Moragammana Gedara, Avanthi2025-09-022025-09-022025-08-192025-08-19http://hdl.handle.net/1993/39276This thesis explores advanced statistical and deep learning models for volatility forecasting and network inference for enhanced portfolio optimization. In the domain of risk forecasting, traditional time series models along with machine learning and deep learning models are evaluated for volatility forecasting. These models are also used to generate model risk forecasts for deep learning models, offering an advanced framework to assess financial system stability. Furthermore, this thesis demonstrates the superiority of the neural network autoregressive model (NNAR) with forecast linear augmented projection (FLAP) over the autoregressive integrated moving average (ARIMA) model with FLAP in forecasting multivariate price and volatility. This performance achievement leads to reduced forecast error variance. The thesis further introduces data-driven fuzzy volatility networks and nonlinear adaptive fuzzy adjacency matrices, which capture model uncertainty in volatility correlations and enable the construction of resilient network structures. These are employed in combination with clustering techniques, network-based community detection methods, and PageRank for portfolio construction, leading to diversified portfolios with improved cumulative returns. Another key innovation is introducing neuro correlation networks using nonlinear correlation measures derived from innovations of NNAR models. Dynamic price networks are used to account for the non-stationarity in financial time series, enabling improved insight into market structure and systemic risk over time. Random matrix theory (RMT) is used to denoise covariance matrices, thereby improving the accuracy of estimation, demonstrating superior performance in portfolio optimization, especially with t-distributed returns. Moreover, the theorem of combined estimating functions, which introduces a new risk measure with a smaller variance, is studied and applied in both risk forecasting and portfolio optimization. Extensive simulations and empirical analysis using stocks, cryptocurrencies, and other assets validate the efficiency of these methods.engRisk forecastingNetwork analysisPortfolio optimizationCombined estimating functions