LUCIDA & FALCON：用多因子策略构建强大的加密资产投资组合

作者：LUCIDA & FALCON

前言

书接上回，我们发布了《用多因子策略构建强大的加密资产投资组合》系列文章的第一篇 — 理论基础篇，本篇是第二篇 — 数据预处理篇。

在计算因子数据前/后，以及测试单因子的有效性之前，都需要对相关数据进行处理。具体的数据预处理涉及重复值、异常值/缺失值/极端值、标准化和数据频率的处理。

一、重复值

数据相关定义：

• 键（ Key ）：表示一个独一无二的索引。 eg . 对于一份有全部 token 所有日期的数据，键是“ token _ id / contract _ address - 日期”
• 值（ Value ）：被键索引的对象就称之为“值”。

诊断重复值的首先需要理解数据“应当”是什么样子。通常数据的形式有：

1. 时间序列数据（ Time Series ）。键是“时间”。 eg .单个 token5 年的价格数据
2. 横截面数据（ Cross Section )。键是“个体”。 eg .2023.11.01当日 crypto 市场所有 token 的价格数据
3. 面板数据（ Panel ）。键是“个体-时间”的组合。 eg .从2019.01.01-2023.11.01 四年所有 token 的价格数据。

原则：确定了数据的索引（键），就能知道数据应该在什么层面没有重复值。

检查方式：

1. pd . DataFrame . duplicated ( subset =[ key1 , key2 , …])
   
   检查重复值的数量： pd . DataFrame . duplicated ( subset =[ key1 , key2 , …]). sum ()
   
   抽样看重复的样本： df [ df . duplicated ( subset =[…])]. sample ()找到样本后，再用 df . loc 选出该索引对应的全部重复样本
2. pd . merge ( df1 , df2 , on =[ key1 , key2 , …], indica to r = True , validate ='1:1')
   
   在横向合并的函数中，加入 indica to r 参数，会生成_ merge 字段，对其使用 dfm ['_ merge ']. value _ counts ()可以检查合并后不同来源的样本数量
   
   加入 validate 参数，可以检验合并的数据集中索引是否如预期一般（1 to 1、1 to many 或 many to many ，其中最后一种情况其实等于不需要验证）。如果与预期不符，合并过程会报错并中止执行。

二、异常值/缺失值/极端值

产生异常值的常见原因：

1. 极端情况。比如token价格0.000001$或市值仅50万美元的token，随便变动一点，就会有数十倍的回报率。

2. 数据特性。比如token价格数据从2020年1月1日开始下载，那么自然无法计算出2020年1月1日的回报率数据，因为没有前一日的收盘价。

3. 数据错误。数据提供商难免会犯错，比如将12元每token记录成1.2元每token。

针对异常值和缺失值处理原则：

1. 删除。对于无法合理更正或修正的异常值，可以考虑删除。
2. 替换。通常用于对极端值的处理，比如缩尾（ Winsorizing ）或取对数（不常用）。

3. 填充。对于缺失值也可以考虑以合理的方式填充，常见的方式包括均值（或移动平均）、插值（ Interpolation ）、填 0  df.fillna(0)、向前df.fillna('ffill')/向后填充df.fillna('bfill')等，要考虑填充所依赖的假设是否合。

   机器学习慎用向后填充，有 Look - ahead bias 的风险

针对极端值的处理方法：

1.百分位法。

通过将顺序从小到大排列，将超过最小和最大比例的数据替换为临界的数据。对于历史数据较丰富的数据，该方法相对粗略，不太适用，强行删除固定比例的数据可能造成一定比例的损失。

2.3σ / 三倍标准差法

标准差 σfactor 体现因子数据分布的离散程度，即波动性。利用 μ±3×σ 范围识别并替换数据集中的异常值，约有99.73% 的数据落入该范围。该方法适用前提：因子数据必须服从正态分布，即 X∼N(μ,σ2)。

其中，μ=∑ⁿᵢ₌₁⋅ Xi / N , σ²=∑ⁿᵢ₌₁=( xi -μ)²/ n   ，因子值的合理范围是[μ−3×σ,μ+3×σ]。

对数据范围内的所有因子做出如下调整：

该方法不足在于，量化领域常用的数据如股票价格、token价格常呈现尖峰厚尾分布，并不符合正态分布的假设，在该情况下采用3σ方法将有大量数据错误地被识别为异常值。

3.绝对值差中位数法（ Median Absolute Deviation , MAD ）

该方法基于中位数和绝对偏差，使处理后的数据对极端值或异常值没那么敏感。比基于均值和标准差的方法更稳健。

绝对偏差值的中位数 MAD = median ( ∑ⁿᵢ₌₁( Xi - X median ) )

因子值的合理范围是[ Xmedia n - n × MAD ， Xmedia n ＋ n × MAD ]。对数据范围内的所有因子做出如下调整：

<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;"># 处理因子数据极端值情况</span>
<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">class</span> <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">Extreme</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">object</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">:</span>
    <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">def</span> <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">__init__</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span>s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">,</span> ini_data<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">:</span>
        s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>ini_data <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span> ini_data

    <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">def</span> <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">three_sigma</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span>s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">,</span>n<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">3</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">:</span>
        mean <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span> s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>ini_data<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>mean<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span>
        std <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span> s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>ini_data<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>std<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span>
        low <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span> mean <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">-</span> n<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">*</span>std
        high <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span> mean <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">+</span> n<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">*</span>std
        <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">return</span> np<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>clip<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span>s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>ini_data<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">,</span>low<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">,</span>high<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span>

    <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">def</span> <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">mad</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span>s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">,</span> n<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">3</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">:</span>
        median <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span> s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>ini_data<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>median<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span>
        mad_median <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span> <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">abs</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span>s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>ini_data <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">-</span> median<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>median<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span>
        high <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span> median <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">+</span> n <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">*</span> mad_median
        low <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span> median <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">-</span> n <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">*</span> mad_median
        <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">return</span> np<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>clip<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span>s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>ini_data<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">,</span> low<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">,</span> high<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span>

    <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">def</span> <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">quantile</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span>s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">,</span>l <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span> <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">0.025</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">,</span> h <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span> <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">0.975</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">:</span>
        low <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span> s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>ini_data<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>quantile<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span>l<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span>
        high <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span> s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>ini_data<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>quantile<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span>h<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span>
        <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">return</span> np<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>clip<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span>s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>ini_data<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">,</span> low<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">,</span> high<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span>

三、标准化

1. Z - score 标准化

• 前提： X N （μ，σ）
• 由于使用了标准差，该方法对于数据中的异常值较为敏感

2.最大最小值差标准化（ Min - Max Scaling ）

将每个因子数据转化为在(0,1) 区间的数据，以便比较不同规模或范围的数据，但它并不改变数据内部的分布，也不会使总和变为1。

• 由于考虑极大极小值，对异常值敏感

• 统一量纲，利于比较不同维度的数据。

3.排序百分位（ Rank Scaling ）

将数据特征转换为它们的排名，并将这些排名转换为介于 0 和1之间的分数，通常是它们在数据集中的百分位数。*

• 由于排名不受异常值影响，该方法对异常值不敏感。

• 不保持数据中各点之间的绝对距离，而是转换为相对排名。

其中， min ( Rank ₓ)=0， N 为区间内数据点的总个数。

<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;"># 标准化因子数据</span>
<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">class</span> <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">Scale</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">object</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">:</span>
    <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">def</span> <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">__init__</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span>s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">,</span> ini_data<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">,</span>date<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">:</span>
        s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>ini_data <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span> ini_data
        s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>date <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span> date

    <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">def</span> <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">zscore</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span>s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">:</span>
        mean <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span> s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>ini_data<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>mean<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span>
        std <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span> s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>ini_data<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>std<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span>
        <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">return</span> s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>ini_data<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>sub<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span>mean<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>div<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span>std<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span>

    <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">def</span> <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">maxmin</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span>s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">:</span>
        <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">min</span> <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span> s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>ini_data<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">min</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span>
        <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">max</span> <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span> s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>ini_data<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">max</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span>
        <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">return</span> s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>ini_data<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>sub<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">min</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>div<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">max</span> <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">-</span> <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">min</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span>

    <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">def</span> <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">normRank</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span>s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">:</span>
        <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;"># 对指定列进行排名，method='min'意味着相同值会有相同的排名，而不是平均排名</span>
        ranks <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span> s<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>ini_data<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>rank<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span>method<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">=</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">'min'</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span> 
        <span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">return</span> ranks<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span>div<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span>ranks<span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">.</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">max</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">(</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span><span style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;" data-mce-style="font-size: inherit; font-family: PingFang SC,Helvetica Neue,Helvetica,Arial,Hiragino Sans GB,Heiti SC,Microsoft YaHei,WenQuanYi Micro Hei,sans-serif;">)</span>

四、数据频率

有时获得的数据并非我们分析所需要的频率。比如分析的层次为月度，原始数据的频率为日度，此时就需要用到“下采样”，即聚合数据为月度。

下采样

指的是将一个集合里的数据聚合为一行数据，比如日度数据聚合为月度。此时需要考虑每个被聚合的指标的特性，通常的操作有：

• 第一个值/最后一个值
• 均值/中位数
• 标准差

上采样

指的是将一行数据的数据拆分为多行数据，比如年度数据用在月度分析上。这种情况一般就是简单重复即可，有时需要将年度数据按比例归集于各个月份。

关于 LUCIDA & FALCON

Lucida （https://www.lucida.fund/ ）是行业领先的量化对冲基金，在2018年4月进入Crypto市场，主要交易CTA / 统计套利 / 期权波动率套利等策略，现管理规模3000万美元。

Falcon （https://falcon.lucida.fund /）是新一代的Web3投资基础设施，它基于多因子模型，帮助用户“选”、“买”、“管”、“卖”加密资产。Falcon在2022年6月由Lucida所孵化。

更多内容可访问 https://linktr.ee/lucidaandfalcon