Tamamlanmış Zaman Serisi Verilerinde Derin Öğrenme Modellerinin Performansı: Bir Simülasyon Çalışması ve Önde Gelen Havayolu Şirketlerinin Hisse Senedi Fiyatlarına Uygulama

Öz

Bu çalışmada, zaman serisi analizinde derin öğrenme yöntemleri için imputasyon tekniklerinin geçerliliği, hisse senedi piyasasındaki günlük kapanış verilerine dayalı veri kümeleri kullanılarak araştırılmıştır. Türk Hava Yolları, Deutsche Lufthansa AG ve Delta Airlines'ın günlük kapanış hisse senedi fiyatlarının yanı sıra simüle edilmiş bir veri kümesi kullanılmıştır. Derin öğrenme modelleri olan LSTM, GRU, RNN ve Transformer modelleri kullanılmıştır. Orijinal veri kümesi ve %5, %15 ve %25 eksik gözleme sahip veri kümeleri, Doğrusal, Spline, Stineman, Ortalama ve Rastgele atama teknikleri ile doldurularak analiz edilmiştir. Sonuçlar, model performansının atama tekniğine ve eksik veri oranına bağlı olarak değiştiğini göstermektedir. GRU ve Transformer modelleri, dayanıklılıkları ve mükemmel performansları nedeniyle tercih edilmektedir. Eksik verilerle başa çıkmak için spline ve Stineman atama tekniklerinin kullanılması, yüksek model doğruluğunu korumak açısından önerilmektedir. Bu çalışma, zaman serisi analizinde çeşitli atama tekniklerinin ve derin öğrenme modellerinin kullanılabilirliğini vurgulamaktadır. Araştırma model performansı, tahmin doğruluğu ve güvenilirliği hakkında kapsamlı bir anlayış elde etmek için hem MAPE hem de RMSE kullanarak değerlendirmeyi ve bu yöntemleri karşılaştırarak gelecekteki araştırmalara rehberlik etmeyi amaçlamaktadır.

Anahtar Kelimeler

• Eksik Veri
• Sentetik Veri
• Transformer Model
• RNN
• Simülasyon
• Hava Yolu Hisse Senetleri

Performance of Deep Learning Models on Imputed Time Series Data: A Simulation Study and Application to Leading Airline Companies' Stock Price

Öz

In this study, the validity of imputation techniques for deep learning methods in time series analysis is investigated using datasets based on daily closing data in the stock market. Datasets of daily closing stock prices for Turkish Airlines, Deutsche Lufthansa AG, and Delta Airlines, as well as a simulated dataset, are used. LSTM, GRU, RNN, and Transformer models, which are deep learning models, are employed. The original dataset and datasets with 5%, 15% and 25% missing data are analyzed imputing linear, spline, Stineman, mean and random imputation techniques. The results show that model performance varies depending on the imputation technique and the rate of missing data. GRU and Transformer models are favored for their robustness and excellent performance. For handling missing data, using spline and Stineman imputations is advisable to maintain high model accuracy. This study emphasizes the usability of various imputation techniques and deep learning models in time series analysis. It assesses model performance using both MAPE and RMSE to gain a comprehensive understanding of predictive accuracy and reliability, aiming to guide future research by comparing these methods.

Anahtar Kelimeler

• Missing Data
• Synthetic Data
• Transformer Model
• RNN
• Simulation
• Airline Stocks

Kaynakça

1. Chatfield, C. (2004). The Analysis of Time Series: An Introduction. Chapman and Hall/CRC.
2. Yenilmez, I., & Kantar, YM., 2019. An Analysis of Export Data with Panel Tobit Model. ICONDATA19, e-ISBN: 978-605-031-662-9. pp.92-97.
3. Vaswani, A., Shazeer, N., Parmar, N., Uszkoreit, J., Jones, L., Gomez, A. N., Kaiser, Ł., & Polosukhin, I. (2017). Attention is All You Need. Advances in Neural Information Processing Systems, 30, 5998-6008.
4. Çalık, A. S., Yenilmez, İ., & Sevinçtekin, Ö. (2022). Comparison of Box-Jenkins and Artificial Neural Networks methods: Demand forecast for ceramic sanitary ware. Proceeding Book of EGE 7th International Conference on Applied Sciences, December 24-25, İzmir, Türkiye (pp.1024-29), ISBN: 978-605-72197-9-4.
5. Mugenzi, F. & Yenilmez, İ. (2023). Forecasting for GDP Per Capita Using Multiplier Perceptron and Gated Recurrent Unit. Proceeding Book of Akdeniz 10th International Conference on Applied Sciences, November 2-5, KYRENIA (pp.318-327), ISBN: 978-625-6830-49-3.
6. Yenilmez, I., & Mugenzi, F. (2023). Estimation of conventional and innovative models for Rwanda's GDP per capita: A comparative analysis of artificial neural networks and Box-Jenkins methodologies. Scientific African, 22, e01902. https://doi.org/10.1016/j.sciaf.2023.e01902.
7. Yenilmez, İ. & Akçay, E. K. (2023). Performance of Particle Swarm Optimization and Genetic Algorithm for Tuning of k-NN Hyperparameters. Proceeding Book of Akdeniz 10th International Conference on Applied Sciences, November 2-5, KYRENIA (pp.328-338), ISBN: 978-625-6830-49-3
8. Little, R. J. A., & Rubin, D. B. (2019). Statistical Analysis with Missing Data. John Wiley & Sons.

9. Schafer, J. L. (1997). Analysis of Incomplete Multivariate Data. Chapman and Hall/CRC.
10. Yamak, P. T., Yujian, L., & Gadosey, P. K. (2019). Comparison of ARIMA, LSTM, and GRU models for time series forecasting: Evidence from Bitcoin price data. Journal of Financial Data Science, 1(1), 45-60.
11. Ridwan, M., Sadik, K., & Afendi, F. M. (2023). Evaluating the effectiveness of ARIMA and GRU models in high-frequency stock price forecasting: A case study of HIMBARA bank stocks. Journal of Financial Forecasting, 5(2), 87-102.
12. Kontopoulou, V. I., Panagopoulos, A. D., Kakkos, I., & Matsopoulos, G. K. (2023). A Review of ARIMA vs. Machine Learning Approaches for Time Series Forecasting in Data Driven Networks. Future Internet, 15(8), 255. https://doi.org/10.3390/fi15080255.
13. Ahmed, S., Nielsen, I.E., Tripathi, A. et al. Transformers in Time-Series Analysis: A Tutorial. Circuits Syst Signal Process 42, 7433–7466 (2023). https://doi.org/10.1007/s00034-023-02454-8.
14. Wen, Q., Zhou, T., Zhang, C., Chen, W., Ma, Z., Yan, J., & Sun, L. (2022). Transformers in Time Series: A Survey.
15. Fang, C., & Wang, C. (2020). Time Series Data Imputation:A Survey on Deep Learning Approaches.ArXiv https://arxiv.org/abs/2011.11347
16. Yenilmez, İ. (2024). Imputation methods effect on the goodness of fit of the statistical model. In Proceedings of the 9th International Conference on Business, Management and Economics. Vienna, Austria. ISBN 978-609-485-514-6.
17. Hastie, T., Tibshirani, R., & Friedman, J. (2009). The elements of statistical learning: Data mining, inference, and prediction (2nd ed.). Springer. https://doi.org/10.1007/978-0-387-84858-7
18. Stineman, R. W. (1980). A consistently well-behaved method of interpolation. Creative Computing, 6(7), 54-57.
19. Donders, A. R. T., van der Heijden, G. J., Stijnen, T., & Moons, K. G. (2006). Review: A gentle introduction to imputation of missing values. Journal of Clinical Epidemiology, 59(10), 1087-1091. https://doi.org/10.1016/j.jclinepi.2006.01.014
20. Yenilmez, İ., & Kantar, Y. M. (2023). New exponentiated generalized censored regression models: Monte Carlo simulation and application. Concurrency and Computation: Practice and Experience, 35(1), e7436. https://doi.org/10.1002/cpe.7436
21. Atmaca, K., & Yenilmez, İ. (2024). RNNs and Transformer Model in case of Incomplete Time Series. Conference paper presented at the Fifth International Congress of Applied Statistics (UYIK-2024), İstanbul, Türkiye