根据环比计算同比增长率

Question

给定一个数据集如下：

[{'date': '2017-01', 'CPI': 242.839, 'MoM%': nan, 'YoY%': nan},
 {'date': '2017-02', 'CPI': 243.603, 'MoM%': 0.0031, 'YoY%': nan},
 {'date': '2017-03', 'CPI': 243.801, 'MoM%': 0.0008, 'YoY%': nan},
 {'date': '2017-04', 'CPI': 244.524, 'MoM%': 0.003, 'YoY%': nan},
 {'date': '2017-05', 'CPI': 244.733, 'MoM%': 0.0009, 'YoY%': nan},
 {'date': '2017-06', 'CPI': 244.955, 'MoM%': 0.0009, 'YoY%': nan},
 {'date': '2017-07', 'CPI': 244.786, 'MoM%': -0.0007, 'YoY%': nan},
 {'date': '2017-08', 'CPI': 245.519, 'MoM%': 0.003, 'YoY%': nan},
 {'date': '2017-09', 'CPI': 246.819, 'MoM%': 0.0053, 'YoY%': nan},
 {'date': '2017-10', 'CPI': 246.663, 'MoM%': -0.0006, 'YoY%': nan},
 {'date': '2017-11', 'CPI': 246.669, 'MoM%': 0.0, 'YoY%': nan},
 {'date': '2017-12', 'CPI': 246.524, 'MoM%': -0.0006, 'YoY%': nan},
 {'date': '2018-01', 'CPI': 247.867, 'MoM%': 0.0054, 'YoY%': 0.0207},
 {'date': '2018-02', 'CPI': 248.991, 'MoM%': 0.0045, 'YoY%': 0.0221},
 {'date': '2018-03', 'CPI': 249.554, 'MoM%': 0.0023, 'YoY%': 0.0236},
 {'date': '2018-04', 'CPI': 250.546, 'MoM%': 0.004, 'YoY%': 0.0246},
 {'date': '2018-05', 'CPI': 251.588, 'MoM%': 0.0042, 'YoY%': 0.028},
 {'date': '2018-06', 'CPI': 251.989, 'MoM%': 0.0016, 'YoY%': 0.0287},
 {'date': '2018-07', 'CPI': 252.006, 'MoM%': 0.0001, 'YoY%': 0.0295},
 {'date': '2018-08', 'CPI': 252.146, 'MoM%': 0.0006, 'YoY%': 0.027},
 {'date': '2018-09', 'CPI': 252.439, 'MoM%': 0.0012, 'YoY%': 0.0228},
 {'date': '2018-10', 'CPI': 252.885, 'MoM%': 0.0018, 'YoY%': 0.0252},
 {'date': '2018-11', 'CPI': 252.038, 'MoM%': -0.0033, 'YoY%': 0.0218},
 {'date': '2018-12', 'CPI': 251.233, 'MoM%': -0.0032, 'YoY%': 0.0191},
 {'date': '2019-01', 'CPI': 251.712, 'MoM%': 0.0019, 'YoY%': 0.0155}]

假设我们不知道CPI 列，是否可以根据逐月计算同比增长率，反之亦然？

参考：

https://www.econ.iastate.edu/ask-an-economist/cpi-and-inflation-relationship-between-mom-and-yoy-values

Answer 1

是的，假设您的数据中没有缺少月份，您可以通过滚动（12 个周期）产品从 MoM 增长计算 YoY 增长。但是由于MoM 计算中已有的舍入，您可能会累积一些错误：

df['MoM%'].add(1).rolling(12).apply(lambda x: x.prod()) - 1

0          NaN
1          NaN
2          NaN
3          NaN
4          NaN
5          NaN
6          NaN
7          NaN
8          NaN
9          NaN
10         NaN
11         NaN
12    0.020667
13    0.022091
14    0.023623
15    0.024644
16    0.028022
17    0.028741
18    0.029564
19    0.027101
20    0.022912
21    0.025368
22    0.021985
23    0.019326
24    0.015777
Name: MoM%, dtype: float64

MoM 不四舍五入会更准确：

mom_no_rounding = df['CPI'] / df['CPI'].shift() - 1
mom_no_rounding.add(1).rolling(12).apply(lambda x: x.prod()) - 1

0          NaN
1          NaN
2          NaN
3          NaN
4          NaN
5          NaN
6          NaN
7          NaN
8          NaN
9          NaN
10         NaN
11         NaN
12    0.020705
13    0.022118
14    0.023597
15    0.024627
16    0.028010
17    0.028715
18    0.029495
19    0.026992
20    0.022770
21    0.025225
22    0.021766
23    0.019102
24    0.015512
Name: CPI, dtype: float64