来正常显示中文标签
plt.rcParams['font.sans-serif']=['SimHei']
#用来正常显示负号
plt.rcParams['axes.unicode_minus']=False
plt.plot(range(test.shape[0]),yPre,label="预测值")
plt.plot(range(test.shape[0]),test,label="观测值")
plt.legend()
plt.title('ARIMA预测效果，MAE：%2f'%MAE)
plt.savefig(resultDir+'/ARIMA预测效果.png',dpi=100,bbox_inches='tight')