def __analysis_index(self):
index = self.get_env().query_data(Index_Data).get_data_serise()
index_name = list(index.columns)
index_name.remove(COM_DATE)
index[index_name] = index[index_name].pct_change()/100
index[index_name] = np.log(index[index_name]+1)
index = index.set_index(COM_DATE)
index.index = pd.to_datetime(index.index)
res = pd.DataFrame(columns = ['mean','std','skew','kurt','jarque-Bera','adf','lm'])
for index_name_ in index_name:
fig, ax = plt.subplots()
ax.plot(index[index_name_].dropna(), label=index_name_)
ax.set_xlabel('时间')
ax.set_ylabel('收益率的对数')
ax.set_title(index_name_+'收益率图')
ax.legend()
plt.savefig(os.path.join(RESULTS, index_name_+'.png'))
plt.close()
fig, ax = plt.subplots()
ax.hist(index[index_name_].dropna(),bins =25)
ax.set_xlabel('收益率范围')
ax.set_ylabel('收益率的对数')
ax.set_title(index_name_+'收益率图')
plt.savefig(os.path.join(RESULTS, index_name_+'bar.png'))
plt.close()
res.loc[index_name_] = [
np.nanmean(index[index_name_].dropna()),
np.nanstd(index[index_name_].dropna()),
index[index_name_].dropna().skew(),
index[index_name_].dropna().kurt(),
stats.jarque_bera(index[index_name_].dropna())[0],
adfuller(index[index_name_].dropna())[4]['5%'],
q_stat(acf(index[index_name_].dropna())[1:13],len(index[index_name_].dropna()))[1][-1]
]
res.to_csv(os.path.join(RESULTS,'index_info.csv'))
def plot_correlogram(self, lags=10, title=None):
# NOTE: without passing residuals this meethod can notbe used by the optimal brute force finder
def moving_average(self, a: pd.array, n: int = 3):
ret = np.cumsum(a)
ret[n:] = ret[n:] - ret[:-n]
return ret[n - 1:] / n
matplotlib.use(
'TkAgg'
) # NOTE: necessary due to inheritence of TimeSeries which uses 'Agg'
x = self.data
lags = min(10, int(len(x) / 5)) if lags is None else lags
fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(14, 8))
axes[0][0].plot(x.values) # Residuals
# axes[0][0].plot(moving_average(x, n=21), c='k', lw=1) # moving average of risiduals # FIXME calculate moveaverage
q_p = np.max(q_stat(acf(x, nlags=lags), len(x))[1])
stats = f'Q-Stat: {np.max(q_p):>8.2f}\nADF: {adfuller(x)[1]:>11.2f}'
axes[0][0].text(x=.02, y=.85, s=stats, transform=axes[0][0].transAxes)
probplot(x, plot=axes[0][1])
mean, var, skew, kurtosis = moment(x, moment=[1, 2, 3, 4])
s = f'Mean: {mean:>12.2f}\nSD: {np.sqrt(var):>16.2f}\nSkew: {skew:12.2f}\nKurtosis:{kurtosis:9.2f}'
axes[0][1].text(x=.02, y=.75, s=s, transform=axes[0][1].transAxes)
plot_acf(x=x, lags=lags, zero=False, ax=axes[1][0])
plot_pacf(x, lags=lags, zero=False, ax=axes[1][1])
axes[1][0].set_xlabel('Lag')
axes[1][1].set_xlabel('Lag')
fig.suptitle(title, fontsize=14)
sns.despine()
fig.tight_layout()
fig.subplots_adjust(top=.9)
fig1 = plt.gcf()
print('plotting')
plt.show()
def WhiteNoiseTest(ret, nlags=20, isprintsummary=False):
"""
白雜訊測試：使用 Ljung-Box 檢定
若接受虛無假設則表示為白雜訊(純隨機序列)，回傳值為False
若拒絕虛無假設則表示序列並非隨機的，回傳值為True
"""
acf = stattools.acf(ret, nlags = nlags, qstat = False, \
fft = True, alpha = None, missing = "drop")
n = len(ret)
results = stattools.q_stat(acf, n)
if isprintsummary:
print("Show Ljung-Box Q-statistics: ", results[0])
print("Show corresponding P-values: ", results[1])
if np.any(results[1] < PVal): # 只要有一Q統計量顯著大於0，即滿足條件
if isprintsummary:
print("- - - - - - - - - - - - - - - - - - - - - - - - - -")
print("Some LB stats p < %.2f -> correlated time series!" % PVal)
print("- - - - - - - - - - - - - - - - - - - - - - - - - -")
return True
else: # All p-values > PVal, accept H0 (white noise time series)
if isprintsummary:
print("- - - - - - - - - - - - - - - - - - - - - - - - - -")
print("All LB stats p > %.2f -> white noise time series!" % PVal)
print("- - - - - - - - - - - - - - - - - - - - - - - - - -")
return False
def plot_correlogram(x, fig, axes, lags=40, title=None):
lags = min(10, int(len(x) / 5)) if lags is None else lags
x.plot(ax=axes[0][0])
q_p = np.max(q_stat(acf(x, nlags=lags), len(x))[1])
stats = f'Q-Stat: {np.max(q_p):>8.2f}\nADF: {adfuller(x)[1]:>11.2f} \nHurst: {round(hurst(x.values),2)}'
axes[0][0].text(x=.02, y=.85, s=stats, transform=axes[0][0].transAxes)
probplot(x, plot=axes[0][1])
mean, var, skew, kurtosis = moment(x, moment=[1, 2, 3, 4])
s = f'Mean: {mean:>12.2f}\nSD: {np.sqrt(var):>16.2f}\nSkew: {skew:12.2f}\nKurtosis:{kurtosis:9.2f}'
axes[0][1].text(x=.02, y=.75, s=s, transform=axes[0][1].transAxes)
plot_acf(x=x, lags=lags, zero=False, ax=axes[1][0])
plot_pacf(x=x, lags=lags, zero=False, ax=axes[1][1])
axes[1][0].set_xlabel('Lag')
axes[1][1].set_xlabel('Lag')
fig.suptitle(title, fontsize=20)
fig.tight_layout()
fig.subplots_adjust(top=.9)
def plot_correlogram(x, lags=None, title=None):
lags = min(10, int(len(x)/5)) if lags is None else lags
fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(14, 8))
x.plot(ax=axes[0][0], title='Time Series')
x.rolling(21).mean().plot(ax=axes[0][0], c='k', lw=1)
q_p = np.max(q_stat(acf(x, nlags=lags), len(x))[1])
stats = f'Q-Stat: {np.max(q_p):>8.2f}\nADF: {adfuller(x)[1]:>11.2f}'
axes[0][0].text(x=.02, y=.85, s=stats, transform=axes[0][0].transAxes)
probplot(x, plot=axes[0][1])
mean, var, skew, kurtosis = moment(x, moment=[1, 2, 3, 4])
s = f'Mean: {mean:>12.2f}\nSD: {np.sqrt(var):>16.2f}\nSkew: {skew:12.2f}\nKurtosis:{kurtosis:9.2f}'
axes[0][1].text(x=.02, y=.75, s=s, transform=axes[0][1].transAxes)
plot_acf(x=x, lags=lags, zero=False, ax=axes[1][0])
plot_pacf(x, lags=lags, zero=False, ax=axes[1][1])
axes[1][0].set_xlabel('Lag')
axes[1][1].set_xlabel('Lag')
fig.suptitle(title, fontsize=14)
sns.despine()
fig.tight_layout()
fig.subplots_adjust(top=.9)
def many_paras():
"""
p-value本质是控制假阳性率（False positive rate，FPR）
q-value 控制的是FDR (false discovery rate)
Q-statistic: Qlb=T*(T+2)*sigma(j=1,p)(rj^2/(T-j)) rj残差序列，j阶自相关系数，T观测值的个数，p滞后阶数。
FDR = E（V/R） 错误发现次数V，总的拒绝次数R
acf: 自相关系数 -- y(t)= a0 + a1*y(t-1) + epsilon
p(x(i)|x(i-h)) :sigma(i=1,n-h) ((x(i)-mu)*(x(i+h)-mu)/sigma(i=1,n) ((x(i)-mu)^2))
pacf: 偏自相关系数，k-1个时间滞后 作为已知，只求k -- y(t)= a0 + a1*y(t-1) + ... a1*y(t-k) + epsilon
p(x(i)..x(i-k)|x(i-1)x(i-k+1)) :
ARMA(p，q): AR代表p阶自回归过程，MA代表q阶移动平均过程
ARIMA模型是在ARMA模型的基础上多了差分的操作。
ADF: 白噪声随机干扰项的一阶自回归过程。用单位根 检验，存在就是非平稳。y(t)= mu + fi*y(t-1) + epsilon。p阶要求 p个根的和小于1。
Sma: 移动平均
wma: 加权移动平均
ema: 指数移动平均
ewma: 指数加权移动平均
OBV: On Balance Volume, 多空比率净额= [（收盘价－最低价）－（最高价-收盘价）] ÷（ 最高价－最低价）×V
:return:
"""
# 1. 计算自相关系数
acfs = stattools.acf(SHRet)
# 绘制自相关系数图
plot_acf(SHRet, use_vlines=True, lags=30)
# 2. 计算偏自相关系数
pacfs = stattools.pacf(SHRet)
plot_pacf(SHRet, use_vlines=True, lags=30)
# 3. 进行ADF单位根检验，并查看结果；
adfSHRet = ADF(SHRet)
print(adfSHRet.summary().as_text())
# 4. Q 统计
LjungBox1 = stattools.q_stat(stattools.acf(SHRet)[1:13], len(SHRet))
print(LjungBox1)
# 5. lag即为上述检验表达式中的m，在这里我们选择检验12阶的自相关系数。
LjungBox = stattools.q_stat(stattools.acf(CPItrain)[1:12], len(CPItrain))
# order表示建立的模型的阶数，c(1,0,1)表示建立的是ARMA(1,1)模型；
# 中间的数字0表示使用原始的、未进行过差分（差分次数为0）的数据；
model1 = arima_model.ARIMA(CPItrain, order=(1, 0, 1)).fit()
model1.summary()
model1.conf_int()
# 6. 绘制时间序列模拟的诊断图
stdresid = model1.resid / math.sqrt(model1.sigma2)
plt.plot(stdresid)
plot_acf(stdresid, lags=20)
LjungBox = stattools.q_stat(stattools.acf(stdresid)[1:13], len(stdresid))
print(LjungBox[1][-1])
print(model1.forecast(3)[0])
# 7. Autoregressive conditional heteroskedasticity model 自回归条件异方差模型
# y(t)=b*x(t)+epsilon(t)
# epsilon(t)^2=a0+a1*epsilon(t-1)^2+a2*epsilon(t-2)^2+n(t)
# \sigma_t^{2}=\omega+\sum_{i=1}^{p}\alpha_{i}\epsilon_{t-i}^{2}
# n(t)独立同分布 期望为0，var(n^2)=r^2
am = arch_model(SHret)
model = am.fit(update_freq=0)
print(model.summary())
# 8. 对子 的 处理
pt = TradeTool()
SSD = pt.SSD(priceAf, priceBf)
SSDspread = pt.SSDSpread(priceAf, priceBf)
SSDspread.describe()
coefficients = pt.cointegration(priceAf, priceBf)
CoSpreadF = pt.CointegrationSpread(priceA, priceB, formPeriod, formPeriod)
CoSpreadTr = pt.CointegrationSpread(priceA, priceB, formPeriod,
tradePeriod)
CoSpreadTr.describe()
bound = pt.calBound(priceA, priceB, 'Cointegration', formPeriod, width=1.2)
# 9. 配对 选点
trtl = TradeTool()
account = trtl.TradeSimPair(PAt, PBt, position)
# 10. momentum function
et = ElementTool()
et.momentum(Close, 5).tail(n=5)
momen35 = et.momentum(Close, 35)
signal = []
for i in momen35:
if i > 0:
signal.append(1)
else:
signal.append(-1)
signal = pd.Series(signal, index=momen35.index)
signal.head()
tradeSig = signal.shift(1)
ret = Close / Close.shift(1) - 1
# ret=ret['2014-02-20':]
# ret.head(n=3)
Mom35Ret = ret * (signal.shift(1))
Mom35Ret[0:5]
real_Mom35Ret = Mom35Ret[Mom35Ret != 0]
real_ret = ret[ret != 0]
Rsi12 = et.rsi(BOCMclp, 12)
# 策略
rsi6 = et.rsi(BOCMclp, 6)
rsi24 = et.rsi(BOCMclp, 24)
# rsi6捕捉买卖点
Sig1 = []
for i in rsi6:
if i > 80:
Sig1.append(-1)
elif i < 20:
Sig1.append(1)
else:
Sig1.append(0)
date1 = rsi6.index
Signal1 = pd.Series(Sig1, index=date1)
Signal1[Signal1 == 1].head(n=3)
Signal1[Signal1 == -1].head(n=3)
Signal2 = pd.Series(0, index=rsi24.index)
lagrsi6 = rsi6.shift(1)
lagrsi24 = rsi24.shift(1)
for i in rsi24.index:
if (rsi6[i] > rsi24[i]) & (lagrsi6[i] < lagrsi24[i]):
Signal2[i] = 1
elif (rsi6[i] < rsi24[i]) & (lagrsi6[i] > lagrsi24[i]):
Signal2[i] = -1
signal = Signal1 + Signal2
signal[signal >= 1] = 1
signal[signal <= -1] = -1
signal = signal.dropna()
tradSig = signal.shift(1)
tt = TradeTool()
BuyOnly = tt.strategy_analy(buy, ret)
SellOnly = tt.strategy_analy(sell, ret)
Trade = tt.strategy_analy(tradSig, ret)
Test = pd.DataFrame({
"BuyOnly": BuyOnly,
"SellOnly": SellOnly,
"Trade": Trade
})
# 累计收益率
cumStock = np.cumprod(1 + ret) - 1
cumTrade = np.cumprod(1 + tradeRet) - 1
# 12. 移动平均线
sma5 = et.smaCal(Close, 5)
# 12. 加权移动平均线
wma5 = et.wmaCal(Close, w)
# 12. 指数移动平均线
Ema = et.emaCal(Close, period)
print(Ema)
# 12. 指数加权移动平均线
Ewma = et.ewmaCal(Close, 5, 0.2)
# 13. 布林带
UnicomBBands = et.bbands(Close, 20, 2)
print(UnicomBBands)
multiplier = [1, 1.65, 1.96, 2, 2.58]
price2010 = Close['2010-01-04':'2010-12-31']
tt.CalBollRisk(price2010, multiplier)
# 14. 性能
btt = BackTestTool()
Performance1 = btt.perform(Close, tradSignal1)
print(Performance1)
# 15. 交易, 回测
KDtrade = btt.trade(KDSignal, close)
btt.backtest(KDtrade.Ret, KDtrade.KDtradeRet)
# 16. 上下突破
KDupbreak = et.upbreak(KValue, DValue) * 1
KDupbreak[KDupbreak == 1].head()
KDdownbreak = et.downbreak(KValue, DValue) * 1
KDdownbreak[KDdownbreak == 1].head()
# "金叉"与"死叉"交易策略绩效表现
btt.backtest(KDbreak.Ret, KDbreak.KDbreakRet)
# 17. 成交量指标
cumUpVol = et.VOblock(UpVol)
cumDownVol = et.VOblock(DownVol)
ALLVol = np.array([cumUpVol, cumDownVol]).transpose()
# 18. 判断持有
hold = tt.judge_hold(trade)
# 19. 单交易
TradeAccount = tt.TradeSim(close, hold)
print(TradeAccount)
plot_acf(SHRet, use_vlines=True, lags=30)
plot_pacf(SHRet, use_vlines=True, lags=30)
SHclose = SHindex.Clsindex
SHclose.plot()
plt.title('2014-2015年上证综指收盘指数时序图')
SHRet.plot()
plt.title('2014-2015年上证综指收益率指数时序图')
plot_acf(SHRet, use_vlines=True, lags=30)
plot_pacf(SHRet, use_vlines=True, lags=30)
plot_acf(SHclose, use_vlines=True, lags=30)
adfSHRet = ADF(SHRet)
print(adfSHRet.summary().as_text())
adfSHclose = ADF(SHclose)
print(adfSHclose.summary().as_text())
whiteNoise = np.random.standard_normal(size=500)
plt.plot(whiteNoise, c='b')
plt.title('White Noise')
LjungBox1 = stattools.q_stat(stattools.acf(SHRet)[1:13], len(SHRet))
print(LjungBox1)
print(LjungBox1[1][-1])
LjungBox2 = stattools.q_stat(stattools.acf(SHclose)[1:13], len(SHRet))
print(LjungBox2[1][-1])
##自相关系数
acfs=stattools.acf(SH_ret)
##偏自相关系数
pacfs=stattools.pacf(SH_ret)
plot_acf(SH_ret,use_vlines=True,lags=30)
SH_ret.plot()
plt.title('return')
SH_close.plot()
plt.title('close price')
adfSH_ret=ADF(SH_ret)
print(adfSH_ret)
adfSH_close=ADF(SH_close)
print(adfSH_close)
LjungBox_ret=stattools.q_stat(acfs,len(SH_ret))
LjungBox_ret[1][-1]
HS300_data['close']['2010-01-01':'2016-12-31']
HS300_data['2010-01-01':'2016-12-31']
model1=arima_model.ARIMA(SH_ret,order=(2,0,1)).fit()
model1.summary()
stattools.arma_order_select_ic(SH_ret,max_ma=4)
end) returns = RJ['close_price'].pct_change().dropna() returns.name = 'return' # returns.plot() # returns.column = ['return'] # print(returns) # 计算自相关系数 # acfs = stattools.acf(returns) # # print(acfs) # # 偏自相关系数 # pacfs = stattools.pacf(returns) # # print(pacfs) # # 自相关性图 # plot_acf(returns,use_vlines=True,lags=30) # # 偏自相关性图 # plot_pacf(returns,use_vlines=True,lags=30) # plot_acf(RJ['close_price'],use_vlines=True,lags=30) # # plt.show() # 单位根检验 # adfRJ= ADF(returns) # print(adfRJ.summary().as_text()) # adfClose = ADF(RJ['close_price']) # print(adfClose.summary().as_text()) # 白噪声检验 LB = stattools.q_stat(stattools.acf(returns), len(returns)) print(LB)
@author: Liu
"""
import numpy as np
import pandas as pd
import pandas_datareader as web
import matplotlib.pyplot as plt
import datetime
start=datetime.datetime(2018,1,1)
end=datetime.datetime(2019,6,30)
nasdaq=web.DataReader('^IXIC','yahoo',start,end)
nasdaq=nasdaq.dropna()
nasdaq=pd.DataFrame(nasdaq['Adj Close'].values,index=pd.to_datetime(nasdaq.index),columns=['Price'])
nasdaq=(nasdaq-nasdaq.shift(1))/nasdaq.shift(1)
nasdaq=nasdaq.dropna()
nasdaq.columns=['Return']
nasdaq.tail(3)
traindata=nasdaq[:-3]
from arch.unitroot import ADF
result=ADF(traindata.Return,max_lags=10)
print(result.summary().as_text())
from statsmodels.tsa import stattools
LjungBox=stattools.q_stat(stattools.acf(traindata)[1:12],len(traindata))
LjungBox[1][-1]
import statsmodels.graphics.tsaplots as ts
ts.plot_acf(traindata,use_vlines=True, lags=30)
print(adfReutn.summary().as_text())
# plot_acf(logReturn, lags=20)
# plot_pacf(logReturn, lags=20)
model1 = arima_model.ARIMA(logReturn.values, order=(2, 0, 0)).fit()
model2 = arima_model.ARIMA(logReturn.values, order=(0, 0, 2)).fit()
print("model1.aic=%f \t model2.aic=%f" % (model1.aic, model2.aic))
print(model2.sigma2)
strresid = model2.resid / math.sqrt(model2.sigma2)
# strresid.plot()
plt.subplot(211)
plt.plot(strresid)
# plot_acf(strresid , lags=20)
LinjiuBox = stattools.q_stat(stattools.acf(strresid)[1:13], len(strresid))
print("LinjiuBox:", LinjiuBox[1][-1], '\n', LinjiuBox)
# plt.subplot(212)
print(model2.forecast(10)[0])
print(type(model2.forecast(10)[0]))
test = pd.DataFrame(model2.forecast(10)[0])
test.index = logReturn1.index
test.columns = ['forecast']
test['return1'] = logReturn1.values
logReturn1.columns = ['return1']
print("test:\n", test)
# logReturn1['forecast'] = pd.Series( model2.forecast(10)[0])
#取对数以增加平稳性
inData = np.log(inData) #––––––––––––––––––
#在进行运算之前可以对数据进行归一化，进而降低loss
#scaler = MinMaxScaler()
scaler = MinMaxScaler(feature_range=(0, 1))
inData = scaler.fit_transform(inData.reshape(-1, 1))
'''
#数据平稳化，使Adfuller指数小于-3.435298，并且p-value小于0.05
ADF = adfuller(inData.ravel(),1)
print("ADF:")
print(ADF)
'''
stattools.q_stat(stattools.acf(inData)[1:13], len(inData))[1][-1]
plot_acf(inData, lags=30)
plot_pacf(inData, lags=30)
#定阶ARMA(p,q)
'''order = stattools.arma_order_select_ic(inData,max_ar=3,max_ma=3,ic=['aic','bic','hqic'])
print("(p,q):")
pq = order.bic_min_order
print(order.bic_min_order)#(p,q)'''
#将数据按站点分为SITE_SIZE组
site_names = [] #站点数据列表
site_cnames = [] #站点名字列表
for num in range(0, SITE_SIZE):
site_cnames.append(df.at[num * DATA_SIZE, u'事发街道'])
if num == 0:
import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
from statsmodels.tsa import stattools
from arch import arch_model
SHret = pd.read_table('TRD_IndexSum.txt', index_col='Trddt', sep='\t')
SHret.index = pd.to_datetime(SHret.index)
SHret = SHret.sort_index()
plt.subplot(211)
plt.plot(SHret**2)
plt.xticks([])
plt.title('Squared Daily Return of SH Index')
plt.subplot(212)
plt.plot(np.abs(SHret))
plt.title('Absolute Daily Return of SH Index')
LjungBox = stattools.q_stat(stattools.acf(SHret**2)[1:13], len(SHret))
print(LjungBox[1][-1])
am = arch_model(SHret)
model = am.fit(update_freq=0)
print(model.summary())
close.plot()
plt.title('2014-2015年加權股價指數收盤指數時序圖 ')
taiexRet.plot()
plt.title('2014-2015年加權股價指數收益率指數時序圖')
plot_acf(taiexRet,use_vlines=True,lags=30)
plot_pacf(taiexRet,use_vlines=True,lags=30)
plot_acf(close,use_vlines=True,lags=30)
adf_taiexRet=ADF(taiexRet)
print(adf_taiexRet.summary().as_text())
adfclose=ADF(close)
print(adfclose.summary().as_text())
#生成純隨機序列
whiteNoise=np.random.standard_normal(size=500)
#繪制該序列圖
plt.plot(whiteNoise,c='b')
plt.title('White Noise')
LjungBox1=stattools.q_stat(stattools.acf(taiexRet)[1:13],len(taiexRet))
LjungBox1
LjungBox1[1][-1]
LjungBox2=stattools.q_stat(stattools.acf(close)[1:13],len(taiexRet))
LjungBox2[1][-1]
from statsmodels.graphics.tsaplots import plot_pacf
plot_pacf(df["log_diff_12"].dropna(), method="ywmle", zero=False)
# Method : tsa.seasonal_decompose()
"""
Seasonal decomposition using moving averages.
"""
help(tsa.seasonal_decompose)
# Method : statsmodels.tsa.stattools.q_stat()
"""
Compute Ljung-Box Q Statistic.
Returns q-statistics, p-value
"""
from statsmodels.tsa.stattools import q_stat
q_stat(df["log_diff_12"].dropna(), nobs=len(df["log_diff_12"].dropna()))
# Class : statsmodels.api.tsa.arima.ARIMA()
"""
ARIMA model
"""
m = statsmodels.api.tsa.arima.ARIMA(endog=df["value"],
order=(1, 1, 0),
exog=df["time"])
res = m.fit()
print(res.summary())
# Method : statsmodels.api.qqplot()
"""
Q-Q plot of the quantiles of x versus the quantiles/ppf of a distribution.
"""
from statsmodels.tsa import stattools
import matplotlib.pyplot as plt
import numpy as np
from arch import arch_model
indexRet = pd.read_csv('index.csv', sep='\t')
indexRet.index = pd.to_datetime(indexRet.Date)
indexRet.head()
np.unique(indexRet.CoName)
taiexRet = indexRet.loc[indexRet.CoName == 'TSE Taiex '].ROI
taiexRet.head()
taiexRet.tail()
taiexRet = taiexRet.astype(np.float).dropna()
#繪制收益率平方序列圖
plt.subplot(211)
plt.plot(taiexRet**2)
plt.xticks([])
plt.title('Squared Daily Return of taiex')
plt.subplot(212)
plt.plot(np.abs(taiexRet))
plt.title('Absolute Daily Return of taiex')
LjungBox = stattools.q_stat(stattools.acf(taiexRet**2)[1:13], len(taiexRet))
LjungBox[1][-1]
am = arch_model(taiexRet)
model = am.fit(update_freq=0)
print(model.summary())
for code in codes:
if ar>lines*columns:
pdf.savefig(fig)
fig = plt.figure()
ar=1
fig.add_subplot(lines, columns, ar)
closevalues = pd.Series(np.array(feed.getDataSeries(instrument=code).getCloseDataSeries()))
tsaplots.plot_acf(np.log(closevalues).diff().dropna(), alpha=0.05, lags=40, ax=fig.gca(), title=code)
ar += 1
pdf.savefig(fig)
plt.close('all')
#################################################################################################
#Trying to fit an ARMA model
#################################################################################################
stattools.q_stat()
stattools.acf()
closevalues = pd.Series(np.array(feed.getDataSeries(instrument=codes[1]).getCloseDataSeries()))
# arma = smapi.tsa.ARMA(np.array(np.log(closevalues).diff().dropna()), (0, 5)).fit(maxiter=10000)
arma = smapi.tsa.ARMA(np.array(closevalues), (0, 5)).fit(maxiter=10000)
pvalue = diagnostic.acorr_ljungbox(arma.resid, lags=[20])[1]
print(pvalue)
results = {}
for code in codes:
final_arma = None
final_aic = 1e200
final_order = None
for ar in range(1, 5):
for ma in range(1, 5):
start = datetime.datetime(2018, 1, 1)
end = datetime.datetime(2019, 6, 30)
nasdaq = web.DataReader('^IXIC', 'yahoo', start, end)
nasdaq = nasdaq.dropna()
nasdaq = pd.DataFrame(nasdaq['Adj Close'].values,
index=pd.to_datetime(nasdaq.index),
columns=['Price'])
nasdaq = (nasdaq - nasdaq.shift(1)) / nasdaq.shift(1)
nasdaq = nasdaq.dropna()
nasdaq.columns = ['Return']
traindata = nasdaq
plt.subplot(211)
plt.plot(traindata**2)
plt.xticks([])
plt.subplot(212)
plt.plot(np.abs(traindata))
from statsmodels.tsa import stattools
LjungBox = stattools.q_stat(stattools.acf(traindata**2)[1:13], len(traindata))
LjungBox[1][-1]
from arch import arch_model
am = arch_model(traindata)
model = am.fit(update_freq=0)
print(model.summary())
import pandas as pd
import matplotlib.pyplot as plt
#5.
CRSPday = pd.read_csv('Data/Part4/002/CRSPday.csv')
ibm = CRSPday.ibm
ibm.plot()
from statsmodels.graphics.tsaplots import *
plot_acf(ibm, lags=20)
from statsmodels.tsa import stattools
LjungBox = stattools.q_stat(stattools.acf(ibm)[1:13], len(ibm))
LjungBox[1][-1]
#6.
ge = CRSPday.iloc[:, 3]
ge.plot()
plot_acf(ge, lags=20)
LjungBox = stattools.q_stat(stattools.acf(ge)[1:2], len(ge))
LjungBox[1][-1]
LjungBox = stattools.q_stat(stattools.acf(ge)[1:9], len(ge))
LjungBox[1][-1]
#7.
SP500 = pd.read_csv('Data/Part4/002/SP500.csv')
r500 = SP500.r500
r500.plot()
fig = plot_acf(SHClose, use_vlines=True, lags=30)
fig.savefig("SHRet_acf.png")
# 单位根检验
adfSHRet = ADF(SHRet)
print(adfSHRet.summary().as_text())
adfSHClose = ADF(SHClose)
print(adfSHClose.summary().as_text())
# 白噪声
whiteNoise = np.random.standard_normal(size=500)
fig = plt.figure()
plt.plot(whiteNoise, c="b")
fig.savefig("whiteNoise.png")
# 上证综指的白噪声检测
LB1 = stattools.q_stat(stattools.acf(SHRet)[1:13], len(SHRet))
print(LB1)
print(LB1[1][-1])
LB2 = stattools.q_stat(stattools.acf(SHClose)[1:13], len(SHClose))
print(LB2[1][-1])
# ARMA建模
cpi = pd.read_csv("CPI.csv", index_col="time")
cpi.index = pd.to_datetime(cpi.index)
print(cpi.head())
print(cpi.shape)
# 训练集
CPITrain = cpi[3:]
# 绘制时序图
fig = plt.figure()
plt.plot(cpi)
adfshindex = ADF(shindex)
print(adfshindex.summary().as_text())
whitenoise = np.random.standard_normal(500)
plt.plot(whitenoise,c = 'b')
cpi = ts.get_cpi()
cpi.index = pd.to_datetime(cpi['month'])
cpi = cpi['cpi']
cpitrain = cpi['2016-01-01':'2000-01-01']
cpitrain.plot()
#是否平稳
print(ADF(cpitrain,max_lags=10).summary().as_text())
#是否白噪声
ljb0 = stattools.q_stat(stattools.acf(cpitrain)[1:12],len(cpitrain))
ljb0[1][-1]
#识别ARMA模型参数pq
plot_acf(cpitrain,use_vlineEs=True,lags=30)
plot_pacf(cpitrain,use_vlines=True,lags=30)
model1 = arima_model.ARIMA(cpitrain.values,order=(1, 0, 1)).fit()
model1.summary()
p = np.arange(1,4)
q = np.arange(1,4)
result = dict()
for i in p:
for j in q:
model1 = arima_model.ARIMA(cpitrain.values, order=(i, 0, j)).fit()
import pandas as pd
#3.
CRSPday = pd.read_csv('Data/Part4/004/CRSPday.csv')
ibm = CRSPday.ibm
ibm.plot()
from statsmodels.graphics.tsaplots import *
plot_acf(ibm**2, lags=20)
from statsmodels.tsa import stattools
LjungBox = stattools.q_stat(stattools.acf(ibm**2)[1:13], len(ibm))
LjungBox[1][-1]
#4.
import pandas_datareader.data as web
import datetime as dt
google = web.DataReader('GOOGL', 'yahoo', dt.datetime(2004, 1, 1),
dt.datetime(2015, 12, 31))
google = google.asfreq('M', 'ffill', 'end')
googleRet = (google.Close - google.Close.shift(1)) / google.Close.shift(1)
googleRet = googleRet.dropna()
googleRet.plot()
plot_acf(googleRet, lags=20)
plot_pacf(googleRet, lags=20)
LjungBox = stattools.q_stat(stattools.acf(googleRet)[1:13], len(googleRet))
LjungBox[1][-1]
(googleRet**2).plot()
trend='c',
method='aeg',
maxlag=None,
autolag='aic',
return_results=None)
#return
#coint_t : float
#t-statistic of unit-root test on residuals
#pvalue : float
#MacKinnon’s approximate, asymptotic p-value based on MacKinnon (1994)
#crit_value : dict
#Critical values for the test statistic at the 1 %, 5 %, and 10 % levels based on regression curve. This depends on the number of observations
'''Ljung-Box白噪声检验'''
x = stattools.acf(array, nlags=40, unbiased=False, qstat=False, alpha=None)
nobs = array
stattools.q_stat(x, nobs, type='ljungbox')
# x所检验的自相关系数序列 nobs计算自相关系数序列x所用的样本数n
# return
#检验的统计量array
#p值的array 若p小于0.05 则拒绝原假设 则不是白噪声 存在自相关性
# %%
# ================================================================
# 3. 回归
#=================================================================
# OLS ----------------------------
'''OLS'''
array1 = st.add_constant(array)
model = st.OLS(array_y, array1).fit()
print(model.summary())
print(model.fittedvalues) # fit values
print(model.bic) # bic
logReturn=pd.Series((np.log(clprice))).diff().dropna() logReturn.plot() adf=ADF(logReturn,lags=6) print(adf.summary().as_text()) plot_acf(logReturn,lags=20) plot_pacf(logReturn,lags=20) model1=arima_model.ARIMA(logReturn.values,order=(0,0,2)).fit() model2=arima_model.ARIMA(logReturn.values,order=(2,0,0)).fit() model1.aic model2.aic import math stdresid=model2.resid/math.sqrt(model2.sigma2) stdresid.plot() plot_acf(stdresid,lags=20) LjungBox=stattools.q_stat(stattools.acf(stdresid)[1:13],len(stdresid)) LjungBox[1][-1] pd.Series(model2.forecast(10)[0]).plot()
def q_stat(self, timeseries):
autocorrelation_coefs = stattools.acf(timeseries)
result = stattools.q_stat(autocorrelation_coefs)
QstatResult = namedtuple('QstatResult', 'statistic pvalue')
return QstatResult(result[0], result[1])
CPI=CPI.sort_index() CPItrain=CPI[:-3] CPItrain.tail(n=3) CPItest = CPI[-3:] CPItest CPI.plot(title='CPI 2001-2014') from arch.unitroot import ADF CPItrain=CPItrain.dropna() print(ADF(CPItrain,max_lags=10).summary().as_text()) from statsmodels.tsa import stattools LjungBox=stattools.q_stat(stattools.acf(CPItrain)[1:12],len(CPItrain)) LjungBox[1][-1] from statsmodels.graphics.tsaplots import * import matplotlib.pyplot as plt #將畫面一分為二 axe1=plt.subplot(121) axe2=plt.subplot(122) #在第一個畫面中畫出序列的自相關係數圖 plot1=plot_acf(CPItrain,lags=30,ax=axe1) #在第二個畫面中畫出序列的偏自相關係數圖 plot2=plot_pacf(CPItrain,lags=30,ax=axe2) from statsmodels.tsa import arima_model #order表示建立的模型的階數，c(1,0,1)表示建立的是ARMA(1,1)模型；
#model = sm.tsa.ARMA(y, (2, 1)).fit(trend='nc', disp=0) #Descriptive TSA Statistics stools.adfuller(y) stools.kpss(y) #Plot ACF and PACF tplot.plot_acf(y) tplot.plot_pacf(y) #Fir ARMA Model tsmodel = sm.tsa.ARMA(y, (2, 1)).fit(trend='nc', disp=0) residuals = tsmodel.resid stools.q_stat(tsmodel.resid, nobs=len(tsmodel.resid)) fig = plt.figure() qq_ax = fig.add_subplot() sm.qqplot(y, line='s', ax=qq_ax) plt.show() ############################################################################### #5. Load package datasets. Use data(faithful) to import the waiting time (in min) # between eruptions and the duration (in min) of the eruption for the Old Faithful # geyser in Yellowstone National Park, Wyoming, USA. We would like to forecast # when the next ejection would be. # • The length of the samples? How many variables? # • Perform unit root tests on the data. Is there unit-root in the data? # • Plot ACF and PACF to determine the appropriate order # • Fitting the time series model
