Japan where the number of births is declining more than expected
The news that "the number of births in 2022 will fall below 800,000 for the first time, and the number of births is decreasing at a much faster pace than expected" has become a hot topic. Certainly, when I think about the future of Japan, I think that the number of births is decreasing more than expected, which is a big social problem.
In fact, at the beginning of last year (2022), it is often used in time series analysis Seasonal ARIMA model was used to predict the number of births in 2022 from the number of births by month in 2014-2021. The predicted number of births in 2022 obtained at that time was 839,796. Since the actual number of births was 799,728, the ARIMA model overestimated the predicted value by about 40,000.
Thinking another way, The actual number of births was significantly lower than predicted from historical data. It can also be said.
Prediction of number of births by seasonal ARIMA model
A seasonal ARIMA model is a type of model that fits periodic time series data, and is a combination of a moving average (MA) model, an autoregressive model (AR) model, an integration (I) model, and a periodicity (s) model. It has been constructed.
For the seasonal ARIMA model, the above ARIMA the order of (p,d,q) ,season ARIMA the order of ( P,Q,R ), 1 It is necessary to specify the number of points in the cycle (cycle), and how to determine these orders can be confusing.
In this example, the period is 12 (12-month period), but other orders are determined by the following steps 1 and 2.
Step 1. Determine the order of the seasonal ARIMA model
- Fit a seasonal ARIMA model of various orders (0, 1, 2) using 2014-2020 as training data.
- Using 2021 as validation data, determine the optimal order using the statistic to evaluate the fit (RMSE).
step 2. using the determined order 2022 predict the year ↓
step 1. Using the optimal order determined by 2014 years 2021 season to year ARIMA fit the model, 2022 Predict the year.
In step 1, JMP's Multiple ARIMA models ” to fit seasonal ARIMA models of various orders (729 models in this example). The model with the lowest RMSE (best model) is seasonal ARIMA(2,0,0)(2,0,0)12.
In step 2, the seasonal ARIMA model obtained in step 1 is used to predict the number of births by month in 2022.
The figure below shows the number of births by month. The black dots are the actual number of births, the red line is the predicted number of births from the seasonal ARIMA model, and the red colored interval is the 95% confidence interval for the prediction. indicate.
The light blue area on the right side of the figure is the forecast for each month in 2022, and the predicted value for the number of births in 2022 is obtained by adding the predicted values for January to December. Calculated 839,796 people.
Let's check the chart below, which is an enlarged portion of the measured and predicted values for 2022. Looking at the monthly predicted values (red line) and measured values (black dots) for 2022, In January and August, the actual measurements were barely higher than the forecasts, but in all other months the actual measurements were lower than the forecasts.
Looking at the line of the seasonal ARIMA model, we can see that there are monthly trends such as fewer births in February and more in autumn. It looks like you are.
Birth forecast for 2023
Using the methods in Steps 1 and 2 of the previous section, we will use the birth number data from 2014 to 2022 to predict the number of births in 2023.
The best model is Seasonal ARIMA(2,1,1)(2,1,2)12, and we fitted this model to predict the number of births by month in 2023 as shown below.
Based on these results, the predicted number of births in 2023 is 745,468. The large decline in 2022 is reflected in model selection and projections, and it is predicted that in 2023 there will be a further decrease of more than 50,000 people.
However, these forecast values were obtained from past values using a statistical model called the seasonal ARIMA model. The actual number of births may be significantly higher than expected due to the government's countermeasures against the declining birthrate and changes in social conditions.
The seasonal ARIMA model introduced this time is nothing more than an indication of "this is the forecast for the future based on the past situation." However, compared with the number of births that will be released in the future, it will be a guideline to consider whether it was more or less than predicted. Now , what will happen in 2023? Expect upswing!
