This study addresses critical gaps in financial risk assessment and portfolio optimization by integrating advanced machine learning (ML) and deep learning (DL) techniques to handle the complexities of non-linearity, non-normality, and dynamic correlations among financial assets. This study comprehensively analyzes various dimensionality reduction techniques across different financial assets and time periods. By extracting non-linear features and constructing dynamic, data-driven covariance matrices, both linear and non-linear interactions among assets have been captured. This novel methodology hybridizes ML/DL and statistical approaches to enhance the robustness and resilience of portfolio optimization. The findings demonstrate significant improvements in profitability and stability under varying market conditions, offering a substantial advancement over prior studies. Therefore, this research provides a pioneering framework for more accurate and dynamic financial analysis, setting a novel standard in this research direction.

Forecasting financial asset prices and quantifying associated risks are critical challenges in computational finance. This paper presents an optimal forecast combination framework by integrating advanced time series models and machine learning techniques to enhance prediction accuracy and risk assessment. A novel data-driven risk measure (DDRisknew) based on price differences is introduced, and sign correlation is used to capture risk and mitigate the limitations of traditional risk metrics. Our approach incorporates state-of-the-art forecasting models, including ARIMA, Neural Network Autoregressive, Long Short-Term Memory, XGBoost, and Random Forest, alongside two combination methods: equally weighted averages (FComp_SA) and datadriven optimal weighted averages (FComp_Weighted). Experimental results conducted on a dataset of stocks from ten diverse sectors during the highly volatile COVID-19 period demonstrate the superior performance of FComp_Weighted in minimizing forecasting errors across multiple metrics (RMSE, MAE, MAPE). Moreover, the RMSE of asset price and DDRisknewforecasts using FComp_Weighted models is always lower than the RMSE obtained using the FComp_SA model. This study underscores the importance of combining forecasts and provides a robust, computationally efficient framework for predictive modeling in financial markets. These findings have implications for algorithmic trading, portfolio optimization, and risk management, paving the way for future applications in broader domains like energy and cryptocurrency markets.

Contemporary information technology applications are overwhelmed by big data and require advanced data science analytics for careful investigation, interpretation, and predictions. Data sets in various applications exhibit high frequency with non-linear dynamic variability, and hence, leveraging the strengths of data-driven feature selection and sophisticated machine learning architectures becomes essential.This study proposes two novel architectures- Data-Driven Long Short-Term Memory (DD-LSTM) and Data-Driven Gated Recurrent Unit (DD-GRU), to improve predictive accuracy for highly fluctuating time-series data. Input data are log-transformed and used to derive data-driven risk forecasts and non-linear residuals based on underlying statistical features, which are then integrated with normalized original data into hyperparameter-optimized LSTM and GRU models. Experimental results with a financial dataset show that the proposed frameworks significantly outperform conventional LSTM and GRU by capturing intricate temporal patterns and risk dynamics. DD-GRU, in particular, exhibits greater computational efficiency, making it a robust solution for modeling nonlinear and irregular time-series data. This research not only addresses the critical challenge of optimizing temporal feature selection in high-frequency datasets but also offers a robust framework for analyzing complex temporal patterns across diverse high-frequency data sources.

Forecasting stock market indices is a challenging task due to the inherent complexity, non-linearity, and stochastic nature of financial time series. Although deep learning models, such as Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) architectures, outperform traditional econometric methods in capturing temporal dependencies, their standalone implementations often lack robustness and generalizability. This study presents a novel hybrid framework combining recurrent neural networks with Support Vector Regression (SVR) to address these limitations. The proposed approach integrates the sequential learning capabilities of LSTM and GRU with the nonlinear regression strengths of SVR, achieving superior predictive performance across diverse global indices. Empirical results highlight significant improvements over baseline models in both accuracy and adaptability to varying market conditions. The hybrid framework demonstrates its effectiveness in merging the advantages of its components, providing robust, generalizable predictions with reduced susceptibility to overfitting. These findings pave the way for future research in hybrid financial forecasting methods and their practical applications.

The climate crisis has sparked a global shift toward renewable energy sources, increasing the demand for models that provide accurate risk assessment and forecasting to support informed investment decisions. The novelty of this study is to analyze renewable energy investments through three methodological approaches: risk assessment, deep learning-based volatility forecasting, and renewable energy demand forecasting. First, risk profiles of two renewable energy stocks (NextEra Energy and Iberdrola) and two traditional energy stocks (ExxonMobil and Chevron) are evaluated for the time period 2020 to 2024. Second, deep learning (DL) models such as recurrent neural network (RNN), long short-term memory (LSTM), gated recurrent unit (GRU), bidirectional long short-term memory (BiLSTM), bidirectional gated recurrent unit (BiGRU) are employed, and it is shown that renewable energy stocks have more stable performance across all DL models, with BiLSTM revealed as the most robust architecture. Third, UK liquid biofuel consumption trends are analyzed using multiple forecasting methods, including Mean, Naïve, Seasonal Naïve, Drift, and machine learning models. It is shown that the neural network autoregressive (NNAR) model has the highest forecast accuracy, and among the combined forecast models, constrained least squares achieved the highest forecast accuracy. The results indicate that renewable energy produces lower risk exposure and more stable returns, and improves predictability despite short-term volatility.

This study investigates data-driven financial correlation networks with a particular focus on modeling log returns using a data-driven t-distribution. A key contribution is showing that the covariance matrix of absolute log returns, used in volatility networks can be expressed as a function of the sign correlation and the covariance matrix of log returns. Fuzzy adjacency matrices are introduced to account for the uncertainty inherent in correlation estimates that depend on the degrees of freedom. Using data from 55 stocks across 13 sectors and S&P500 (big data), we compare four different networks based on correlations of log returns, volatility of log returns, data-driven volatility of log returns and sign(±) of returns. Three dynamic networks based on price correlations, ARIMA innovation correlations of the price and neuro innovation correlations of the price are also considered. All seven networks are evaluated using metrics such as average node degree, sparsity, and maximum eigenvalue. Unlike the existing work, the novelty of this study is demonstrating a relationship between data driven volatility networks and recently proposed volatility correlation networks without using distributional properties. Three different community detection algorithms demonstrate that the proposed data-driven volatility network proposed in this paper has a higher modularity score.

The eigenvalues of data-driven exponentially weighted moving average (DDEWMA) covariance matrix of stock returns plays an important role in portfolio optimization. Moreover, the eigenvalues of the Laplacian matrix play a fundamental role in financial network analysis. The novelty of this paper is to apply Random Matrix Theory (RMT) to denoise three covariance matrices ( empirical covariance, neuro covariance and DDEWMA covariance). Simulation study shows that portfolio weights generated using RMT filtered empirical covariance matrices based on both normal and t-distributed returns are more resilient. The networks built from t-distributed returns are more resilient (fewer but stronger connections with smaller average degree of nodes) than the networks built from normally distributed returns. Unlike the existing work, the novelty of this paper is to first show that the superiority of the RMT-filtered DDEWMA covariance model in portfolio optimization and, then show that the networks built from t-distributed returns are more resilient.

Forecasting stock prices and volatility plays a crucial role in making better investment decisions. Recently, there has been a growing interest in studying the Forecast Linear Augmented Projection (FLAP) method for multivariate normally distributed time series to reduce the forecast error variance and mean squared error (MSE) of long-term forecasts. FLAP method consists of three steps: formation of principal components, forecasting original and component series (base forecasts), and then projecting those base forecasts. First, this paper shows that the non-linear prediction (conditional mean) has a smaller MSE than the linear prediction. Then, it demonstrates that for multivariate time series, forecasts using the neural network autoregressive (NNAR) model with FLAP outperform those obtained by the commonly used autoregressive integrated moving average (ARIMA) model forecasts with FLAP (resulting in lower out-of-sample root mean squared error (RMSE) in general). For simulated multivariate data with t-distributed errors, the combined forecast model with NNAR and FLAP outperforms the NNAR forecast model. In the empirical study, we forecast stock price and volatility for 55 most traded stocks and S&P500 index using the ARIMA model with FLAP and the NNAR model with FLAP. The results show that FLAP is more effective in reducing forecast error variance and RMSE for non-stationary multivariate price and volatility forecasts.

Recently, there has been a growing interest in studying both long-term and short-term forecasts of electricity demand using dynamic regression models with seasonal ARIMA (SARIMA) errors and neural network autoregression (NNAR) models. Most of the electricity demand forecasting models investigated in the literature involved two features: temperature and day type, and only the point forecasts of temperature are used to obtain forecasts of electricity demand. However, it is crucial to acknowledge that temperature fluctuates throughout the day, and it is more appropriate to incorporate the forecast error variability and use the fuzzy forecasts of the temperature as an input to forecast electricity demand. This paper uses a novel fuzzy two-step approach to generate fuzzy forecasts of electricity demand. In step 1, fuzzy forecasts of temperature are obtained by incorporating additional features such as precipitation, irradiance, snowfall, snow mass, cloud cover, and air density. Thirteen distinct models, including neural network regression models and Facebook industrial Prophet models, are fitted to temperature data, and the best forecasting model for temperature is selected based on forecast accuracy measures. In step 2, the fuzzy forecasts of the temperature are used as a feature with day type (weekday/weekend/holiday) to obtain fuzzy forecasts of electricity demand. The superior performance of neural network fuzzy forecasts of electricity demand in terms of forecast accuracy is demonstrated for Ontario electricity demand data.

Recently, there has been a growing interest in using neuro volatility models in fuzzy forecasting and fuzzy option pricing. Neuro volatility models are used to model and predict financial market volatility by extending the neural network autoregressive (NNAR) model for nonlinear nonstationary times series data. In financial risk forecasting, various risk forecasting models for volatility are used to obtain the volatility forecasts, and the model risk ratio based on all the models is calculated to assess the stability of the financial system. However, the recently proposed neuro volatility models (based on neural networks such as LSTM, NNAR, etc.) are not used in evaluating the model risk. In this paper, novel 'neuro model risk forecasts' are obtained by including recently proposed neuro volatility models, and the resiliency of the financial system is studied. Unlike the existing model risk ratio forecasting based on linear volatility models, the driving idea is to use more appropriate nonlinear nonstationary neuro volatility forecasting models to obtain the model risk forecasts. The proposed model risk forecasts in this paper have been evaluated through extensive experiments, and it is shown that the model risk ratio can effectively serve as a metric for assessing the resilience and stability of the targeted financial system.

For many Markov chains that arise in applications (health, finance, etc.), state spaces are huge, and existing matrix methods may not be practical or even not possible to implement. In the literature, the expected waiting time for Markov chain (with a smaller number of states) generated patterns are obtained by finding an appropriate pattern matrix and solving a set of linear equations. In this paper, a fuzzy transition probability (TP) matrix is introduced, and a data-driven fuzzy pattern mining algorithm is proposed for sequence data of any length. The proposed algorithm, which avoids the inversion of the pattern matrix, is applicable to Markov chains with huge state spaces. The proposed algorithm studies two examples involving DNA sequence data with 3954 base pairs and patterns generated by the log-returns of the stocks/cryptocurrencies. Expected weighting times are compared with the traditional matrix approach. Incorporating stochastic variation in the TP estimates through fuzzy matrices, the new approach provides an alternative path to produce$\alpha$-cuts for TP matrices. The main contribution of this paper is to fit an appropriate MC model to a given sequence data and use the proposed fuzzy pattern mining algorithm to obtain resilient probabilistic forecasts and expected waiting time to reach patterns of interest.

Recently, there has been a growing interest in utilizing empirical correlations of log returns to examine financial network models for stock prices by representing stocks as nodes and their relationships as edges. In this paper, empirical cor-relation, data-driven correlation, and cosine similarity matrices are used to obtain adjacency matrices for connectedness. For a given number of nodes, the simplest Erdos and Rényi (ER) model can be obtained by fixing the number of stocks and estimating the probability for any two vertices to be connected by an edge. Unlike existing work, the driving idea in this paper is to estimate the probability with the median cross-correlation to construct the ER network for observed volatility. Moreover, to address the uncertainty associated with these estimates of connectedness, this study introduces data-driven non-linear adaptive symmetric fuzzy adjacency matrices. In the literature, a certain thresh-old is identified for a network considering its connectedness. In this study, threshold and fuzzy parameters for the corre-sponding minimally connected fuzzy networks are determined, revealing unique network structures and the most significant stocks/cryptocurrencies (nodes with the highest number of links). Furthermore, as an application of the suggested fuzzy networks, three clustering approaches, fuzzy network clustering, k-means clustering, and Sharpe ratio clustering, are applied followed by the PageRank algorithm to construct optimal portfolios. A comparison of the constructed portfolios suggests that the fuzzy networks and clustering techniques are capable of yielding high cumulative returns during the study period.

Constructing resilient portfolios is of crucial and utmost importance to investment management. This study compares traditional and data-driven models for building resilient portfolios and analyzes their performance for stocks (S&P 500) and highly volatile cryptocurrency markets. The study investigates the performance of traditional models, such as mean-variance and constrained optimization, and a recently proposed data-driven resilient portfolio optimization model for stocks. Moreover, the study analyzes these methods with evolving S&P CME bitcoin futures index and the Crypto20 index. These analyses highlight the need for further investigation into traditional and data-driven approaches for resilient portfolio optimization, including higher-order moments, particularly under varying market conditions. This study provides valuable insights for investors and portfolio managers aiming to build resilient portfolios that could be used in different market environments.

Recently there has been a growing interest in studying fuzzy option pricing using Monte Carlo (MC) methods for diffusion models. The traditional volatility estimator has a larger asymptotic variance. In this paper, data-driven neuro-volatility estimates with smaller variances are used to obtain direct volatility forecasts. Asymmetric nonlinear adaptive fuzzy numbers are used to address ambiguity and vagueness associated with volatility estimates. This study uses fuzzy set theory and data-driven volatility forecasts to study call option prices of the S&P 500 index. Four modeling approaches have been considered, Black-Scholes (BS) model, Monte Carlo option pricing with normal / t errors, and the Jump-Diffusion (JD) model. Fuzzy α-cuts of option prices are presented and discussed under different parameter values. Our experimental study suggests that the JD model predicts the call option price more accurately compared to BS, normal errors, and t errors using the volatility estimate obtained using the Bayesian approach.

A profitable data-driven algorithmic trading algorithm will benefit from a dynamic system that can produce accurate hedge ratio estimates and short-term innovation volatility forecasts. Commonly used pairs and multiple trading strategies are constructed using the Kalman Filter (KF) and exploiting mean reversion in co-integrated nonstationary stock prices. However, KFs are sensitive to model errors. Misspecified modelling produces unstable solutions for dynamic systems. Fading-Memory Filter (FMF) uses a discounting weight to past observations. Compared to a standard KF, FMF addresses more recent observations and is more resilient (less sensitive) to modelling errors. However, the FMF algorithm does not provide slope parameter covariance matrix updates and innovation volatility forecasts. This paper proposes a novel resilient FMF algorithm for pairs trading and multiple trading by defining an appropriate data-driven innovation volatility forecasting model. The FMF-based strategies are implemented through some experiments on the hourly prices (high-frequency data) of Bitcoin, Ethereum and Litecoin. It is shown that the proposed FMF trading strategies outperform the existing KF trading strategies and they are more profitable in the bear market over time, especially for continuous falling of prices and the short-lived and sharp rally recovery where prices are not stationary.

Data-driven volatility models and neuro-volatility models have the potential to revolutionize the area of Computational Finance. Volatility measures the variation of a time series data, and thus it is also a driving factor for the risk forecasting of returns from investment in cryptocurrencies. A cryptocurrency is a decentralized medium of exchange that relies on cryptographic primitives to facilitate the trustless transfer of value between different parties. Instead of being physical money, cryptocurrency payments exist purely as digital entries on an online ledger called blockchain that describe specific transactions.Many commonly used risk forecasting models do not take into account the uncertainty associated with the volatility of an underlying asset to obtain the risk forecasts. Some tools from the fuzzy set theory can be incorporated into the forecasting models to account for this uncertainty. Interest in the use of hybrid models for fuzzy volatility forecasts is growing. However, a major drawback is that the fuzzy coefficient hybrid models used in fuzzy volatility forecasts are not data-driven. This paper uses fuzzy set theory with data-driven volatility and data-driven neuro-volatility forecasts to study the fuzzy risk forecasts. The study focuses on long-term volatility forecasts with daily price data while briefly exploring forecasting models with high-frequency (hourly) data as an avenue for future research. Simple yet effective models incorporating fuzziness to obtain fuzzy risk volatility forecasts and fuzzy VaR forecasts are presented. The key underlying idea, unlike the existing risk forecasting, is the use of a hybrid nonlinear adaptive fuzzy model for volatility.

Pairs trading strategies are constructed based on exploiting mean reversion in security prices, which have been demonstrated to perform well for stocks. However, their performance is not widely studied for cryptocurrencies, which are usually discerned as inefficient and unpredictable. One significant advantage of pairs trading is that potential profits can be generated regardless of the overall market movement. The pairs trading has the potential to be profitable for cryptocurrencies in bear markets and with intraday data. Kalman filter (KF) algorithms are popular for pairs trading to update the hedge ratio dynamically. They reduce the arbitrariness in parameter optimization by putting constraints on the parameter space. However, a major drawback is that the innovation volatility estimate calculated by using a KF algorithm is always affected by the initial values and outliers. An effective resilient filtering approach to estimate the innovation volatility is presented in this paper for cryptocurrencies. This paper presents rolling regression pairs trading strategies, traditional KF pairs trading strategies and resilient filter pairs trading strategies. The proposed trading strategies have been evaluated through some experiments on hourly Bitcoin USD and Ethereum USD prices and it is shown that the proposed resilient filter trading strategy is much more stable to initial values than the traditional KF trading strategy.

Recently there has been a growing interest in applying neural network modelling from natural language processing to financial time series prediction problems in computational finance. Cryptocurrency price prediction is a challenging problem with non-stationary market price and volatility clustering. Cryp-tocurrency data tends to be non-stationary, which means that predictive information extracted using deep learning techniques on observed data can not be used with future data. Moreover, there is a very little signal in cryptocurrency data to indicate the future direction of the market. This paper proposes a sensible way to frame the prediction problem as a dynamic regression problem by defining the features in the feedforward neural networks and the target as an appropriate average of the historical data. The novelty of this paper is to use deep learning algorithms and statistical bootstrapping to obtain cryptocurrency price prediction and the corresponding prediction intervals. It is shown that neural networks are capable of modelling nonlinearity directly for nonlinear time series models. The proposed hybrid approach is evaluated using simulated and cryptocurrency data through numerical experiments. Moreover, Gaussian and boot-strap prediction intervals for the price and the volatility of the prediction errors, are also discussed in some detail.

The forecasting problems in Computational Finance involve modelling the vagueness and imprecision inherent to the financial markets. Fuzzy set theory has a unique ability to quantitatively and qualitatively model and analyze such problems. Volatility forecasting plays an important role in financial risk management and in option pricing. Recently, there has been a growing interest in data-driven volatility models and neurovolatility models for risk forecasting of stocks and index funds. However, even these state-of-the-art models do not take into account the fuzzy volatility in their risk forecasts.Cryptocurrencies are a novel financial asset class based on the Blockchain technology. Cryptocurrencies have gained popularity among retail investors as a financial asset with high risks and high returns. The extremely volatile nature of cryptocurrencies (compared to traditional assets) makes forecasting their volatility more challenging. A simple algorithmic trading approach, Simple Moving Average (SMA) crossover strategy, is used to calculate the Algo returns. This paper provides fuzzy forecasts of the volatility of Algo returns using the data-driven Exponentially Weighted Moving Average (DD-EWMA) and neuro models for six major cryptocurrencies. We also compute and compare fuzzy volatility forecasts of four major tech stocks and Chicago Board Options Exchange’s (CBOE) volatility index (VIX) using DD-EWMA and neuro models. Our experimental results show that the data-driven models produce better forecasts for cryptocurrencies as compared to the neuro models, while for the regular stocks and indexes, no such definitive conclusion could be drawn.