python实现技术指标(简单移动平均，加权移动平均线，指数移动平均线)

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移动平均线是最常见的技术指标，它能够去除时间序列的短期波动，使得数据变得平滑，从而可以方便看出序列的趋势特征。常见的移动平均线有简单移动平均线，加权移动平均线，指数移动平均线。

一. 简单移动平均(SMA)

简单移动平均线(Simple Moving Average)，很好理解，就是将过去n个窗口内的价格进行算术平均
$$SM{A}_t(n)=\frac{1}{n}(X_{t-n+1}+X_{t-n+2}+...+X_t)$$

以下是贵州茅台从$\mathrm{2018.6.1}$到$\mathrm{2019.12.31}$收盘价的简单移动平均线。

import pandas as pd
import baostock as bs
import matplotlib.pyplot as pltdef get_data(code, start_date, end_date):lg = bs.login()rs = bs.query_history_k_data_plus(code,"date,code,open,high,low,close,volume",start_date=start_date, end_date=end_date,frequency="d", adjustflag="3")data_list = []while (rs.error_code == '0') & rs.next():data_list.append(rs.get_row_data())result = pd.DataFrame(data_list, columns=rs.fields)bs.logout()result['date'] = pd.to_datetime(result['date'])result['open'] = result['open'].astype(float)result['high'] = result['high'].astype(float)result['low'] = result['low'].astype(float)result['close'] = result['close'].astype(float)result['volume'] = result['volume'].astype(float)result.set_index(result['date'], inplace=True)return resultif __name__ == '__main__':data = get_data('sh.600519', '2018-06-01', '2019-12-31')data['SMA10'] = data['close'].rolling(10).mean()data['SMA20'] = data['close'].rolling(20).mean()fig = plt.figure(figsize=(20, 10))ax = fig.add_subplot()ax.plot(data.index, data['close'], linestyle='--', label='close')ax.plot(data.index, data['SMA10'], label='SMA10')ax.plot(data.index, data['SMA20'], label='SMA20')ax.legend()plt.show()

二. 加权移动平均(WMA)

加权移动平均(Weighted Moving Average)在计算平均值时，对最近的数据赋予的权重比历史数据的权重要大。
$$WMA(n{)}_t=\frac{n{X}_t+(n-1)X_{t-1}+...+2X_{t-n+2}+X_{t-n+1}}{n+(n-1)+...+2+1}$$

以下是贵州茅台从$\mathrm{2018.6.1}$到$\mathrm{2019.12.31}$收盘价的加权移动平均线。

import numpy as np
import pandas as pd
import baostock as bs
import matplotlib.pyplot as pltdef get_data(code, start_date, end_date):lg = bs.login()rs = bs.query_history_k_data_plus(code,"date,code,open,high,low,close,volume",start_date=start_date, end_date=end_date,frequency="d", adjustflag="3")data_list = []while (rs.error_code == '0') & rs.next():data_list.append(rs.get_row_data())result = pd.DataFrame(data_list, columns=rs.fields)bs.logout()result['date'] = pd.to_datetime(result['date'])result['open'] = result['open'].astype(float)result['high'] = result['high'].astype(float)result['low'] = result['low'].astype(float)result['close'] = result['close'].astype(float)result['volume'] = result['volume'].astype(float)result.set_index(result['date'], inplace=True)return resultif __name__ == '__main__':data = get_data('sh.600519', '2018-06-01', '2019-12-31')n = 10weights = np.array(range(1, n + 1))weights_sum = np.sum(weights)data['WMA10'] = data['close'].rolling(window=n, min_periods=n).apply(lambda x: np.sum(x * weights) / weights_sum)fig = plt.figure(figsize=(20, 10))ax = fig.add_subplot()ax.plot(data.index, data['close'], linestyle='--', label='close')ax.plot(data.index, data['WMA10'], label='WMA10')ax.legend()plt.show()

三. 指数移动平均(EMA)

指数移动平均(Exponential Moving Average)跟加权移动平均类似，只是它对最近的数据赋予了更高的权重。
$$EM{A}_t=\alpha X_t+(1-\alpha )EM{A}_{t-1}$$
$\alpha$一般取$2/(n+1)$, $n$为数据序列长度，pandas中计算EMA一般可以使用ewm方法。

以下是贵州茅台从$\mathrm{2018.6.1}$到$\mathrm{2019.12.31}$收盘价的指数移动平均线。

import numpy as np
import pandas as pd
import baostock as bs
import matplotlib.pyplot as pltdef get_data(code, start_date, end_date):lg = bs.login()rs = bs.query_history_k_data_plus(code,"date,code,open,high,low,close,volume",start_date=start_date, end_date=end_date,frequency="d", adjustflag="3")data_list = []while (rs.error_code == '0') & rs.next():data_list.append(rs.get_row_data())result = pd.DataFrame(data_list, columns=rs.fields)bs.logout()result['date'] = pd.to_datetime(result['date'])result['open'] = result['open'].astype(float)result['high'] = result['high'].astype(float)result['low'] = result['low'].astype(float)result['close'] = result['close'].astype(float)result['volume'] = result['volume'].astype(float)result.set_index(result['date'], inplace=True)return resultif __name__ == '__main__':data = get_data('sh.600519', '2018-06-01', '2019-12-31')[['date', 'close']]data['EMA10'] = data['close'].ewm(span=10, adjust=True).mean()fig = plt.figure(figsize=(20, 10))ax = fig.add_subplot()ax.plot(data.index, data['close'], linestyle='--', label='close')ax.plot(data.index, data['EMA10'], label='EMA10')ax.legend()plt.show()

四. 对比三种均线

1. 三种均线的权重对比

从权重思维来看，三种方法都可以认为是加权平均。

• SMA：权重系数一致
• WMA：权重系数随时间间隔线性递减
• EMA：权重系数随时间间隔指数递减

下面通过程序展示三种均线的权重系数的递减情况

import numpy as np
import pandas as pd
import matplotlib.pyplot as pltif __name__ == '__main__':n = 30# 简单移动平均权重weight_sma = np.ones(n)# 加权移动平均weights_wma = range(1, n + 1)weights_wma /= np.sum(weights_wma)weights_wma = weights_wma[::-1]# 指数移动平均alpha = 2 / (n + 1)t = np.array(range(0, n))weights_ema = alpha * (1 - alpha) ** tdf = pd.DataFrame({"SMA30-Weights": weight_sma, "WMA30-Weights": weights_wma, "EMA30-Weights": weights_ema})ax = df.plot.bar(subplots=True, figsize=(16, 6), title=['', '', ''])plt.show()

从上图中的权重系数随时间间隔衰减情况可以看出，指数移动平均系数衰减较快，也因此一般也能更快的发现趋势的变化。

2. 三种均线可视化

下面展示贵州茅台从2018.6.1到2019.12.31收盘价的三种移动均线。

import numpy as np
import pandas as pd
import baostock as bs
import matplotlib.pyplot as pltdef get_data(code, start_date, end_date):lg = bs.login()rs = bs.query_history_k_data_plus(code,"date,code,open,high,low,close,volume",start_date=start_date, end_date=end_date,frequency="d", adjustflag="3")data_list = []while (rs.error_code == '0') & rs.next():data_list.append(rs.get_row_data())result = pd.DataFrame(data_list, columns=rs.fields)bs.logout()result['date'] = pd.to_datetime(result['date'])result['open'] = result['open'].astype(float)result['high'] = result['high'].astype(float)result['low'] = result['low'].astype(float)result['close'] = result['close'].astype(float)result['volume'] = result['volume'].astype(float)result.set_index(result['date'], inplace=True)return result# 简单移动平均
def sma_demo(data, n):data['SMA20'] = data['close'].rolling(window=n, min_periods=n).mean()return data# 加权移动平均
def wma_demo(data, n):weights = np.array(range(1, n + 1))weights_sum = np.sum(weights)data['WMA20'] = data['close'].rolling(window = n, min_periods=n).apply(lambda x: np.sum(x * weights) / weights_sum)return data# 指数平均
def ema_demo(data, n):data['EMA20'] = data['close'].ewm(span=n, min_periods=n, adjust=True).mean()return dataif __name__ == '__main__':data = get_data('sh.600519', '2018-06-01', '2019-12-31')[['close']]data = sma_demo(data, 20)data = wma_demo(data, 20)data = ema_demo(data, 20)fig = plt.figure(figsize=(30, 20))ax = fig.add_subplot()ax.plot(data.index, data['close'], linestyle='--', label='close')ax.plot(data.index, data['SMA20'], label='SMA20')ax.plot(data.index, data['WMA20'], label='WMA20')ax.plot(data.index, data['EMA20'], label='EMA20')ax.legend()plt.show()

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