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.

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.

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 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.

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.

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.

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.

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.