Examining Oil Prices for Chaos, Entropy, Fractionality and Complexity, and Modeling the Impacts of Economic Policy Uncertainty and Geopolitical Risks: GARCH-MIDAS-LSTM Approach

Abstract

As the leading energy source, oil price volatility has crucial effects in energy markets, and geopolitical risks (GPRs) and economic policy uncertainties contribute to its volatility. Further, chaos, long-range dependence, fractionality, and complexity significantly reduce modeling and forecast performances. At the first stage, daily oil prices, and monthly global and USA-based GPRs, and economic policy uncertainty (EPU) are examined with a battery of tests for chaos, entropy, fractionality, complexity, and volatility, followed by a second stage that focuses on modeling daily oil prices with mixed-frequency deep neural networks (DNNs) GARCH-mixed-frequency data sampling (MIDAS)-long short-term memory (LSTM) for 28 December 1995-30 October 2023, a period including USA-China Trade War, Russia-Ukraine War, and COVID-19 as prominent GPR and policy uncertainty factors. Findings indicate R/S = 33.2 and modified R/S = 3.42, along with fractionality parameter estimates d = 0.93, 0.94, 0.88, with heteroskedasticity-robust estimators confirming long-range dependence and fractionality. Lyapunov exponents are estimated as lambda = 0.91 and lambda = 0.89, which identify type of chaos with moderate level of dependence on initial conditions. Shannon entropy (SE) and Tsallis entropy (TE) and Kolmogorov-Sinai complexity (KSC) measures are calculated as 6.41, 9.25, and 10.04, whereas Hurst exponent (HE) is estimated as 0.99, highlighting low level of entropy and predictability and high level of complexity for oil prices. At the modeling stage, LSTM-augmented mixed-frequency model estimates indicate theta parameters equal to 0.16 for monthly EPU with the highest effect, followed by theta = 0.139 and 0.088 for global and USA-based GPRs, contributing to upsurges in price volatility. The % RMSE error reduction of models in one-step-ahead forecasts ranges between -15.67% and -41.77%. Most importantly, out-of-sample forecast RMSE reduction reaches -59.56% to -78.08% indicating significant forecast gains, and results are robust for various forecast horizons. These findings have important implications for policymakers and investors in energy markets.