Artificial Intelligence for Long-Memory Economic Time Series: Methodological Approaches and Applications of LSTM and GRU Models

This thesis investigates whether Long Short-Term Memory (LSTM) neural networks can improve the forecasting performance of long-memory time series compared to classical statistical models, and whether their effectiveness is greater when used as standalone forecasting tools or as components of hybrid models. The research combines a theoretical review of long-memory processes, classical statistical models, and neural network architectures with an empirical study based on Italian inflation time-series data. The methodology includes stationarity testing, fractional differencing estimation, implementation of benchmark ARFIMA-type models, development of LSTM and GRU neural networks, hyperparameter tuning, cross-validation, and out-of-sample forecasting evaluation. The findings demonstrate that neural-network approaches, particularly LSTM and GRU architectures, are capable of effectively modeling the temporal dynamics present in long-memory economic series. The empirical results show that GRU and LSTM models can outperform classical statistical benchmarks in forecasting accuracy, especially when nonlinear relationships are significant. At the same time, hybrid structures widely presented in the literature did not consistently outperform standalone models. The findings demonstrate that neural network approaches, particularly LSTM and GRU architectures, can effectively model the temporal dynamics of long-memory economic series. Empirical results suggest that GRU and LSTM models can outperform classical statistical benchmarks in forecasting accuracy, particularly when nonlinear relationships are significant. However, hybrid structures discussed in the literature did not consistently outperform standalone models. These results should be interpreted with caution, as performance varies across forecasting horizons and series lengths.