This study explores dynamic pair trading strategies in the volatile cryptocurrency market, leveraging Hamilton–Jacobi–Bellman (HJB) optimal control frameworks alongside reinforcement learning (RL) techniques. The HJB Mean Reverting strategy achieved a cumulative return of 20.28%, providing intuitive, rule-based allocations albeit with moderate volatility. The Error Correction HJB variant, restricted to spread components without market index exposure, demonstrated exceptional stability – with a very low annualized volatility of 0.5% – and consistent, though modest, annualized returns of 3.65%. RL agents, constrained to allocate within spread components and enhanced through mean reversion and error correction mechanisms, delivered competitive cumulative returns ranging from 34% to 50%, with Sharpe ratios consistently above 1.2 and controlled drawdowns around 5–10%, illustrating robust adaptability to complex market dynamics. Together, these results highlight the complementary strengths of theoretical optimal control and data-driven reinforcement learning in achieving profitable and risk-managed trading strategies in rapidly evolving cryptocurrency markets.

ABSTRACT Europe’s energy landscape has undergone profound disruptions following the escalation of the Russo-Ukrainian war, exposing deep structural vulnerabilities in the continent’s persistent reliance on fossil fuels. The crisis intensified political and economic tensions across the longstanding European Eastern divide, as the abrupt suspension of Russian gas disrupted energy security, triggered unprecedented price volatility, and accentuated disparities in the capacity of European Union Member States to pursue their green transitions. This paper investigates the asymmetric dynamics of fossil-fuel dependency and renewable energy expansion across ten Central/East European countries (CEEs, namely Bulgaria, the Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, Slovakia, and Slovenia) by applying a GARCH(1,1) and GARCH-MIDAS framework to examine short-run volatility characterizing the countries’ leading stock markets; such volatility stems from long-run macroeconomic and geopolitical pressures resulting from fossil fuels energy pressures. The research findings provide evidence of pronounced volatility clustering and slow mean reversion across countries, with the volatility half-life confirming substantial heterogeneity in shock persistence. Policymakers need to carefully consider the heterogeneous nature of volatility transmission mechanisms across the CEEs, the importance of country-specific structural and geopolitical factors, and their implications for volatility dynamics in small open economies during their energy transitions.

Financial markets in emerging economies such as Nigeria often exhibit nonlinear dynamics, volatility clustering, and regime shifts that traditional linear models failed to capture. To address these complexities, this study developed a Bayesian Regime-Switching Threshold Autoregressive (RS-TAR) model to analyze daily All-Share Index (ASI) returns in the Nigerian Stock Exchange. The model employed Markov Chain Monte Carlo (MCMC) methods to estimate posterior parameters, transition probabilities, and regime-specific volatility. Results revealed two distinct regimes: a low-volatility state characterized by faster mean reversion and a high-volatility state marked by strong persistence, with the probability of remaining in the crisis regime exceeding ( > 0.8500), indicating prolonged instability once shocks occur. Bayesian posterior predictive distributions were used to compute Value-at-Risk (VaR) and Expected Shortfall (ES), providing robust measures of downside risk. Comparative analysis showed that RS-TAR significantly outperformed benchmark autoregressive (AR) and GARCH models, with Diebold–Mariano tests confirming superior predictive accuracy. The study concludes that RS-TAR is effective in detecting structural breaks, modeling nonlinear market behavior, and enhancing risk forecasting in the Nigerian financial market. These findings underscore the importance of adopting advanced nonlinear and regime-switching approaches in emerging economies, offering practical insights for investors, regulators, and portfolio managers seeking to better understand and manage risks in volatile environments.

Rigid bronchoscopy (RB) forms an indispensable part of the interventional bronchoscopist's skills, allowing the performance of complex airway interventions for a variety of benign and malignant airway disorders. Experiential data on the procedure is limited, particularly in adults. We conducted a retrospective analysis of medical records from 82 adult patients who underwent RB at our center. The primary objective was to evaluate the clinical indications, procedural outcomes, complication rates, and overall efficacy of RB in this cohort. Collected data included patient demographics, presenting symptoms, etiological diagnoses, and anesthesia-related parameters such as induction agents, maintenance protocols, sedation strategies, and the use of neuromuscular blockade. Post-procedural outcomes and follow-up mortality were also assessed. The mean patient age was 56.2±12.6 years, with 71.9% males. Common symptoms were cough (90.2%) and dyspnea (82.9%). Malignancies accounted for 90.2% of cases, with lung cancer being the most prevalent (68.2%). RB was primarily performed for stenting (63.4%) and tumor debulking (29.2%). Total intravenous anesthesia was used in 92.6%, with mean induction and reversal times of 75.3±4.3 seconds and 10.69±2.4 minutes, respectively. Minor complications occurred in 29.3% (bleeding 29.3%, bronchospasm 17.1%, and hypoxia 13.4%) and major complications in 2.4%. After the procedure, immediate extubation was achieved in 49 patients (59.8%), while 24 (29.3%) required short-term ventilator support (<24 h) and 9 (11.0%) required prolonged support (>24 h). The median hospital stay was 7 days (interquartile range 5-11). Symptomatic improvement at discharge was observed in 72/82 patients (87.8%). In-hospital mortality was 6.1% (5/82), mainly due to severe infections (hospital-acquired or ventilator-associated pneumonia) or massive endobronchial bleeding. Among patients with available follow-up (n=52), 3-month mortality was 11.5% (n=6). In this real-world cohort, RB demonstrated a high success rate with minimal complications, reinforcing its role as a critical tool in managing complex airway conditions. The procedure demonstrated high efficacy, particularly in malignant cases, with acceptable complication rates. Dedicated training is essential to enhance experience, gain expertise, and ensure optimal outcomes while minimizing procedural risks.

Accurate estimation of the mean-reversion speed α in the AR(1) process Xt+1=(1−α)Xt+εt is central to energy-commodity modelling. Classical estimators such as GARCH, jump-diffusion, and regime-switching produce model-conditioned estimates by embedding α within distributional assumptions, so that different model choices yield different α^ values from the same series without a principled criterion to adjudicate. We propose a distribution-free neural estimator based on a Temporal Convolutional Network (TCN) trained on synthetic AR(1) series with Sinh-ArcSinh (SAS) innovations. Distribution-free here means that no parametric family is assumed for the innovation distribution at inference time: the estimator imposes no distributional hypothesis when processing a new series. The SAS family serves as a training vehicle—not a model for the real data—chosen for its ability to span a broad range of tail weights and asymmetry profiles. The theoretical foundation is spectral invariance: the Yule–Walker equations establish that the autocorrelation structure ρk=(1−α)k depends on α alone, provided innovations are uncorrelated across lags—a condition satisfied not only by i.i.d. innovations but also by conditionally heteroscedastic processes such as GARCH. The TCN therefore generalises to volatility-clustering environments without modification, learning to extract α from temporal dependence alone, independently of the marginal innovation distribution and of the temporal variance structure. On held-out test series the estimator outperforms all classical competitors, with the advantage growing monotonically with non-Gaussianity. A robustness analysis on three out-of-distribution innovation families and on AR(1)-GARCH(1,1) processes empirically validates the spectral invariance guarantee across both marginal and temporal variance structure, including near-integrated GARCH processes where innovation kurtosis far exceeds the training range. The distribution-free α^ enables a two-stage pipeline in which α and the innovation distribution are characterised independently—a decoupling structurally impossible in classical likelihood-based approaches. Once trained, the TCN acts as a universal mean-reversion estimator applicable to any price series without re-fitting. Applied to four energy markets—Italian natural gas (PSV price), Italian electricity (PUN price), US Henry Hub, and US PJM West Hub—spanning log-return kurtosis from near-Gaussian to strongly heavy-tailed, the TCN yields robust, distribution-free estimates of mean-reversion speed.

ABSTRACT The debt‐to‐GDP (DG) ratio should predict Treasury returns and primary surpluses according to the present‐value identity, yet empirical evidence remains elusive. This paper resolves this puzzle by decomposing the DG ratio into a slow mean‐reversion component and a local mean‐reversion component. We show that the local mean reversion of the DG ratio delivers substantially improved out‐of‐sample forecasting gains of Treasury debt returns and surpluses, outperforming the original DG ratio, the historical average benchmark, and the adjusted ratios subject to structural breaks. In contrast, the slow mean‐reversion component obscures predictive information by incorporating persistent, nonfundamental variation. Our findings are robust to alternative decomposition methods and DG ratio definitions (including nonmarketable debt). We develop a revised fiscal present‐value model to rationalize the findings.

The evolution over time of the Consumer Price Index (CPI) is regarded as a key indicator of the general health and direction of any given economy. As the CPI continues to rise, the purchasing power of consumers decreases and their spending habits change significantly, making it imperative for policymakers to understand the underlying reasons that lead to such changes. A key component of the CPI basket is represented by the food and beverages items, within which eggs have undergone a significant price increase during the past years. Egg prices have a significant impact on consumers, given that eggs are a staple product, serving as the lowest cost protein alternative. This paper analyzes the long term behavior of the average egg price (cost per Dozen) in the U.S. by looking at the statistical properties of the series and using a methodology based on the concept of fractional integration. The primary goal is to determine whether the average egg price exhibits traits of long memory or mean reversion. Long memory describes the scenario where observations from a distant past have an influence on the present value of the series. Conversely, mean reversion refers to the phenomenon where data points eventually return to the long-term average after deviating from the mean for a certain period. The analysis also explores the relationship between egg prices and the Producer Price Index (PPI) through cointegration methods. Preliminary findings indicate that long memory takes place in both series and mean reversion in the PPI. Also, the two series seem to be cointegrated. This suggests the presence of a stable long-run equilibrium relationship between the Average Egg price and the Producer Price Index in the U.S., indicating a sustained co-movement between the two variables over time.

Can machine learning generate statistically validated alpha in equity markets while adapting to changing market conditions? This study addresses this question by proposing a regime-aware LightGBM framework conditioned on market regimes detected via a rolling Hidden Markov Model, eliminating look-ahead bias. Backtested on 51 NASDAQ-100 constituents (2015–2026), the strategy achieved a portfolio Sharpe ratio of 1.18 (95% CI: [0.53, 1.84]) and outperformed four baseline models. The key findings include the following: (i) cross-asset features (Bitcoin as a leading indicator) contribute the most predictive value; (ii) macroeconomic indicators outweigh traditional technical indicators for high-beta stocks; (iii) the model autonomously adapts its decision logic across regimes, shifting from mean reversion in bear markets to risk appetite monitoring in bull markets. While block bootstrap tests confirm statistical significance (p&lt;0.001), the Deflated Sharpe Ratio (0.69) does not reach formal significance after multiple testing correction—an honest finding we report transparently.

Infrastructure concessions, especially for transportation projects, are long-term investments subject to demand volatility. Yet disruptive events, such as the COVID-19 pandemic but not limited to it, may negatively affect demand for traffic infrastructure, thus impacting the returns and the attractiveness of the project to the private investor and result in lengthy and costly contract renegotiations. While historical demand series indicate that such events, some with localized effects and others with more global consequences, occur more frequent than might initially be perceived, their impacts are usually transitory in nature. We propose an innovative supporting mechanism called Minimum Demand Guarantee (MDG) with the Term Extension Clause (MDG-TEC) to hedge the effects of such disruptive events and minimize the need to contract renegotiations. This model combines an MDG with a concession time-term extension proportional to the observed reduction in the demand and the length of this reduction, which are modeled as European call options under the real options approach. In a novel approach, traffic demand is modeled as a mean reversion diffusion process with drift to which negative Poison jumps are added to simulate such disturbances. The results show that this model can be effective in minimizing demand risk and the need for renegotiations, without creating additional fiscal liabilities for the government.

This study examines the role of volatility mean reversion in option pricing and evaluates the performance of commonly used volatility estimators within a broad market context. Using a comprehensive dataset of end-of-day option chains for the 100 most actively traded U.S. equities from 2018 to 2023, we apply several established statistical techniques—including unit root tests, variance ratio analysis, Hurst exponent estimation, and GARCH modeling—to quantify the presence and strength of mean reversion in volatility. To assess the accuracy and practical usability of volatility metrics for option valuation, we compare realized volatility, GARCH-based forecasts, range-based estimators, and widely used implied volatility measures such as the VIX and daily implied volatility averages, benchmarking each against contract-specific implied volatility. The results indicate that more than 65% of the analyzed tickers exhibit statistically significant mean-reverting behavior, and that the 30-day average implied volatility consistently provides the most reliable predictive performance among the tested metrics, while range-based estimators perform poorly when applied to end-of-day data. Finally, backtests of six delta-neutral option strategies informed by these findings did not yield consistent profitability or statistically significant outperformance, suggesting that although volatility mean reversion is measurable, its direct application to systematic trading remains challenging.

Glidepath, Lifestyle or Target Date Funds have emerged as the leading form for defined contribution funds in the US in recent years. Although there is theoretical support for this form of pension investment portfolio, many question its efficacy when compared with holding a high percentage of equities throughout. In this article, we present international evidence on the time diversification aspects of bond and equity returns over the past 100 years and show how this impacts our understanding of the appropriate asset composition of pension savings into retirement. For a sample of 13 developed countries since 1926, we examine the properties of equity and bond aggregate returns using variance ratio tests and find that equity markets show mean reversion, but bond markets possess mean aversion. In contrast to the existing literature, which focuses on lifetime utility and wealth comparisons, we compare the accumulation and decumulation experiences of each country using the Perfect Contribution and Perfect Withdrawal Rates and find that the Glidepath changing asset allocation strategies are inferior to 100% equity portfolios, adding to the evidence that challenges the benefits of Target Date Funds.

The impact of different ownership structures on a firm’s stock performance is a well-known problem of corporate finance, especially for developing markets with novel governance structures. This research analyses ownership structure, firm-specific characteristics, and stock returns for the Nigerian consumer goods firms listed on the Nigerian Exchange Group for the years 2015 to 2024. This research used agency, stewardship, and resource dependence theories and a Dynamic Generalized Method of Moments (GMM) estimator to solve the problem of endogeneity and stock returns. This research revealed s, among other things, a high degree of stock return mean reversion which signifies market adjustment. There is a positive, but weakly significant relationship with firm size and return, and firm age, leverage, managerial ownership, institutional ownership, and ownership concentration, show little to no significant relationship. The validity of the model and the strength of the instruments is confirmed by diagnostic tests. These findings show that firm characteristics and market dynamics (as opposed to ownership structure) are the most important drivers of stock returns. Furthermore, this research contributes to emerging market finance and emphasizes the role of transparency, quality of disclosure, and institutional governance in the improvement of capital markets.

We study dynamic asset allocation when returns display short-run momentum yet revert to a hidden long-run mean. We extend the two-factor specification of [Koijen, R.S., Rodriguez, J.C. and Sbuelz, A., Momentum and mean reversion in strategic asset allocation. Manage. Sci., 2009, 55, 1199–1213.] into a partially observable linear-Gaussian economy. We estimate the unobservable drift of the return process with a Kalman–Bucy filter and exploit the separation principle to characterize the optimal portfolio and its value under partial information. The optimal weight splits into a myopic momentum bet, an intertemporal hedge, and an information-hedging component that scales with the filter's conditional error variance. Closed-form expressions for the indifference value of information show that the premium for perfect drift observability rises with the noise-to-signal ratio. A simulation study enables us to interpret our theoretical results, and a real data application reveals that the partial-information strategy behaves more smoothly, yet still outperforms a naïve benchmark.

This study conducts a bivariate volatility analysis of crude oil prices and Nigeria’s exchange rate using data from 2010 to 2024 (180 observations). It employs descriptive statistics, cross-correlation, Granger causality, Johansen cointegration tests, and both VAR and DBEKK MGARCH frameworks to capture dynamic interactions and volatility persistence. The VAR results show a positive effect of crude oil prices on the exchange rate (0.1574, p = 0.0368) and mean reversion in the exchange rate (−0.158, p = 0.0344), with limited short-run causality at lag 1. DBEKK MGARCH estimates reveal pronounced volatility clustering with asymmetric persistence across series. Crude oil price volatility exhibits strong baseline and ARCH/GARCH dynamics, with A1(1,1) = 0.674 and B1(1,1) = 0.529, while cross-channel instantaneous spillovers are weak (M(1,2) = 0.287, not statistically significant, p = 0.872). The unconditional baseline reflects substantial volatility (M(1,1) = 12.986, p = 0.0216) and a persistent second channel with B1(2,2) = 1.010 and A1(2,2) = 0.286, indicating very strong persistence and long-lasting volatility in that channel. Exchange rate volatility is highly responsive to shocks, with A1(2,2) = 0.286 and B1(2,2) = 1.010, and M(2,2) = -2.474 (p<0.001), suggesting a damping but dominant persistence pattern in the second variance component. The cross-channel influence remains weak under diagonal BEKK, as evidenced by a non-significant M(1,2) and relatively small cross-covariance terms. Overall, a substantial long-run correlation exists between the volatility processes, linking oil-price and currency risks (strong co-movement in volatility). Implications emphasize continuous volatility monitoring and hedging to mitigate persistent risk, and policies to stabilize currency markets and enhance resilience to oil-price shocks through hedging, reserves management, and macroprudential tools.

The Efficient Market Hypothesis (EMH) posits that asset prices adjust rapidly to new information, leaving no scope for systematic excess returns. The COVID-19 pandemic represented an unprecedented global shock, generating substantial volatility across financial markets, including those in emerging African economies. This study examines the volatility dynamics and informational efficiency of the Nigerian Stock Exchange (NGX) All-Share Index before and after the COVID-19 lockdown. Using daily data from January 2018 to December 2022, the analysis applies GARCH (1,1) models under Gaussian, Student’s t, and Generalized Error Distribution assumptions to evaluate return dependence and volatility persistence across sub-periods. The empirical results confirm that returns are stationary in both pre- and post-lockdown phases. However, significant lagged return effects are observed across periods, indicating short-run return dependence inconsistent with strict weak-form efficiency. Volatility clustering is pronounced in the pre-lockdown period but weakens after the lockdown, with relatively rapid mean reversion of shocks in both phases. These findings suggest that the COVID-19 shock intensified volatility temporarily without fundamentally restructuring the informational dynamics of the Nigerian market. The study contributes to the emerging-market literature by distinguishing between volatility stabilisation and informational efficiency, demonstrating that reduced volatility persistence does not necessarily imply the elimination of return predictability. Strengthening market transparency and improving information dissemination remain essential for enhancing long-term market efficiency and resilience.

Hyperparameter optimization for cryptocurrency trading strategies encounters distinct challenges owing to continuous operation, volatility rates 3–4 times higher than equity indices, and price dynamics influenced by market sentiment. Bayesian optimization (Tree-Structured Parzen Estimator, TPE) and evolutionary algorithms (Differential Evolution, DE) are great for machine learning, but there are not many systematic comparisons for trading cryptocurrencies. This research evaluates Random Sampling, TPE, and DE through 36 factorial experiments, comprising 3 trading strategies (3, 4, and 5 hyperparameters) × 3 optimizers × 4 cryptocurrency pairs (BTC/USDT, ETH/USDT, INJ/USDT, SOL/USDT), resulting in 14,400 backtesting trials with walk-forward validation. TPE won 75% of strategy–asset pairs (9 of 12), reaching 90% of optimal performance within 13–17% of trial budgets. We find strategy-specific optimizer compatibility: mean-reversion strategies show DE underperformance independent of topology (−1% to −8%), whereas trend-following strategies show consistent DE competitiveness across assets (+13% to +37%). Most notably, for the same strategy, parameter space topology differs significantly between assets (trend following: 4.6% viable on BTC to 82% on ETH = 17.8×; mean reversion: 10.8% on ETH to 92% on SOL = 8.5×), indicating that topology results from strategy–asset interaction rather than intrinsic properties. Complete testing failures and widespread severe overfitting point to regime non-stationarity as a fundamental problem. Among the contributions are: (1) evidence shows that topological effects are dominated by optimizer–strategy compatibility (DE fails on mean-reversion strategies even in 92% viable spaces, but succeeds on trend-following strategies regardless of topology, spanning 13.6–82% viable spaces); (2) this is the first systematic Bayesian versus evolutionary comparison across 4 cryptocurrency assets; (3) parameter space topology emerges from strategy–asset interaction, varying up to 17.8-fold; and (4) single-period backtests inadequately identify parameter instability.

ABSTRACT This study investigates mean reversion and volatility in five NSE sectoral indices (Nifty FMCG, IT, Media, Financial Services, and Bank) spanning their inception to 2023. Stationarity was tested using ADF and PP methods, while rescaled range analysis estimated the Hurst Exponent, which was below 0.5 for all indices, confirming mean reversion. The Ornstein-Uhlenbeck model measured reversion speed, ranging from 0.899 to 0.988 across sectors. Volatility analysis indicates that FMCG is the most stable (0.013) and IT is the most volatile (0.04). Results highlight sector-specific variations in mean-reverting behaviour and volatility, offering insights for investors and risk management strategies.

The paper analyzes the volatility trends of the Saudi Arabian Tadawul All Share Index (TASI) and the S&amp;P 500 index, focusing on the COVID-19 pandemic as a key market shock. The analysis incorporates daily stock return data covering the period from January 2015 to May 2025. The volatility of emerging and developed markets is examined through EGARCH and GARCH approaches to study characteristics such as volatility clustering and asymmetry. The effect of the pandemic is directly embedded by introducing COVID-19 dummy variables into the models. Empirical findings suggest that both indices are characterized by volatility clustering, and the EGARCH model is more appropriate than the GARCH model for estimating asymmetric volatility, particularly during crisis periods. Additionally, the COVID-19 dummy variable is statistically significant in the EGARCH model, as opposed to the GARCH model. The results support the leverage effect, indicating that negative shocks have a more significant impact on market volatility than positive ones. The S&amp;P 500 showed a faster recovery after the COVID-19 crisis, whereas TASI was slower in mean reversion, indicating structural and behavioral divergence between the markets. This comparative study contributes to the literature by providing a clear picture of volatility dynamics in diverse financial contexts and highlighting the superiority of EGARCH models during crisis periods. The findings offer guidance to policymakers aiming to improve market stability and to investors seeking diversification into both developing and mature markets.

Abstract We assess the degree of persistence for 36 U.S. states’ hate crime rates using fractional integration. For 9 states the hate crime rate exhibits mean reversion. The hate crime rate tends to an upward trend for 5 states (possibly reflecting increased hate crime reporting/compliance through time) and for 3 states there is evidence that the hate crime rate reverts to a downward trend. This is consistent with an evolving natural rate over the sample for these 8 states. For 17 states law enforcement expenditures aimed at deterrence will at best lower offending in the short run because the hate crime will return to its constant or evolving natural rate in the long run. Corrective policies designed to change the natural rate are recommended for these states. The results for the District of Columbia and Utah are ambiguous, and for the remaining 17 states there is no reversion to a natural hate crime rate.

We present a supervised learning method to estimate two local descriptors of time-series dynamics, the mean-reversion rate θ and a heavy-tail estimate α, from short windows of data. These parameters summarize recovery behavior and tail heaviness and are useful for interpreting stochastic signals in sensing applications. The method is trained on synthetic, dimensionless Ornstein-Uhlenbeck processes with α-stable noise, ensuring robustness for non-Gaussian and heavy-tailed inputs. Gradient-boosted tree models (CatBoost) map window-level statistical features to discrete α and θ categories with high accuracy and predominantly adjacent-class confusion. Using the same trained models, we analyze daily financial returns, daily sunspot numbers, and NASA POWER climate fields for Austria. The method detects changes in local dynamics, including shifts in the financial tail structure after 2010, weaker and more irregular solar cycles after 2005, and a redistribution in clear-sky shortwave irradiance around 2000. Because it relies only on short windows and requires no domain-specific tuning, the framework provides a compact diagnostic tool for signal processing, supporting the characterization of local variability, detection of regime changes, and decision making in settings where long-term stationarity is not guaranteed.