Python-for-data-移动窗口函数
本文中介绍的是，主要的算子是：
- rolling算子
- expanding算子
- ewm算子
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移动窗口函数
统计和通过其他移动窗口或者指数衰减而运行的函数，称之为移动窗口函数
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import pandas as pd
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close_px_all = pd.read_csv("./examples/stock_px_2.csv"
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close_px = close_px_all[["AAPL","MSFT","XOM"]]
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| AAPL | MSFT | XOM | |
|---|---|---|---|
| 2003-01-02 | 7.40 | 21.11 | 29.22 |
| 2003-01-03 | 7.45 | 21.14 | 29.24 |
| 2003-01-06 | 7.45 | 21.52 | 29.96 |
| 2003-01-07 | 7.43 | 21.93 | 28.95 |
| 2003-01-08 | 7.28 | 21.31 | 28.83 |
| ... | ... | ... | ... |
| 2011-10-10 | 388.81 | 26.94 | 76.28 |
| 2011-10-11 | 400.29 | 27.00 | 76.27 |
| 2011-10-12 | 402.19 | 26.96 | 77.16 |
| 2011-10-13 | 408.43 | 27.18 | 76.37 |
| 2011-10-14 | 422.00 | 27.27 | 78.11 |
2292 rows × 3 columns
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close_px.AAPL.plot()
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rolling算子
rolling算子，行为和resample和groupby类似
rolling可以在S或者DF上通过一个window进行调用
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# 图形更加地平滑：根据250日滑动窗口分组，而不是直接分组
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appl_std250 = close_px.AAPL.rolling(250,min_periods=10).std()
2003-01-09 NaN
2003-01-10 NaN
2003-01-13 NaN
2003-01-14 NaN
2003-01-15 0.077496
2003-01-16 0.074760
2003-01-17 0.112368
Freq: B, Name: AAPL, dtype: float64
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# 滚动窗口函数需要窗口中所有的值必须是非NaN值
<matplotlib.axes._subplots.AxesSubplot at 0x11ee210d0>
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在DF上调用移动窗口函数作用到每列
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close_px.rolling(60).mean().plot(logy=True)
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## rolling算子接收固定大小的时间偏置字符串
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| AAPL | MSFT | XOM | |
|---|---|---|---|
| 2003-01-02 | 7.400000 | 21.110000 | 29.220000 |
| 2003-01-03 | 7.425000 | 21.125000 | 29.230000 |
| 2003-01-06 | 7.433333 | 21.256667 | 29.473333 |
| 2003-01-07 | 7.432500 | 21.425000 | 29.342500 |
| 2003-01-08 | 7.402000 | 21.402000 | 29.240000 |
| ... | ... | ... | ... |
| 2011-10-10 | 389.351429 | 25.602143 | 72.527857 |
| 2011-10-11 | 388.505000 | 25.674286 | 72.835000 |
| 2011-10-12 | 388.531429 | 25.810000 | 73.400714 |
| 2011-10-13 | 388.826429 | 25.961429 | 73.905000 |
| 2011-10-14 | 391.038000 | 26.048667 | 74.185333 |
2292 rows × 3 columns
扩展均值算子 expanding
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# 调用扩展均值算子
2003-01-02 NaN
2003-01-03 NaN
2003-01-06 NaN
2003-01-07 NaN
2003-01-08 NaN
...
2011-10-10 18.521201
2011-10-11 18.524272
2011-10-12 18.527385
2011-10-13 18.530554
2011-10-14 18.533823
Freq: B, Name: AAPL, Length: 2292, dtype: float64
指数加权函数
指定一个常数衰减因子为观测值提供更多的权重。常用指定衰减因子的方法：使用span（跨度）
ewm算子
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# 将苹果公司的股票价格的60日均线和span=60的EW移动均线进行比较
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ewma60 = appl_px.ewm(span=30).mean()
rolling和ewm对比
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ma60.plot(style="k--",label="Simple MA")
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ewma60.plot(style="k-",label="EWMA")
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二元移动窗口函数rolling+corr
一些统计算子，例如相关度和协方差等需要同时操作两个时间序列。
例如，金融分析中的股票和基准指数的关联性问题：计算时间序列的百分比变化pct_change()
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close_px_all[:5]
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| AAPL | MSFT | XOM | SPX | |
|---|---|---|---|---|
| 2003-01-02 | 7.40 | 21.11 | 29.22 | 909.03 |
| 2003-01-03 | 7.45 | 21.14 | 29.24 | 908.59 |
| 2003-01-06 | 7.45 | 21.52 | 29.96 | 929.01 |
| 2003-01-07 | 7.43 | 21.93 | 28.95 | 922.93 |
| 2003-01-08 | 7.28 | 21.31 | 28.83 | 909.93 |
计算苹果和标普500的相关性
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spx_px = close_px_all["SPX"] # 选择某列的数据
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returns = close_px.pct_change() # 计算整个数据的百分比变化
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# 调用rolling后，corr聚合函数可以根据spx_rets计算滚动相关性
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计算全部公司和标普500的相关性
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corr = returns.rolling(125,min_periods=100).corr(spx_rets)
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自定义移动窗口函数
在rolling及其相关方法上使用apply方法提供了一种在移动窗口中应用自己设计的数组函数的方法。
唯一要求：该函数从每个数组中产生一个单值(缩聚)，例如使用rolling()...quantile(q)计算样本的中位数
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# 定值的百分位数:scipy.stats.percentileofscore
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score_at_2percent = lambda x: percentileofscore(x,0.02)
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