如何计算Tick数据分布中POC的上下一倍标准差？

现有如下Tick数据：

,timestamp,close,security_code,volume,bid_volume,ask_volume
2024-04-02 01:00:00.128123+00:00,2024-04-02 01:00:00.128123+00:00,18465.5,NQ,1,0,1
2024-04-02 01:00:00.128123+00:00,2024-04-02 01:00:00.128123+00:00,18465.5,NQ,1,0,1
2024-04-02 01:00:03.782064+00:00,2024-04-02 01:00:03.782064+00:00,18465.25,NQ,1,0,1
2024-04-02 01:00:04.112603+00:00,2024-04-02 01:00:04.112603+00:00,18465.0,NQ,1,0,1
2024-04-02 01:00:04.112603+00:00,2024-04-02 01:00:04.112603+00:00,18465.0,NQ,1,0,1
2024-04-02 01:00:04.112603+00:00,2024-04-02 01:00:04.112603+00:00,18464.75,NQ,1,0,1
2024-04-02 01:00:04.112603+00:00,2024-04-02 01:00:04.112603+00:00,18464.75,NQ,1,0,1
2024-04-02 01:00:05.759876+00:00,2024-04-02 01:00:05.759876+00:00,18464.5,NQ,1,0,1
2024-04-02 01:00:06.273686+00:00,2024-04-02 01:00:06.273686+00:00,18464.75,NQ,5,5,0

已通过以下Python代码计算出实时最高价（high）、最低价（low）和成交量密集点（POC）：

import pandas as pd, matplotlib.pyplot as plt
from collections import defaultdict

df = pd.read_csv("csv/nq_out_daily.csv")
df.drop('Unnamed: 0', inplace=True, axis=1)

df['timestamp'] = pd.to_datetime(df['timestamp'])
df["timestamp"] = df['timestamp'].dt.strftime('%d-%m-%Y %H:%M:%S')

summary = {"high": [], "low": [], "poc": []}

dist = defaultdict(float)
current_high = current_low = None
for idx, (timestamp, tick, ask, bid) in enumerate(zip(df.timestamp, df.close, df.ask_volume, df.bid_volume)):

    current_high = tick if (current_high is None or tick > current_high) else current_high
    current_low = tick if (current_low is None or tick < current_low) else current_low
    dist[tick] += 1

    summary["high"].append(current_high)
    summary["low"].append(current_low)
    summary["poc"].append(max(dist, key=dist.get))


# plot the summary
fig = plt.figure()
x = range(len(summary["high"]))

plt.scatter(x, summary["high"], s=1)
plt.scatter(x, summary["low"], s=1)
plt.scatter(x, summary["poc"], s=1)

plt.legend(['high', 'low', 'poc'])
plt.savefig(f"distribution.png")
plt.close(fig)

如何计算POC的上下一倍标准差？

要计算POC的上下一倍标准差，需基于价格对应的成交量分布计算加权标准差（权重为各价格的累计成交量），再用POC值加减该标准差得到区间。具体步骤和修改后的代码如下：

核心逻辑 #

1. 利用已有的dist字典维护每个价格的累计成交量
2. 计算价格的加权平均值（以成交量为权重）
3. 计算加权标准差：公式为 $\sigma = \sqrt{\frac{\sum w_i \times (x_i - \mu)^2}{\sum w_i}}$，其中$\mu$是加权均值，$w_i$是价格$x_i$的累计成交量
4. 实时计算POC的上下一倍标准差并加入结果集合

修改后的完整代码 #

import pandas as pd, matplotlib.pyplot as plt
from collections import defaultdict
import math

df = pd.read_csv("csv/nq_out_daily.csv")
df.drop('Unnamed: 0', inplace=True, axis=1)

df['timestamp'] = pd.to_datetime(df['timestamp'])
df["timestamp"] = df['timestamp'].dt.strftime('%d-%m-%Y %H:%M:%S')

summary = {"high": [], "low": [], "poc": [], "poc_upper_std": [], "poc_lower_std": []}

dist = defaultdict(float)
current_high = current_low = None

for idx, (timestamp, tick, ask, bid) in enumerate(zip(df.timestamp, df.close, df.ask_volume, df.bid_volume)):
    # 更新实时高低点和成交量分布
    current_high = tick if (current_high is None or tick > current_high) else current_high
    current_low = tick if (current_low is None or tick < current_low) else current_low
    dist[tick] += 1

    # 获取当前POC
    current_poc = max(dist, key=dist.get)
    
    # 计算加权均值和加权标准差
    total_volume = sum(dist.values())
    weighted_mean = sum(price * vol for price, vol in dist.items()) / total_volume
    weighted_variance = sum(vol * (price - weighted_mean)**2 for price, vol in dist.items()) / total_volume
    weighted_std = math.sqrt(weighted_variance)
    
    # 计算POC上下一倍标准差
    poc_upper = current_poc + weighted_std
    poc_lower = current_poc - weighted_std
    
    # 存入结果集合
    summary["high"].append(current_high)
    summary["low"].append(current_low)
    summary["poc"].append(current_poc)
    summary["poc_upper_std"].append(poc_upper)
    summary["poc_lower_std"].append(poc_lower)


# 新增标准差曲线的绘图
fig = plt.figure()
x = range(len(summary["high"]))

plt.scatter(x, summary["high"], s=1)
plt.scatter(x, summary["low"], s=1)
plt.scatter(x, summary["poc"], s=1)
plt.scatter(x, summary["poc_upper_std"], s=1, color='orange')
plt.scatter(x, summary["poc_lower_std"], s=1, color='orange')

plt.legend(['high', 'low', 'poc', 'poc_upper_std', 'poc_lower_std'])
plt.savefig(f"distribution_with_std.png")
plt.close(fig)

说明 #

• 代码中每次循环都会实时计算截至当前tick的加权标准差，确保poc_upper_std和poc_lower_std是随时间更新的实时值
• 加权标准差考虑了不同价格的成交量权重，更贴合成交量分布的实际离散程度
• 新增的绘图代码会把POC的上下标准差曲线也画出来，方便可视化观察

内容的提问来源于stack exchange，提问作者Jan