marl2en/predictfuture

demonstration of uni-variate time series prediction by predicting monthly births in Sweden for the next 12 months

predictFuture

demonstration of uni-variate time series prediction by predicting monthly births in Sweden for the next 12 months

Followup on prediction for 2023 with real data

The prediction was too pessimistic, but the trend remains unchanged (see forecast for 2024 and trend)

Forecast of total numbers of births per month for 2024 (Sweden)

Historic Trend 2000 - 2023 (2024: predicted trend)

Birth rates decline since 2018-2019, but at a faster rate since 2021.

real data 2019-2022

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 !!!