Laurena Ramadani

• Generative Adversarial Networks for Time Series Simulation Generative Adversarial Networks (GANs), first introduced by Ian Goodfellow in 2014, have revolutionized the architecture of deep neural networks by enabling the generation of realistic data across various domains. In this study, we apply GANs to the generation of synthetic financial data, aiming to replicate real-world patterns. This approach allows us to extend limited historical datasets, train machine learning models more effectively, and conduct simulations for various financial applications. In this study, we focus on two types of GANs: ForGAN and TimeGAN. ForGAN, a variant of Conditional GANs (cGAN), is designed to model the probability distribution of the one-step ahead value in a time series, specifically xt+1 by conditioning on historical data x0,x1,...,xt. We applied ForGAN to two distinct datasets: the first being 15-minute electricity consumption data from Germany’s intraday market, a more regular and seasonal dataset; and the second, the Standard & Poor’s 500 (S&P 500) index, which represents financial data characterized by volatility and non-stationarity. Our analysis involved addressing several key aspects of the data: the impact of data transformation techniques, the treatment of outliers, and extensive hyperparameter tuning to enhance the model’s performance. These adjustments were essential to accurately simulate future time periods for both datasets, allowing us to assess the strengths and limitations of ForGAN in handling distinct types of time series data. In addition to generating future data, we extended our study to financial applications, particularly in the areas of Value at Risk (VaR) estimation and portfolio optimization. Two portfolio optimization approaches were examined: the Markowitz mean-variance method and the Maximization of the Expected Growth Rate. A crucial task in portfolio optimization is estimating key parameters such as means and covariances. However, in many cases, there is insufficient historical data to accurately estimate these parameters. To address this, we generated additional data using ForGAN. In order to preserve correlations between assets, we applied Principal Component Analysis (PCA) to the joint log returns of stock prices for Amazon, Apple, and Netflix, trained separate GANs for each principal component, and then transformed the generated data from each component back into the log return space to estimate the parameters relevant for portfolio optimization, on standard training data and simulated data by GANs in order to compare their performance. To further compare the performance of ForGAN with PCA, we employed another GAN model, TimeGAN. TimeGAN uses an embedding network to represent the data in a lower dimensional space, allowing it to capture temporal dependencies and relationships across time points. However, while TimeGAN excels at preserving temporal patterns, the dimensionality reduction can introduce inaccuracies, particularly in retaining correlations between assets. For GAN with PCA, on the other hand, effectively maintains these correlations, providing a more reliable framework for portfolio optimization. Finally, we evaluated the reliability of GAN-generated data against historical data by using synthetic data where conditions are more controlled and the exact solution is known. Our analysis demonstrated that GAN-generated data led to improved portfolio allocations. Additionally, confidence intervals (CIs) for key parameters, such as drift, volatility, and correlation, were generally narrower for the GAN-generated data, indicating potentially higher precision and reliability in certain financial modeling settings. This suggests that, under the right circumstances, GAN-generated data can provide more reliable estimates.