過去最低と言われている2023年の出生数ですが、ARIMAモデルでは想定以上に良い結果という結論に・・・ 2024年の出生数予測も

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The other day, it was reported that the number of births in Japan in 2023 (preliminary figures) will be 758,631, the lowest ever. The number has decreased by about 5.1% compared to 2022, and the situation is urgent due to the declining birthrate. However, when compared with predictions based on past data, it can be seen positively that this level of decline was enough to keep things in check.

In this blog, we will introduce the answers to the prediction of the number of births in 2023 using the ARIMA model, which was conducted at the same time last year, and the prediction of the number of births in 2024 using a time series model.

How accurate was the number of births in 2023 predicted by the ARIMA model at the same time last year?

Around the same time last year (2023), I wrote a blog about predicting the number of births in 2023 by applying the ARIMA model to data on the number of births (monthly) up to 2022. The Ministry of Health, Labor and Welfare has just released the monthly number of births for 2023, so let's check your answers.

Published number of births in 2023 (actual value): 758,631 people

Predicted number of births in 2023 predicted by ARIMA model: 745,468 people

Surprisingly, the ARIMA model predicted even more pessimistically. The actual number of births (actual measurements) was approximately 13,000 more than the predicted value.

The figure below compares the monthly actual measured values ​​(points) and the predicted values ​​by the ARIMA model (red line).

Looking at the graph, you can see that the predictions made by the ARIMA model are relatively accurate from January to April. However, from May onwards, there are an increasing number of months in which there is a large discrepancy between the actual measured value and the predicted value. In particular, the number of births in May, June, July, November, and December was significantly higher than predicted.

One of the reasons why the number of births has decreased significantly in recent years is the spread of the new coronavirus. If we go back about 10 months from May 2023 to July 2022, this may be the time when the idea of ​​coexistence as a countermeasure against the new coronavirus began to take root.

Predicting the number of births in 2024 using JMP’s time series model

Let's look at the trends in the number of births over the 10-year period from 2014 to 2023. The line below shows the number of births per month, but we have added a smooth blue line.

This data shows that the number of births is clearly on a downward trend, and a further decline in the number of births is expected from 2024 onwards.

In JMP, in addition to the ARIMA model, you can fit a state-space smoothing model using a platform called [Time Series Prediction] as a model fitting/prediction method for time series data.

Let me briefly explain this model.

In time series analysis, the idea is to break down the time series data (Y: original series) that is the subject of analysis into trend factors (T), seasonal factors (S), and error factors (E).

A state space smoothing model is a model defined based on these trend factors (T), seasonal factors (S), and error factors (E).

However, there are various possible models for expressing the original series Y using T, S, and E, depending on whether factors are added (additive) or multiplied (multiplicative), as shown below. .

Y = T + S + E

Y = (T*S)*E

Y = (T+S) *E

・・・

・・・

JMP can fit a total of 30 types of models (=2 x 5 x 3) at once by combining variations of error (2 types), trend (5 types), and seasonal (3 types) as shown below. Masu.By default, 19 of these models are fitted and the best model is selected using the model evaluation metrics.

Predicting the number of births in 2024 using the state space smoothing method is performed in the following two steps.

Step 1. Determine the best model
- Apply the 19 models shown above using the years 2014 to 2022 as training data.
- Using 2023 as validation (pending) data, determine the optimal model using statistics for evaluating fit (RMSE).

Step 2. Use the determined model to predict 2024

The optimal model determined in step 1 is applied to the data from 2014 to 2023 to predict 2024.

When performing the above on the [Time Series Forecasting] platform, check the "Forecast Settings".

NAhead specifies how far past the current data to predict. In this example, we are forecasting from January to December 2024 using data up to 2023, so the forecast is as of 12.

For the period , enter the expected period for this time series. Since it is monthly data, enter 12.

For the model selection method , we select "RMSE" as the evaluation method for "prediction performance." NHoldBack enters the number of data to be used as validation data. In this example, we will treat the period from January to December 2023 as validation data, so enter 12.

Click the Run button to fit 19 models and calculate the RMSE (reference statistic) for each.

In this example, the model with the smallest RMSE is "MAM (period = 12)", so this model is considered the optimal model.

By the way, MAM indicates that the error is multiplicative, the trend is additive, and the season is multiplicative.

This is the result of predicting the number of births in 2024 using the optimal model. The green part on the right side of the figure predicts the number of births per month in 2024.

The table below summarizes the prediction of the number of births in 2024 using state space smoothing obtained by following these steps, and the prediction using the ARIMA model obtained using the same steps.

model	2024Forecast of births in 2020
state space smoothing	726,440 people
ARIMA	729,368 people

Both models predict that the number of births in 2024 will be in the 720,000 range. It is predicted that the number of births will further decrease, but this is only a prediction based on the past number of births.

Currently, many positive factors are intertwined, including the removal of movement restrictions due to the coronavirus, the strengthening of government childcare support policies, and improving economic conditions. I believe that there is a good chance that these factors will be successful and that the number of births in 2024 will exceed predictions.

by Naohiro Masukawa (JMP Japan)

Naohiro Masukawa - JMP User Community