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选择期货CFFEX.IF1808，截止到当日的1000条收盘价格走势：
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | # encoding: utf-8
import talib
from talib.abstract import SMA
import numpy as np
import pandas as pd
import math
import datetime
from collections import deque
from gm.api import * #掘金
import matplotlib.pyplot as plt
import matplotlib as mpl
import mpl_finance as mpf
import matplotlib.dates as mpd
import seaborn as sns
import statsmodels.tsa.stattools as ts
import statsmodels.api as sm
from statsmodels.tsa.arima_model import ARMA
from scipy import stats
from statsmodels.graphics.api import qqplot
set_token('****************************') #自行填写自己的token
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1 2 3 4 5 6 7 | now=datetime.datetime.now().date()
last_day=get_previous_trading_date(exchange='SHSE',date=now)
index_futures=get_continuous_contracts(csymbol='CFFEX.IF',start_date=last_day,end_date=last_day)
#print index_futures
strike_info=history_n(symbol='CFFEX.IF1808',frequency='60s',end_time='2018-07-01',fields='symbol,close,frequency,cum_volume',count=1000,df=True)
strike_info.dropna()
price=np.array(strike_info['close'])
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一个时间序列，他可能是有趋势的，是不平稳的，所以如果不平稳需要做差分。
ADF检测结果：
95%置信区间，p=0.0076，99%置信区间下，p=-3.5。对模型做一阶差分，希望得到一个平稳的时间序列
一阶差分后，模型基本平稳：
1 2 3 | p=ts.adfuller(strike_info['close'])[0]
#print p
price_log=strike_info['close'].diff()
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AR（p）模型，PACF会在lag=p时截尾，也就是，PACF图中的值落入宽带区域中。
MA（q）模型，ACF会在lag=q时截尾，同理，ACF图中的值落入宽带区域中。
用ACF（自相关系数）或者PACF（偏自相关系数）观察模型：
1 2 3 4 5 6 | fig = plt.figure(figsize=(12,8))
ax1=fig.add_subplot(211)
fig = sm.graphics.tsa.plot_acf(strike_info['close'],lags=40,ax=ax1)
ax2 = fig.add_subplot(212)
fig = sm.graphics.tsa.plot_pacf(strike_info['close'],lags=40,ax=ax2)
plt.show()
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优先选择PACF图，因为PACF大约在lag=1时截尾，即PACF的值落入宽带区域中
选择AR(P=1)的模型进行自回归拟合，得到拟合效果：
1 2 3 4 5 6 7 8 9 | arma_mod80 = sm.tsa.ARMA(strike_info['close'],(1,0)).fit()
print(arma_mod80.aic,arma_mod80.bic,arma_mod80.hqic)
resid = arma_mod80.resid
print(sm.stats.durbin_watson(arma_mod80.resid.values))
print(stats.normaltest(resid))
fig = plt.figure(figsize=(12,8))
ax = fig.add_subplot(111)
fig = qqplot(resid, line='q', ax=ax, fit=True)
plt.show()
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检验：计算得到序列的残差，基本为白噪音
1 2 3 4 5 6 | fig = plt.figure(figsize=(12,8))
ax1 = fig.add_subplot(211)
fig = sm.graphics.tsa.plot_acf(resid.values.squeeze(), lags=40, ax=ax1)
ax2 = fig.add_subplot(212)
fig = sm.graphics.tsa.plot_pacf(resid, lags=40, ax=ax2)
plt.show()
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用自回归拟合的模型进行预测，结果如下：
1 2 3 4 5 6 7 8 9 | fig=plt.figure(figsize=(15,7))
price2=strike_info=history_n(symbol='CFFEX.IF1808',frequency='60s',end_time='2018-07-01',fields='symbol,close,frequency,cum_volume',count=1000,df=True)['close']
price3=strike_info=history_n(symbol='CFFEX.IF1808',frequency='60s',end_time=now,fields='symbol,close,frequency,cum_volume',count=1000,df=True)['close']
print len(price2)
fit = arma_mod80.predict(0, 1100)
plt.plot(range(1100),fit[:1100],label='predict')
plt.plot(price2,label='price')
plt.legend(loc=4)
plt.show()
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