数据平滑
数据的平滑处理通常包含有降噪、拟合等操作。降噪的功能意在去除额外的影响因素，拟合的目的意在数学模型化，可以通过更多的数学方法识别曲线特征。
案例：绘制两只股票收益率曲线。收益率 =（后一天收盘价-前一天收盘价） / 前一天收盘价
使用卷积完成数据降噪。
# 数据平滑import numpy as npimport matplotlib.pyplot as mpimport datetime as dtimport matplotlib.dates as mddef dmy2ymd(dmy): """ 把日月年转年月日 :param day: :return: """ dmy = str(dmy, encoding='utf-8') t = dt.datetime.strptime(dmy, '%d-%m-%Y') s = t.date().strftime('%Y-%m-%d') return sdates, bhp_closing_prices = \ np.loadtxt('bhp.csv', delimiter=',', usecols=(1, 6), unpack=True, dtype='M8[D],f8', converters={1: dmy2ymd}) # 日月年转年月日vale_closing_prices = \ np.loadtxt('vale.csv', delimiter=',', usecols=(6,), unpack=True) # 因为日期一样,所以此处不读日期# print(dates)# 绘制收盘价的折现图mp.figure('APPL', facecolor='lightgray')mp.title('APPL', fontsize=18)mp.xlabel('Date', fontsize=14)mp.ylabel('Price', fontsize=14)mp.grid(linestyle=":")# 设置刻度定位器# 每周一一个主刻度,一天一个次刻度ax = mp.gca()ma_loc = md.WeekdayLocator(byweekday=md.MO)ax.xaxis.set_major_locator(ma_loc)ax.xaxis.set_major_formatter(md.DateFormatter('%Y-%m-%d'))ax.xaxis.set_minor_locator(md.DayLocator())# 修改dates的dtype为md.datetime.datetiemdates = dates.astype(md.datetime.datetime)# 计算两只股票的收益率,并绘制曲线bhp_returns = np.diff(bhp_closing_prices) / bhp_closing_prices[:-1]vale_returns = np.diff(vale_closing_prices) / vale_closing_prices[:-1]mp.plot(dates[1:], bhp_returns, color='red', alpha=0.1,label='bhp returns')mp.plot(dates[1:], vale_returns, color='blue',alpha=0.1, label='vale returns')#卷积降噪kernel = np.hanning(8)kernel/=kernel.sum()bhp_convalved = np.convolve(bhp_returns,kernel,'valid')vale_convalved = np.convolve(vale_returns,kernel,'valid')mp.plot(dates[8:],bhp_convalved,color='dodgerblue',alpha=0.8,label='bhp convalved')mp.plot(dates[8:],vale_convalved,color='orangered',alpha=0.8,label='vale convalved')mp.legend()mp.gcf().autofmt_xdate()mp.show() 
对处理过的股票收益率做多项式拟合。
# 数据平滑import numpy as npimport matplotlib.pyplot as mpimport datetime as dtimport matplotlib.dates as mddef dmy2ymd(dmy): """ 把日月年转年月日 :param day: :return: """ dmy = str(dmy, encoding='utf-8') t = dt.datetime.strptime(dmy, '%d-%m-%Y') s = t.date().strftime('%Y-%m-%d') return sdates, bhp_closing_prices = \ np.loadtxt('bhp.csv', delimiter=',', usecols=(1, 6), unpack=True, dtype='M8[D],f8', converters={1: dmy2ymd}) # 日月年转年月日vale_closing_prices = \ np.loadtxt('vale.csv', delimiter=',', usecols=(6,), unpack=True) # 因为日期一样,所以此处不读日期# print(dates)# 绘制收盘价的折现图mp.figure('APPL', facecolor='lightgray')mp.title('APPL', fontsize=18)mp.xlabel('Date', fontsize=14)mp.ylabel('Price', fontsize=14)mp.grid(linestyle=":")# 设置刻度定位器# 每周一一个主刻度,一天一个次刻度ax = mp.gca()ma_loc = md.WeekdayLocator(byweekday=md.MO)ax.xaxis.set_major_locator(ma_loc)ax.xaxis.set_major_formatter(md.DateFormatter('%Y-%m-%d'))ax.xaxis.set_minor_locator(md.DayLocator())# 修改dates的dtype为md.datetime.datetiemdates = dates.astype(md.datetime.datetime)# 计算两只股票的收益率,并绘制曲线bhp_returns = np.diff(bhp_closing_prices) / bhp_closing_prices[:-1]vale_returns = np.diff(vale_closing_prices) / vale_closing_prices[:-1]mp.plot(dates[1:], bhp_returns, color='red', alpha=0.1,label='bhp returns')mp.plot(dates[1:], vale_returns, color='blue',alpha=0.1, label='vale returns')#卷积降噪kernel = np.hanning(8)kernel/=kernel.sum()bhp_convalved = np.convolve(bhp_returns,kernel,'valid')vale_convalved = np.convolve(vale_returns,kernel,'valid')mp.plot(dates[8:],bhp_convalved,color='dodgerblue',alpha=0.1,label='bhp convalved')mp.plot(dates[8:],vale_convalved,color='orangered',alpha=0.1,label='vale convalved')#多项式拟合days = dates[8:].astype('M8[D]').astype('i4')bhp_p = np.polyfit(days,bhp_convalved,3)bhp_val = np.polyval(bhp_p,days)vale_p = np.polyfit(days,vale_convalved,3)vale_val = np.polyval(vale_p,days)mp.plot(dates[8:],bhp_val,color='orangered',label='bhp polyval')mp.plot(dates[8:],vale_val,color='blue',label='vale polyval')mp.legend()mp.gcf().autofmt_xdate()mp.show() 
通过获取两个函数的焦点可以分析两只股票的投资收益比。
# 数据平滑import numpy as npimport matplotlib.pyplot as mpimport datetime as dtimport matplotlib.dates as mddef dmy2ymd(dmy): """ 把日月年转年月日 :param day: :return: """ dmy = str(dmy, encoding='utf-8') t = dt.datetime.strptime(dmy, '%d-%m-%Y') s = t.date().strftime('%Y-%m-%d') return sdates, bhp_closing_prices = \ np.loadtxt('bhp.csv', delimiter=',', usecols=(1, 6), unpack=True, dtype='M8[D],f8', converters={1: dmy2ymd}) # 日月年转年月日vale_closing_prices = \ np.loadtxt('vale.csv', delimiter=',', usecols=(6,), unpack=True) # 因为日期一样,所以此处不读日期# print(dates)# 绘制收盘价的折现图mp.figure('APPL', facecolor='lightgray')mp.title('APPL', fontsize=18)mp.xlabel('Date', fontsize=14)mp.ylabel('Price', fontsize=14)mp.grid(linestyle=":")# 设置刻度定位器# 每周一一个主刻度,一天一个次刻度ax = mp.gca()ma_loc = md.WeekdayLocator(byweekday=md.MO)ax.xaxis.set_major_locator(ma_loc)ax.xaxis.set_major_formatter(md.DateFormatter('%Y-%m-%d'))ax.xaxis.set_minor_locator(md.DayLocator())# 修改dates的dtype为md.datetime.datetiemdates = dates.astype(md.datetime.datetime)# 计算两只股票的收益率,并绘制曲线bhp_returns = np.diff(bhp_closing_prices) / bhp_closing_prices[:-1]vale_returns = np.diff(vale_closing_prices) / vale_closing_prices[:-1]mp.plot(dates[1:], bhp_returns, color='red', alpha=0.1,label='bhp returns')mp.plot(dates[1:], vale_returns, color='blue',alpha=0.1, label='vale returns')#卷积降噪kernel = np.hanning(8)kernel/=kernel.sum()bhp_convalved = np.convolve(bhp_returns,kernel,'valid')vale_convalved = np.convolve(vale_returns,kernel,'valid')mp.plot(dates[8:],bhp_convalved,color='dodgerblue',alpha=0.1,label='bhp convalved')mp.plot(dates[8:],vale_convalved,color='orangered',alpha=0.1,label='vale convalved')#多项式拟合days = dates[8:].astype('M8[D]').astype('i4')bhp_p = np.polyfit(days,bhp_convalved,3)bhp_val = np.polyval(bhp_p,days)vale_p = np.polyfit(days,vale_convalved,3)vale_val = np.polyval(vale_p,days)mp.plot(dates[8:],bhp_val,color='orangered',label='bhp polyval')mp.plot(dates[8:],vale_val,color='blue',label='vale polyval')#求两个多项式函数的焦点diff_p = np.polysub(bhp_p,vale_p)xs = np.roots(diff_p)print(xs.astype('M8[D]'))#['2011-03-23' '2011-03-11' '2011-02-21']mp.legend()mp.gcf().autofmt_xdate()mp.show()