统计模型应用--平稳性

平稳性

from numpy import cumsum , log,  polyfit, sqrt, std, subtract

from numpy.random import randn

def hurst(ts):

      lags = range(2, 100)

      tau = [sqrt(std(subtract(ts[lag:], ts[:-lag]))) for lag in lags]

      poly = polyfit(log(lags), log(tau), 1)

      return poly[0]*2.0

gdm = log(cumsum(randn(100000))+1000) #构造的布朗运动

mr = log(randn(100000)+1000)  #构造的均值回复

tr = log(cumsum(randn(100000)+1)+1000) #构造趋势的时间序列

print("hurst(GBM): %s" % hurst(gdm))

print("hurst(MR): %s" % hurst(mr))

print("hurst(TR): %s" % hurst(tr))

print("hurst(AMZN): %s" % hurst(amzn['AdjClose'])) # 股票价格的随机游走

协整-配对交易

对于单个股票来讲，平均回复交易策略几乎失效没用，因此平均回复交易策略应用于投资组合

def plot_price_series(df, tsl, ts2):
    months = mdates.MonthLocator()
    fig, ax = plt.subplots()
    ax.plot(df.index, df[ts1], label=ts1)
    ax.plot(df.index, df[ts2], label=ts2)
    ax.xaxis.set_major_locator(months)
    ax.xaxis.set_major_formatter(mdate.DateFormatter('%b %Y'))
    ax.set_xlim(datetime.datetime(2012,1,1),datetime.datetime(2013,1,1))
    ax.grid(True)
    fig.autofmt.xdate()
    plt.xlabel('Month/Year')
    plt.ylabel('Price($)')
    plt.title('%s and %s Daily Prices' % (ts1, ts2))
    plt.legend()
    plt.show()
def plot_scatter_series(df, ts1, ts2):
    plt.xlabel('%s Price($)' % ts1)
    plt.ylabel('%s Price($)' % ts2)
    plt.title('%s and %s Price Scatterplot' % (ts1, ts2))
    plt.scatter(df[ts1],df[ts2])
    plt.show()
def plot_residuals(df):
    months = mdate,MonthLocator()
    fig, ax = plt.subplots()
    ax.plot(df.index, df['res'], label='Residuals')
    ax.xaxis.set_major_locator(months)
    ax.xaxis.set_major_foematter(mdates.DateFormatter('%b %Y'))
    ax.set_xlim(datetime.datetime(2012,1,1),datetime.datetime(2013,1,1))
    ax.grid(True)
    fig.autofmt_xdate()
    plt.xlabel('Month/Year')
    plt.ylabel('Price($)')
    plt.title('Residual Plot')
    plt.legend()
    plt.plot(df['res'])
    plt.show()
if __name__ == "__main__":
   start = datetime.datetime(2012,1,1)
   end = datetime.datetime(2013,1,1)
   arex = web.DataReader("AREX","quandl", start,end).sort_index()
   wll = web.DataReader("WLL", "quandl", start,end),sort_index()
   df =pd.DataReader(index=arex.index)
   df["AREX"] = arex["AdjClose"]
   df["WLL"] = wll["AdjClose"]
   plot_price_series(df,"AREX"，"WLL")
   plot_scatter_series(df,"AREX"，"WLL")
   y=df['WLL']
   x=df['AREX']
   res = sm.OLS(y,x).fit()
   beta_hr = res.params.AREX
   df["res"] = df['WLL'] - beta_hr*df["AREX"]
   plot_residuals(df)
   cadf = ts.adfuller(df["res"])
   pprint.pprint(cadf)