根据月环比计算同比增长率

Question

给定如下数据集:

[{'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CPI列对我们来说是未知的，是否有可能根据月比月来计算年比增长率，在Python中反之亦然?

参考:

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

Answer 1

是的，您可以通过滚动(12期)产品从MoM增长中计算YoY增长，假设您的数据中没有缺少月份。但是，由于在MoM计算中已经使用了舍入，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

如果MoM没有四舍五入，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