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A time series analysis study of green finance investment returns under the Sustainable Development Goals (SDGs)

Xiaojia Pan

Xiaojia Pan

Department of Economics and Law, Concord University College Fujian Normal UniversityFuzhou, China
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Pan, Xiaojia
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Lili Liu

Lili Liu

Center of Financial Risk Management Research, College of Finance, Fujian Jiangxia UniversityFuzhou, China
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Liu, Lili
  
Sep 29, 2025
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Published Online: Sep 29, 2025
Received: Jan 09, 2025
Accepted: Apr 30, 2025
DOI: https://doi.org/10.2478/amns-2025-1086
Keywords
© 2025 Xiaojia Pan and Lili Liu, published by Sciendo.
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1.

PSO-LSTM model flowchart
PSO-LSTM model flowchart

Figure 2.

The lowest price of a bank from January 2010 to December 2014
The lowest price of a bank from January 2010 to December 2014

Figure 3.

First order difference sequence diagram
First order difference sequence diagram

Figure 4.

Self-related results
Self-related results

Figure 5.

Partial self-correlation
Partial self-correlation

Figure 6.

Model of residual difference Q-Q diagram
Model of residual difference Q-Q diagram

Figure 7.

Prediction of the ARIMA model
Prediction of the ARIMA model

Figure 8.

The prediction of the LSTM model and ARIMA-PSO-LSTM model
The prediction of the LSTM model and ARIMA-PSO-LSTM model

Figure 9.

The PSO algorithm optimized the comparison results
The PSO algorithm optimized the comparison results

Figure 10.

Comparison of three energy prediction models
Comparison of three energy prediction models

The return of the forecast model green financial investment

Model Running time Training time
ARIMA 0.0621 0
PSO-LSTM 0.0859 115.1623
ARIMA-PSO-LSTM 0.0669 115.1623

Forecast accuracy of green financial investment model

Model RMSE MAE
ARIMA 0.11976 0.3967
PSO-LSTM 0.0639 0.2614
ARIMA-PSO-LSTM 0.0108 0.1201

The prediction error of the two prediction models is compared

Model ARIMA ARIMA-PSO-LSTM
MAE 5.68171 3.78381
MSE 59.06123 52.44168
RMSE 8.04989 6.03049
MAPE(%) 35.05587 21.03775
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