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.

Pairs trading and multiple trading strategies are types of market-neutral strategies to use a pair or a combination of stocks and other financial instruments with co-integration or co-movements to generate potential profits, which may not be affected by the direction of the overall market. Commonly used pairs and multiple trading strategies are constructed using the Kalman Filter (KF) to utilize mean reversion in nonstationary but co-integrated asset prices. In this paper, we propose novel resilient pairs trading and multiple trading strategies using the combination of the KF algorithm and the KF innovation volatility interval forecasts using neural networks. The proposed trading strategies are implemented and investigated using the hourly prices of Bitcoin, Ethereum and Bitcoin Cash in the bear market. Those crypto assets are selected because they move in the same direction in the long term and have high trading volumes. The experimental results reveal performance for the proposed trading strategies with the upper and lower trading intervals using KF innovation volatility interval forecasts superior to that of the trading strategies with upper and lower trading bands using KF innovation volatility point forecasts. The performance and robustness of the proposed trading strategies using a proper assumption of transaction costs have also been examined. The strategies using innovation volatility interval forecasts consistently generate higher profits and a more robust number of transactions with or without transaction costs than those using innovation volatility point forecasts.

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.

One of the recent developments in computational finance has been the rise in using graph-based approaches to analyse stock market dynamics systematically. In algo trading literature, stocks for pairs trading and multiple trading are commonly selected by using Engle Granger and Johansen co-integration tests. Identifying all pairs eligible for trading in large datasets, entails a significant computational burden. In this paper, price correlation-based dynamic networks and differenced price series-based correlation networks and their importance ranks are used to pre-select pairs for trading. Algorithmic trading profits using commonly used co-integration methods are compared with the profits made by proposed correlation-based financial networks. Unlike the existing work, the novelty of the paper is that it uses data-driven correlation-based financial network approach to propose a stock selection method for pairs trading. In this paper, profit per transaction is used to compare the trading strategies. The superiority of the financial network stock selection method is discussed as well in some detail.

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.

There have been several studies in the literature discussing the profitability with various trading strategies. Two common strategies are pairs trading and momentum strategies. The momentum strategy aims to exploit the phenomenon of momentum, where securities that have performed well in the past are likely to continue performing well in the future. The concept behind a pairs trading of stocks is similar to the statistical idea of cointegration. The goal of pairs trading is to profit from the relative price movements of the two assets, rather than from the absolute price movements of either asset. This strategy is generally implemented using algorithmic trading techniques, and it is often used by traders and investors to take advantage of mispricing in the market. In this study we first compare these two strategies and implement them to study for their profitability. We considered two major cryptocurrencies (Bitcoin and Ethereum) for these two trading strategies and show that with daily price data, dual momentum strategy generates significantly better results than the pairs trading strategy.

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.

The market focuses on the Cboe Volatility Index (VIX) or Fear Index, an option-implied forecast of 30 calendar-day realized volatility of S&P 500 returns derived from a cross-section of vanilla options. The VIX is determined using a formula that derives the market’s expectation of realized one-month standard deviation of returns backed out from the near-term call and put options on the S&P 500 index. Market participants such as traders, asset managers, and risk managers, keenly watch the VIX index, and are interested in achieving accurate intelligent probabilistic forecasts of the VIX, and also of the realized volatility of individual stocks. These volatility forecasts are useful to options traders placing bets on the future volatility of individual stocks. This paper examines models that only utilize past values of the VIX and document improvements in forecasting the VIX (and its volatility) over different horizons. The approaches include long short-term memory (LSTM) models, simple moving average methods, data-driven neuro volatility techniques, and industry models like Prophet. Uniquely, we propose a novel VIX price interval forecasting model. The driving idea, unlike the existing VIX price forecasting models, is that the proposed novel LSTM interval forecasting method trains two LSTMs to obtain price forecasts and the forecast error volatility forecasts. All the proposed forecasting methods also avoid model identification and estimation issues, especially for a series like the VIX which is non-stationary. We compare models and document which ones perform best for varied horizons.

Long-term electricity load forecasts are the main in-puts of production planning and scheduling at different horizons and load forecasting plays an important role in balancing the electricity grid. Forecast (prediction) intervals provide the mea-sure of uncertainty of the point forecasts (predictions). However, a data-driven innovation distribution approach is not available to calculate long-term prediction intervals when using deep learning neural networks dynamic regression (NNDR) models. In this paper, a feedforward NNDR model for long-term electricity demand forecasting is introduced and the corresponding data-driven prediction intervals (PIs) are obtained. The novelty of this paper is to use long-term point forecasts and model innovation residuals to obtain three classes of PIs by using data-driven innovation distribution, nonlinear adaptive trapezoidal fuzzy numbers and bootstrapping. It is shown that NNDR models and dynamic regression models with Seasonal Autoregressive Integrated Moving Average (SARIMA) errors (DRSARIMA) are capable of modelling seasonality as well as nonlinearity for demand and other features such as temperature and a day type indicator. NNDR models and DRSARIMA models are evaluated through numerical experiments and the results show that the proposed NNDR model outperforms the DRSARIMA model to forecast demand during the volatile period. It is also shown that innovation residuals from DRSARIMA and NNDR follow heavy-tailed$t$distributions. The data-driven probabilistic Student$t$PIs have higher coverage probabilities than either trapezoidal fuzzy PIs or the bootstrap PIs for both DRSARIMA and NNDR models.

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.

Electricity price forecasting plays an important role in decision making on bidding strategies of selling and buying electricity. This paper computes one day-ahead (DA) quantile forecasts of electricity prices in a highly volatile market by applying regression models to a pool of point forecasts. Three data-driven forecasting methods are implemented to generate DA point forecasts of the Ontario market’s electricity prices. In order to generate the three sets of point forecasts, we use: i) the triple exponential smoothing (TES) method, ii) a neural network (NN) that combines layers of Convolutional neurons and gradient recurrent units (GRU), iii) an extreme gradient boosted (XGB) non-linear regression approach. Performance of the three models compared against a benchmark which considers the forecast of electricity prices as the average price of the same hour and day during the last four weeks. The TES method decreases the mean absolute error (MAE) of the benchmark model from 10.29 to 9.42. The Convolutional GRU (ConvGRU) model and XGB regression also reduce the MAE to 8.20 and 7.06, respectively. Finally, quantile regression averaging (QRA) is applied to the pool of point forecasts obtained by TES, ConvGRU, and XGB methods to compute DA quantile forecasts of electricity prices. Moreover, the QRA method is further developed in this work by employing gradient boosting non-linear regression (GBR). Our analysis using real data reveals that the GBR method provides more reliable quantiles as well as tighter prediction intervals with smaller forecasting errors than QRA.

Supply chain literature reveals that study of resilient supply chains and bullwhip effect (BE) have been receiving special attention during pandemic for supply chains with seasonal as well as nonseasonal demand components. The BE phenomenon has been detected in various industries and sectors, and causes multiple inefficiencies such as higher costs of producing more than needed, wastage and transportation costs. As a result, BE forecast is of great importance for academics and supply chain managers. Despite the multitude of studies that have emerged addressing this issue, the impact of the quality of dynamic forecasts on the BE has received limited coverage in the literature. Optimal dynamic forecasts of the demand could allow managers to mitigate the upstream amplification of orders (and thus the BE), as well as reduce unnecessary inventory costs. Order quantity and BE in a supply chain depend on the forecast of the future demand. Usually minimum mean square error (MMSE) forecasts of the future demand are obtained by fitting an appropriate seasonal auto-regressive moving average (ARMA) time series model. However, a major drawback of the MMSE forecasting method is that it does not provide the associated risk forecasts. In this paper, a simple yet effective machine learning demand forecasting approach without fitting any time series model is presented.Specifically, a novel data driven machine learning algorithm that bypasses traditional forecasting steps and allows forecast weights to be optimized by minimizing the one-step ahead forecast error sum of squares (FESS) is proposed. A novel stability metric of a supply chain is proposed as the risk adjusted forecast of the future demand. It is shown that the risk adjusted forecasts can be used to check whether a given supply chain is resilient. In order to be more resilient and competitive in the current market, business leaders around the world agree that it is necessary to modernize and make major changes to their supply chain strategies. Demand risk forecasts obtained by the proposed machine learning approach allow supply chain managers to enhance the forecasting power of the order quantity and construct more resilient supply chains. The performance of proposed approach is evaluated through numerical experiments using simulated data and weekly demand data of two products. The results show that the performance of the proposed forecasts and risk adjusted forecasts of the future demand are better than the commonly used MMSE forecasts of the future demand.

Algorithmic trading uses a computer program that follows a defined set of instructions (an algorithm) to place a trade and can generate profits at a speed and frequency that is impossible for a human trader. Current state-of-the-art in algorithmic trading uses Kalman filtering (KF) and maximum informative resilient filtering (MIRF) that allow traders to enhance the predictive power of statistical models and improve trading strategies. There has been a growing interest in using MIRF in pairs trading, and a major drawback is that a threshold value (assumed to be one) is selected in an ad hoc way rather than maximizing the Sharpe ratio. In this paper, a novel random weights innovation volatility forecasting (RWIVF) algorithm is introduced to obtain the optimal data-driven weights of past observed volatilities instead of the equal weights by extending the Bollinger bands algo-tradinng strategy. RWIVF algorithm is also compared with the commonly used KF algorithm. Autocorrelations of the absolute values of the innovations in multiple trading are used to demonstrate that the innovations are non-normal with time-varying volatility. Performance of the RWIVF algorithm is shown using the experiments on cointegrated exchange-traded funds (ETFs). Analyses also explain how our approach can improve the performance of the trading strategies. The proposed novel resilient (robustness to initial values) trading strategies to the volatile stock market are also discussed in some detail.

There has been a growing interest in studying risk forecasting using data-driven exponential weighted moving average (DD-EWMA) volatility models as well as nonlinear neuro volatility models based on Neural network (NN). However, the recently proposed volatility forecasting models have not been used to study portfolio optimization. Large kurtosis of the portfolio return sequence shows that it follows a heavy-tailed t distribution. Significant sample autocorrelations of the absolute portfolio returns and squared portfolio returns suggest that time-varying volatility models are more appropriate to model the volatility. In this paper, a DD-EWMA portfolio volatility forecasting model is used to study the generalized portfolio optimization using the intelligent probabilistic risk forecasts based on data-driven t distribution of the portfolio returns. Optimal portfolio weights are obtained by minimizing the corresponding risk forecasts of portfolio volatility, mean absolute deviation (MAD), Value-at-Risk (VaR), and conditional Value-at-Risk (CVaR) for minimum risk forecast portfolios. Moreover the portfolio weights of the generalized tangency portfolios with different risk measures are obtained by maximizing the corresponding portfolio Sharpe ratio (PSR) forecasts. Experiments are conducted to show that the DD-EWMA volatility forecasting model is most computationally efficient (less computing time), whereas neuro volatility model takes longer time to obtain one-step ahead portfolio volatility forecasts. Moreover, the superiority of the portfolio selection based on data-driven volatility forecasts over the portfolio selection based on volatility estimates is demonstrated through numerical experiments using ten frequently traded stocks.

Portfolio risk management is an important success factor in an organization’s ability to deliver more business value. Moreover, constructing a true resilient portfolio is impossible without the inclusion of higher-order moments such as skewness and kurtosis. Recently there has been a growing interest in using machine learning methods with empirical variance covariance matrix of returns to study Markowitz portfolio optimization. A major drawback is that the tangency portfolios constructed by using the existing portfolio risk measures such as portfolio standard deviation, value-at-risk (VaR), conditional value-at-risk (CVaR), maximum absolute deviation (MAD) are always affected by the larger skewness and kurtosis of the portfolio return. This paper develops a set of metrics that extend the traditional portfolio Sharpe ratio (PSR) to measures that include skewness and kurtosis. Using a random portfolio approach, the paper demonstrates how to use these new metrics and optimize portfolios. Inclusion of higher moments such as skewness and kurtosis in portfolio risk management acknowledges the risk of asymmetric and heavy-tailed returns and can help in constructing resilient portfolios. For portfolio optimization, simple yet effective novel data-driven resilient portfolio risk measures incorporating skewness and kurtosis are presented in this paper. The results show that the performance of maximum mean-risk portfolios using the proposed portfolio risk measures based on volatility correlation and sign correlation outperform the commonly used tangency portfolio using portfolio standard deviation.

Recently, there has been a growing interest in portfolio optimization using graphical LASSO (GL) machine learning method, by assuming normality for asset returns. However, a major drawback is that most of the asset returns follow non-normal distributions and sample percentiles are used to study the portfolio optimization with Value-at-Risk (VaR) as a risk measure. In this paper, a data-driven random weights algorithm (RWA) and a sign correlation based portfolio return distribution are used to study the fuzzy portfolio optimization. The superiority of RWA over the commonly used genetic algorithm (GA) in computing the optimal portfolio weights is demonstrated by comparing the computing time. When comparing the estimate of the risk tolerance coefficient and the theoretical value for tangency portfolios with volatility as a risk measure, RWA outperforms (smaller absolute error) the GA. The novelty of this paper is the use of RWA and GA to calculate the fuzzy estimates (interval estimates) of the risk tolerance coefficient/optimal weights and using the sign correlation to obtain the data-driven distribution of the portfolio returns. More specifically the novelty is to obtain the fuzzy estimates of the risk tolerance coefficient and portfolio weights by modelling the portfolio volatility as an asymmetric triangular fuzzy number from the data-driven observed portfolio volatilities. In particular, the proposed RWA as well as GA lead to machine learning solutions for the portfolio optimization problems without a closed form solution and provide fuzzy estimates of the risk tolerance coefficient and the optimal portfolio weights.

Electricity is a special commodity that has to be kept available at all times. In fact, power plants need to have accurate forecast of electricity demand in order to provide enough electricity for customers. Final customers are able to establish their own power plants to decrease their dependency on the grid. For example rooftop photovoltaic panels are getting more popular among residential customers. It seems that meteorological variables such as solar irradiance play an important role in load forecasting. Moreover, temperature is also a main determinant of electricity demand. In this paper, we propose a model for short-term load forecasting which consists of hourly weather data (including seasonal variation as well) and historical load data. Machine learning algorithms such as support vector regression (SVR), least absolute shrinkage and selection operator (LASSO) regression and a multilayer neural network (NN) are used for short-term load forecasting. In order to improve the forecast accuracy (smaller mean absolute error) of NN, we propose a dual phase forecasting method. In the first phase, data driven double exponential smoothing (DDDES) is used to generate electricity load forecasts. In the second phase, the results of first phase forecasting are fed into a multilayer NN to have more accurate forecasts of electricity demand. It is shown that NN outperforms the other two methods. Our data analysis shows a significant improvement in terms of performance where maximum mean absolute error (MAE) decreases from 367.26 to 115.30.

Volatility forecasts and stock price forecasts play major roles in algorithmic trading. In this paper, joint forecasts of volatility and stock price are first obtained and then applied to algorithmic trading. Interval forecasts of stock prices are constructed using generalized double exponential smoothing (GDES) for stock price forecasts and data-driven exponentially weighted moving average (DD-EWMA) for volatility forecasts. Multi-stepahead interval forecasts for nonstationary stock price series are obtained. As an application, one-step-ahead interval forecasts are used to propose a novel dynamic data-driven algorithmic trading strategy. Commonly used simple moving average (SMA) crossover trading strategy and Bollinger bands trading strategy depend on unknown parameters (moving average window sizes) and the window sizes are usually chosen in an ad hoc fashion. However the proposed trading strategy does not depend on the window size, and is data-driven in the sense that the optimal smoothing constants of GDES and DD-EWMA are chosen from the data. In the proposed trading strategy, a training sample is used to tune the parameters: smoothing constant for GDES price forecasts, smoothing constant for DD-EWMA volatility forecasts, and the tuning parameter which maximizes Sharpe ratio (SR). A test sample is then used to compute cumulative profits to measure the out-of-sample trading performance using optimal tuning parameters. An empirical application on a set of widely traded stock indices shows that the proposed GDES interval forecast trading strategy is able to significantly outperform SMA and the buy and hold strategies for the majority of stock indices.

Many of the challenges and opportunities of data science in finance involve recursive smoothing, forecasting, filtering and pattern mining. Recently there has been a growing interest in using filtered estimates for dynamic hedge ratios for pairs trading. Moreover, rolling estimates and forecasts are used for pattern mining in technical analysis. Kalman filtering algorithms were successfully applied in pairs trading with only two co-integrated assets. In this paper, pairs trading strategy is extended to multiple trading (with more than two assets) strategy. Recently proposed non-Gaussian maximum informative filtering algorithms for dynamic state space models are used to obtain the filtered estimates of hedge ratios and applied in multiple trading. It is shown that the proposed multiple trading strategy outperforms (with higher profits) the commonly used pairs trading strategy using real data. A data-driven approach for selecting a parameter which maximizes the Sharpe ratio (SR) to generate optimal trading signals is also discussed in some detail.

Regularization methods allow data scientists and risk managers to enhance the predictive power of a statistical model and improve the quality of risk forecasts. Financial risk forecasting is about forecasting volatility, Value at Risk (VaR), expected shortfall (ES) and model risk ratio. While regularized estimates have been shown to perform well in model selection and parameter estimation, their applications in financial risk forecasting has not yet been studied. In this paper, regularized adaptive forecasts and computationally efficient forecasting algorithms for volatility, VaR, ES and model risk are studied using various regularization methods such as ridge, lasso and elastic net. Sample sign correlation of standardized log returns (standardized by volatility forecasts) is used to identify the conditional distribution of the log returns series and provide regularized interval forecasts as well as regularized probability forecasts. Superiority of the regularized risk forecasts is demonstrated using different volatility models including a recently proposed generalized data-driven volatility model in [8]. Validation of the regularized risk forecasts using real financial data is given. Regularized probabilistic forecasts for stationary time series models are also discussed in some detail.

Recently there has been a growing interest in using machine learning methods with empirical variance covariance matrix of returns to study Markovitz portfolio optimization. The statistical technique of graphical LASSO (GL) for stock selection in the portfolio assumes that the asset returns are normally distributed, independent random variables with constant variance. In this paper sign correlations and the autocorrelations of the absolute values of the returns are used to show that the returns are non-normal with time-varying volatility. We use the recently proposed data-driven exponentially weighted moving average (DDEWMA) volatility model to estimate the covariance matrix of asset returns in Markowitz portfolio optimization. Empirical results with big data (consists of 444 stocks for a period of 7 years downloaded from Yahoo Finance) show that the proposed DDEWMA variance covariance matrix model outperforms (larger Sharpe ratio) the model with empirical variance covariance matrix.

The explosion of algorithmic trading has been one of the most prominent trends in the finance industry. In this paper, two strategies for algorithmic trading such as Bollinger bands and the simple moving average (SMA) crossover strategy are studied in the fuzzy settings. The commonly used Bollinger bands trading strategy assumes that the difference between an asset's price and its SMA is normally distributed. However, it is shown that a data-driven t distribution is more appropriate to model the difference between an asset's price and its SMA. A novel data-driven fuzzy Bollinger bands strategy is proposed for algo trading. A good strategy should have a good algo return on investment with low algo volatility. Therefore, forecasting algo volatility and identifying an appropriate distribution of algo returns play a crucial role in algo trading. Sharpe Ratio (SR) is a measure of average algo return earned in excess of the risk-free rate per unit of algo volatility. For a class of SMA crossover strategies with varying window sizes, fuzzy estimates of SR are computed based on various risk measures including the data-driven volatility estimate (DDVE). SR fuzzy forecasts are computed using two recently proposed volatility forecasting models such as data-driven exponentially weighted moving average (DD-EWMA) and data-driven neuro volatility models. The main reason of using the fuzzy approach is to provide α-cuts (interval forecasts) of the SR. An empirical application on a set of widely traded technology stocks shows that the proposed models deliver forecasts of SR with small errors.

Quantitative finance has been evolving over last several decades and combining randomness and fuzziness of the parameters has found growing interest among researchers to solve forecasting problems. Superiority of the fuzzy forecasting method over the minimum mean square forecasting had been demonstrated for fuzzy coefficient (linear as well as nonlinear) time series models in Thavaneswaran et al. [5]. However, many proposed fuzzy forecasting methods remain difficult to use in practice and there is a need for data-driven approach to fit the fuzzy coefficient volatility models. A neural network (NN) system can uniformly approximate any real nonlinear function on a compact domain to any degree of accuracy. Artificial NN (ANNs) have been applied to finance problems such as stock index prediction and bankruptcy prediction. In this paper, we introduce a novel direct data-driven neuro predictive model for conditional volatility and study the fuzzy value-at-risk (VaR) forecasts. We apply this model to forecast VaR with actual financial data. Our model shows considerable promise as a decision making and risk managing tool.

Recently there has been a growing interest in combining randomness and fuzziness to solve option pricing problems in finance using volatility models such as GARCH (generalized autoregressive conditional heteroskedasticity) and Heston-Nandi GARCH. The possibility theory for fuzzy option pricing (for real option, European option and binary option) has been demonstrated in the literature by fuzzifying the parameters such as volatility. However, many fuzzy option pricing approaches remain difficult to use with real data. A neural network (NN) is a highly parameterized model, widely promoted as a universal approximator such that with enough data it could learn any smooth predictive relationship. In this paper we first introduce a novel data-driven feed forward NN predictive model for conditional variance and demonstrate the superiority of the proposed model for option pricing over other volatility models. Using the NN predictive model, two different fuzzy estimates of the sensitivity measure vega (ν, which measures the dependence of option price on volatility σ) are proposed. We use different estimates of the sensitivity measure and compute the α-cuts of the fuzzy call price.