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 np import matplotlib.pyplot as mp import datetime as dt import matplotlib.dates as md def 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 s dates, 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.datetiem dates = 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 np import matplotlib.pyplot as mp import datetime as dt import matplotlib.dates as md def 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 s dates, 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.datetiem dates = 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 np import matplotlib.pyplot as mp import datetime as dt import matplotlib.dates as md def 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 s dates, 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.datetiem dates = 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()