predictFuture
demonstration of uni-variate time series prediction by predicting monthly births in Sweden for the next 12 months
real data
change of trend
prediction for 2023
yearly change of births last 100 years
forecast of fbprophet after bug fix
fbprophet forecast 12 months
| Year-Month | lower | mean | upper | real |
|---|---|---|---|---|
| 2022-12 | 6748 | 7017 | 7305 | 7522 |
| 2023-01 | 7849 | 8159 | 8437 | 8277 |
| 2023-02 | 7281 | 7590 | 7889 | 7921 |
| 2023-03 | 8085 | 8414 | 8752 | not released |
| 2023-04 | 7924 | 8258 | 8592 | |
| 2023-05 | 8394 | 8755 | 9075 | |
| 2023-06 | 8095 | 8470 | 8851 | |
| 2023-07 | 8181 | 8555 | 8930 | |
| 2023-08 | 7973 | 8377 | 8784 | |
| 2023-09 | 7130 | 7546 | 7970 | |
| 2023-10 | 6931 | 7369 | 7820 | |
| 2023-11 | 6067 | 6512 | 6992 |
sarimax forecast 12 months
| Year-Month | lower | mean | upper | real |
|---|---|---|---|---|
| 2022-12 | 6836 | 7277 | 7719 | 7522 |
| 2023-01 | 7469 | 7963 | 8456 | 8277 |
| 2023-02 | 7113 | 7607 | 8102 | 7921 |
| 2023-03 | 7728 | 8223 | 8718 | not released |
| 2023-04 | 7363 | 7857 | 8352 | |
| 2023-05 | 8087 | 8581 | 9076 | |
| 2023-06 | 8018 | 8512 | 9007 | |
| 2023-07 | 7793 | 8288 | 8783 | |
| 2023-08 | 7911 | 8406 | 8901 | |
| 2023-09 | 7002 | 7497 | 7992 | |
| 2023-10 | 6804 | 7299 | 7793 | |
| 2023-11 | 6167 | 6662 | 7157 |
Poisson Regression
To investigate causes of dropping birth count different regressors are used in a Poisson Regression Model.
100 random selecteded samples were used for training and testing. (see poisson2.py)
Mean absolute percentage error (mape) is about 5%.
Parameters used for the model are:
- year
- month
- population size
- surplus of migration
- CPI (Consumer Price Index)
- Vaccination Status of pregnant women (simulation, see https://jamanetwork.com/journals/jama/fullarticle/2790608)
expr = """births ~ year + month + population + surplus + cpi + jabs"""
| parameter | mean | std |
|---|---|---|
| Intercept | 15.93 | 7.81 |
| year | 0.09 | 0.06 |
| month | 0.0 | 0.01 |
| population | -0.83 | 0.87 |
| surplus | 0.0 | 0.0 |
| cpi | -0.01 | 0.0 |
| jabs | -0.05 | 0.02 |
| pvalues | mean | std |
|---|---|---|
| Intercept | 0.04 | 0.15 |
| year | 0.07 | 0.17 |
| month | 0.27 | 0.33 |
| population | 0.15 | 0.25 |
| surplus | 0.0 | 0.0 |
| cpi | 0.01 | 0.06 |
| jabs | 0.02 | 0.11 |
pvalues under 0.05 are migration surplus, cpi and vaccination status (jabs).
Migration had no impact on births during this period (jan/2019 - nov/2022)
- cpi = -0.01 (pvalue:0.01) means: higher inflation has (little) negative effekt on births
- jabs = -0.05 (pvalue:0.02): more jabs -> less births. Model is quite confident about that.
Rolling Regression
Instead of a linear reggression with statsmodel we choose PYMC to analyse possible causes for a dropping birth rate. "PyMC is a Python package for Bayesian statistical modeling and probabilistic machine learning." (Wikipedia)
Instead of the number of births per month we use: y = (number of births per month)/(number of women in fertile age). Women in fertile age: 15-49 is about 2.2 millions and rising. (data3.csv: Women) Because the numbers of births is now diveded by the number of women in fertile age, we don't use population size or migration surplus as a variable. The mean age of the population didn't changed that much in four years (2019-2022).
Variables used:
--- known Unknowns (factors suspected to have an influence, but uncertain how much) ---
- CPI (Consumer Price Index) - economic hardship for young families (beta_cpi)
- Vaccination status (beta_jabs)
--- unknown Unknowns ---
- beta_unknown
These variables are changing with time. Modeled as Gaussian Randomwalks.
The model fits well. Trend and seasonality look fine.
Plot of model parameters trace.
For more information, see rhat and summary3.csv.
Inflation (CPI) had a little negative effect on births since 2021.
Estimated effect of mRNA vaccins on births.
Effect of unknowns.
State Space Model (SSM)
Monthly births 2019-2022. Predict births for 2023 with:
- SSM with UnobservedComponents of statsmodel library.
- structural timeseries (trend,seasonality,autoregressive) with pymc3 (bayesianStateSpaceModel.py)
Gradient plot
| Year-Month | lower (5%) | mean | upper (95%) | real |
|---|---|---|---|---|
| 2023-01 | 8114 | 8532 | 8955 | 8277 |
| 2023-02 | 7605 | 8056 | 8539 | 7921 |
| 2023-03 | 8247 | 8833 | 9473 | |
| 2023-04 | 8118 | 8779 | 9517 | |
| 2023-05 | 8465 | 9263 | 10133 | |
| 2023-06 | 8177 | 9034 | 9982 | |
| 2023-07 | 8239 | 9177 | 10241 | |
| 2023-08 | 8063 | 9065 | 10204 | |
| 2023-09 | 7357 | 8343 | 9464 | |
| 2023-10 | 7194 | 8241 | 9428 | |
| 2023-11 | 6461 | 7463 | 8623 | |
| 2023-01 | 6237 | 7266 | 8438 |
!!! For more information look at the pdf file !!!