金融数据的特征工程

给模型可比较的输入

250 这个价格对模型毫无意义：它取决于股票，又会随时间上升，所以 2020 年的数值永远不像 2010 年的。特征工程把原始数据变成跨时间、跨资产可比较的输入：用收益率代替价格，用波动率代替区间，用标准化分数代替绝对水平。好的特征对结果的影响比模型选择更大，而且每个特征只能描述当天已知的信息。

import numpy as np

prices = np.array([100.0, 101.0, 99.0, 102.0, 104.0, 103.0, 106.0])

window = 3
momentum = np.full(len(prices), np.nan)
momentum[window:] = prices[window:] / prices[:-window] - 1          # the return over the last 3 days
print(np.round(momentum, 4))                                        # nan for the first 3 days: no price 3 days back

向后看的窗口

大多数特征是向后看的窗口的统计量：包含今天在内的最近 n 个值。动量比较今天与 n 天前；滚动波动率是最近 n 个收益率的标准差；滚动 z 分数说明今天距窗口均值有多少个窗口标准差。用 sliding_window_view 可以把所有窗口当作矩阵的行，沿某个轴计算统计量，不需要循环。前 n - 1 天没有完整窗口，保持为 nan。

import numpy as np

prices = np.array([100.0, 101.0, 99.0, 102.0, 104.0, 103.0, 106.0])
returns = np.diff(prices) / prices[:-1]
window = 3

windows = np.lib.stride_tricks.sliding_window_view(returns, window)        # every 3-day window as a row
vol = np.full(len(returns), np.nan)
vol[window - 1:] = windows.std(axis=1, ddof=1)
print(np.round(vol, 4))                                                    # nan nan then one value per complete window

p_windows = np.lib.stride_tricks.sliding_window_view(prices, window)
z = np.full(len(prices), np.nan)
z[window - 1:] = (prices[window - 1:] - p_windows.mean(axis=1)) / p_windows.std(axis=1, ddof=1)
print(np.round(z, 3))                                                      # how unusual each price is for its last 3 days

# Features put prices of different stocks on the same footing
import numpy as np

cheap = np.array([5.0, 5.2, 5.1, 5.4, 5.5])
dear = np.array([500.0, 520.0, 510.0, 540.0, 550.0])           # ten times the price, the same movements
print(cheap[-1] / cheap[-3] - 1, dear[-1] / dear[-3] - 1)        # identical momentum, about 0.0784 for both
print(dear[-1] - dear[-3], cheap[-1] - cheap[-3])                # price changes (40.0 and 0.4) would not be comparable

目标向前看

模型要预测的是目标，通常是未来 h 天的收益率：prices[t + h] / prices[t] - 1。它是唯一允许向前看的一列，最后 h 天因为未来尚未发生而为 nan，训练前要去掉这些行。常见的错误是特征意外包含了目标，例如居中的窗口、用全部数据算出的统计量，或把未来收益率当作输入。检验很简单：加入后面的日期时，第 t 天的特征不应该改变。

import numpy as np

def forward_return(prices, horizon):
    out = np.full(len(prices), np.nan)
    out[:-horizon] = prices[horizon:] / prices[:-horizon] - 1
    return out

def momentum(prices, window):
    out = np.full(len(prices), np.nan)
    out[window:] = prices[window:] / prices[:-window] - 1
    return out

prices = np.array([100.0, 101.0, 99.0, 102.0, 104.0, 103.0, 106.0])
print(np.round(momentum(prices, 2), 4))                 # looks back: known on each day
print(np.round(forward_return(prices, 2), 4))           # looks forward: the target, nan for the last 2 days

# The prefix test: a feature computed on the first 5 days equals the first 5 values of the full computation
print(np.allclose(momentum(prices[:5], 2), momentum(prices, 2)[:5], equal_nan=True))      # True

• 把价格变成可比较的特征：动量 prices[t] / prices[t - n] - 1、滚动波动率、滚动 z 分数，均基于包含今天的向后窗口。
• sliding_window_view 把每个窗口当作一行，统计量无需循环；前 n - 1 天保持为 nan。
• 未来收益率 prices[t + h] / prices[t] - 1 是目标而非特征；用前缀检验检查每个特征。

下一节：滚动前向验证，按时间真实流逝的顺序检验模型。

实验：评分内容

• 用 momentum 度量趋势25 分
• 用 rolling_vol 跟踪近期风险25 分
• 用 rolling_zscore 表示今天有多反常25 分
• 用 forward_return 定义预测目标25 分