The challenge the researchers set out to address is structural. Exchange-rate returns may exhibit linear dependence, nonlinear relationships, regime-switching behavior, and volatility clustering, often simultaneously. Classical linear models such as ARIMA capture short-term linear dynamics but collapse when data turn complex. Nonlinear and machine learning methods handle intricate patterns but their superiority is not universal, and gains often prove sample-specific. The authors therefore built an Adaptive Time-Varying Weighted Hybrid Forecasting framework, abbreviated ATW-HyF, that combines three complementary paradigms: ARIMA for linear temporal dependence, a two-regime SETAR model for threshold-driven regime switching, and a feedforward artificial neural network for nonlinear approximation.

The genuinely novel element lies in how the framework weights its components. Conventional hybrid models rely on fixed or equal weights, implicitly assuming that model performance remains stable over time, an assumption rarely satisfied in foreign exchange markets. ATW-HyF instead updates inverse-RMSE weights recursively over a rolling window of twenty forecast errors. Models that recently produced lower errors receive larger performance scores and greater influence in the convex combination, while unreliable components are demoted automatically. The mechanism is grounded in the classical theory of optimal forecast combination, which holds that combining multiple forecasts under the minimum-variance principle reduces forecast uncertainty relative to any individual model.

The framework comes in two versions. ATW-HyF A produces adaptive point forecasts by dynamically combining the one-step-ahead predictions of ARIMA, SETAR, and ANN. ATW-HyF B extends this architecture with a GARCH(1,1) volatility layer that models the conditional variance of the hybrid forecast residuals, capturing volatility clustering and time-varying forecast uncertainty. The result is a unified mean-variance forecasting system that jointly predicts both the direction of exchange-rate returns and the evolving uncertainty surrounding them, information that matters for risk management applications such as Value-at-Risk and Expected Shortfall.

Evaluation was rigorous. The researchers employed an expanding rolling-origin, or walk-forward, procedure in which models are re-estimated at every forecast origin using only past observations, eliminating look-ahead bias. Prices were transformed into continuously compounded log returns to stabilize variance and remove nonstationarity. Performance was measured with RMSE, MAE, MAPE, sMAPE, MASE, and Theil’s inequality coefficient, while pairwise comparisons relied on the Diebold-Mariano test corrected for small samples using the Harvey-Leybourne-Newbold adjustment. The computational scale was substantial: roughly 2,510 recursive forecasting iterations per currency pair, more than 7,500 cycles and over 30,000 model estimations across three series, all implemented in Python with open-source libraries and a fixed random seed for reproducibility.

The evidence came from both simulation and real markets. In simulations built from a two-regime threshold autoregressive process with 600 observations, ATW-HyF B achieved the lowest forecast errors of all competing models, with an RMSE of 1.0140 and MAE of 0.8075, edging out the standalone ANN and the ATW-HyF A variant. This demonstrated that adaptive weighting combined with volatility modeling is particularly effective when the underlying process exhibits nonlinear and time-varying dynamics, even when volatility clustering is relatively weak.

The empirical results, however, told a more nuanced story. Using daily data from April 2016 to April 2026 with 2,610 observations per series, the study examined three currency pairs: the emerging-market USD/NGN pair and the major pairs EUR/USD and GBP/USD. Descriptive statistics revealed striking differences. USD/NGN returns displayed extreme kurtosis of 115.5 and strong positive skewness, reflecting heavy tails and policy-driven disruptions, while EUR/USD and GBP/USD were comparatively stable yet still non-normal. Jarque-Bera tests rejected normality for all series, and ADF tests confirmed stationarity, while autocorrelation functions dropped quickly to zero, indicating weak serial dependence that makes return prediction inherently difficult.

On these real series, no single model dominated. The ARIMA-ANN hybrid achieved the lowest forecast errors for USD/NGN, with an RMSE of 0.013085, and for EUR/USD, with an RMSE of 0.004809, suggesting that combining linear dynamics with nonlinear learning was sufficient for those markets. ATW-HyF B performed best for GBP/USD, recording the lowest RMSE of 0.006487. Notably, ATW-HyF A and ATW-HyF B produced effectively identical point forecast accuracy on the empirical data, implying that the GARCH volatility layer did not enhance mean forecasts, though it complemented the framework by quantifying forecast uncertainty.

The statistical tests added a twist that elevates the study beyond simple error rankings. Although ARIMA-ANN produced the lowest average forecast errors, the HLN-corrected Diebold-Mariano comparisons showed that ATW-HyF B achieved 18 statistically significant pairwise wins across all currency pairs, while no competing model recorded more than two. ATW-HyF B significantly outperformed the random walk benchmark for all three series, and it beat SETAR everywhere. The distinction between lowest average errors and most consistent statistical superiority highlights why forecast evaluation should combine error-based measures with formal predictive accuracy tests.

The broader lesson is that forecasting performance depends on the characteristics of the underlying exchange-rate series rather than on model complexity alone. Adaptive forecast combination provides a flexible alternative to conventional fixed-weight hybrids, allowing forecasting systems to adjust to changing market conditions, while volatility modeling improves usefulness for forecasting under uncertainty. The authors position the framework as an adaptive benchmark against which computationally intensive deep learning approaches, including LSTM and Transformer architectures, can be evaluated in future work, and recommend extending validation to stock indices, cryptocurrencies, commodity prices, and crisis periods to further establish robustness and generalizability.

Subject of Research: Machine learning and financial forecasting

Article Title: Data-driven adaptive hybrid models for exchange rate return forecasting

Article References: Adesina, O. S., & Obokoh, L. O. (2026). Data-driven adaptive hybrid models for exchange rate return forecasting. Frontiers in Big Data, 9, Article 1917723. https://doi.org/10.3389/fdata.2026.1917723

Image Credits: AI Generated

DOI: 10.3389/fdata.2026.1917723

Keywords: exchange rate forecasting, hybrid models, machine learning, GARCH, ARIMA, neural networks, time series, financial econometrics, Data-driven, adaptive, hybrid, models

The research, which forms part of Pham’s doctoral work at National Economics University in Hanoi, analyzes a balanced panel of 135 Vietnamese listed industrial firms covering the period from 2016 to 2024. That window is analytically valuable because it spans years of robust pre-pandemic expansion, the sharp disruption of COVID-19, and the uneven recovery that followed. By holding the sample constant across all nine years, the authors ensure that every firm contributes equally to the analysis, avoiding the selection biases that can creep in when companies enter or exit a dataset mid-study. The result is a comprehensive portrait of how the financial anatomy of Vietnam’s industrial listed sector has evolved through one of the most turbulent stretches in modern economic history.

What sets the study apart methodologically is its three-stage analytical framework, which begins with a technique rarely applied to corporate finance in emerging markets: compositional data analysis. Financial statements are inherently compositional in nature, because the components of a balance sheet or income statement are constrained to sum to a fixed total. Treating raw ratios without accounting for this constraint can produce misleading statistical artifacts, a problem long recognized in fields like geology and ecology but often ignored in financial research. By applying compositional data methods, the authors respect the true geometry of financial statement data, ensuring that the relative structure of assets, liabilities, and equity is analyzed in a mathematically coherent way.

Building on that foundation, the researchers employed Ward’s hierarchical clustering to sort firm-year observations into recurring financial profiles. Ward’s method is a clustering algorithm that merges observations in a way that minimizes the increase in within-group variance at each step, producing compact and internally coherent groups. Rather than forcing firms into arbitrary categories defined by regulators or rating agencies, the clustering lets the data speak for itself, revealing natural groupings based on the relative composition of each firm’s financial statements. The analysis identified four distinct financial profiles, ranging from financially robust firms to the most vulnerable companies whose balance sheets signal elevated structural risk.

The second stage of the framework tackles a persistent problem in performance research: the proliferation of accounting ratios. Analysts can compute dozens of measures covering profitability, leverage, liquidity, efficiency, and growth, but these indicators overlap heavily and often move together in ways that obscure rather than clarify a firm’s true condition. Pham and Dao addressed this by applying principal component analysis to eleven accounting ratios, distilling them into three composite indices that capture the dominant dimensions of variation across the sample. The first index summarizes overall Performance, the second captures Financial Risk, and the third measures Management Efficiency. Principal component analysis works by identifying linear combinations of the original variables that explain the maximum possible variance, effectively compressing a crowded dashboard of ratios into a small set of orthogonal summary scores that retain most of the informational content.

With firms classified into profiles and composite indices constructed, the third stage estimated the relationships between financial risk, management efficiency, and performance using interactive two-way fixed-effects regression models. Fixed-effects models control for time-invariant characteristics of each firm and for shocks common to all firms in a given year, which helps isolate the genuine association between the explanatory indices and performance from confounding factors such as managerial quality or industry-wide cycles. The models included interaction terms between the indices and profile membership, allowing the strength of each relationship to differ across the four financial profiles. Standard errors were clustered at the firm level to account for serial correlation in the residuals of individual companies over time.

The headline findings are both intuitive and consequential. Financial risk was negatively associated with performance across all four profiles, confirming that firms carrying heavier structural financial burdens tend to underperform regardless of their position on the risk spectrum. Crucially, however, the strength of this adverse relationship was not uniform. The most financially vulnerable profile exhibited the strongest negative association, suggesting that risk is not merely a drag on performance but an increasingly punishing one as a firm’s balance sheet deteriorates. This nonlinearity carries a clear implication for investors and policymakers: the marginal cost of additional leverage or liquidity strain is highest precisely where firms can least afford it.

Management efficiency told a different story. The composite index of efficiency was positively associated with performance in several of the identified profiles, and the relationship was significantly stronger in the largest profile of firms. In other words, operational discipline, asset utilization, and cost control appear to translate into superior performance most powerfully for the broad middle of Vietnam’s industrial listed sector, where competitive pressures reward managerial skill most directly. For the smallest and most vulnerable groups, the payoff to efficiency gains appears more muted, possibly because structural financial fragility overwhelms the benefits of good management, or because such firms face constraints that prevent efficient practices from being fully exploited.

Robustness testing is where the study earns particular credibility. The authors re-estimated their models using Driscoll-Kraay inference, a technique designed to handle cross-sectional dependence in panel data, where shocks to one firm may spill over to others through supply chains, credit markets, or common exposure to macroeconomic conditions. They also considered lagged profile membership, addressing the concern that a firm’s current performance might influence its profile classification rather than the other way around. The main patterns remained broadly consistent under both checks, indicating that the core conclusions are not artifacts of a particular statistical assumption or of simultaneity between classification and outcomes.

The broader significance of the research extends beyond Vietnam’s borders. Emerging markets often lack the deep institutional infrastructure of developed economies, making it harder for investors, creditors, and regulators to distinguish genuinely resilient firms from those that merely look healthy on headline metrics. A profile-based approach offers a complementary lens: instead of asking whether a firm beats a uniform sector-wide benchmark, analysts can ask whether a firm’s financial structure, risk exposure, and management efficiency combine in ways characteristic of resilient or fragile archetypes. As Vietnam continues to attract foreign investment and its industrial firms take on longer-term sustainability-oriented projects, the capacity to match assessment methods to financial profiles may prove essential for channeling capital toward the companies best positioned to sustain growth through the next decade of global economic uncertainty.

Subject of Research: Financial performance assessment of Vietnamese listed industrial firms using compositional data analysis and principal component analysis

Article Title: Evaluating the financial performance of Vietnamese listed industrial firms using compositional data analysis and PCA indexing

Article References: Pham, V. H., & Dao, T. T. B. (2026). Evaluating the financial performance of Vietnamese listed industrial firms using compositional data analysis and PCA indexing. Discover Sustainability. https://doi.org/10.1007/s43621-026-04976-y

Image Credits: AI Generated

DOI: 10.1007/s43621-026-04976-y

Keywords: Vietnam, financial performance, compositional data analysis, principal component analysis, financial risk, management efficiency, hierarchical clustering, panel data, listed firms, industrial sector, corporate financial resilience, financial econometrics

The starting point for the research is the HAR model, one of the most influential tools in realized volatility forecasting. Realized volatility is estimated from intraday price data, typically by summing squared five-minute returns, and is far more informative than the squared daily returns used in older GARCH-style models. HAR summarizes the recent past with a handful of interpretable averages, typically over one, five, and twenty-two days, mirroring the daily, weekly, and monthly rhythms of market participants. Its simplicity makes it remarkably robust, but it has two structural blind spots. It is essentially univariate, ignoring how volatility transmits from one market to another, and its linear averages can miss nonlinear information hiding inside the look-back window, such as the particular shape of a volatility path that rises slowly and then collapses.

To handle cross-market transmission, the authors build on a 2025 framework called GSPHAR, which embeds a directed spillover network directly into the forecasting architecture. The network is constructed using the Diebold-Yilmaz connectedness framework: a vector autoregression with a lag order of 22 is fitted to standardized realized volatility, and a generalized forecast error variance decomposition with a 22-day horizon quantifies how much shocks in one market drive forecast uncertainty in another. Crucially, this graph is estimated only on the training sample to avoid look-ahead bias, then sparsified by keeping only the strongest quarter of links. Because the graph is directed, with volatility flowing asymmetrically between markets, the model uses the magnetic Laplacian, a spectral operator that encodes direction through complex phases, allowing a graph Fourier transform that preserves which way information travels.

The genuine innovation of Sig-GSPHAR lies in what it adds to this spectral backbone. For each market, the model takes the raw 22-day window of realized volatility, augments it with a normalized time channel to form a two-dimensional path, and computes a truncated path signature of depth four. Path signatures, rooted in the rough path theory developed by Terry Lyons and building on work by Kuo-Tsai Chen from the 1950s, convert a sequential path into a structured collection of iterated integrals. The first level captures simple increments, the second captures interactions between pairs of increments, and higher levels encode progressively richer temporal structure. A key theoretical property guarantees that linear functions of signatures can approximate any continuous nonlinear functional of the path, meaning the model can learn complex within-window dynamics without resorting to massive black-box recurrent networks.

The mathematics also dictates a careful trade-off. The magnitude of the depth-k signature terms scales with the k-th power of the path’s total variation, divided by k factorial. A single large jump inside the look-back window therefore inflates the higher-order coordinates, making them noisy and potentially misleading descriptions of what follows, since volatility typically mean-reverts after extreme spikes. This factorial bound explains why the authors cap the truncation depth at four: deeper signatures grow geometrically in dimension and inject noise rather than signal. An ablation study confirms the prediction, with depth four consistently delivering the best performance across all five volatility proxies, while depth two is too shallow to capture nonlinear interactions and depth five degrades generalization. A learnable sigmoid gate, shared across markets and time, further suppresses uninformative signature channels.

The empirical evaluation covers 29 stock market indices from June 2009 to May 2022, spanning 3,395 daily observations per market and five realized volatility proxies: five-minute realized variance, bipower variation, median realized volatility, realized kernel variance with a Parzen kernel, and realized semivolatility. All models were trained under an identical protocol, with the same chronological 70/30 split, the same 22-day look-back, and the same tuning budget, ensuring that performance differences reflect modeling choices rather than experimental design. For one-step-ahead forecasts, Sig-GSPHAR achieved the lowest error in 114 of 145 market-proxy pairs for mean squared error and 112 of 145 for mean absolute error. Paired one-sided Wilcoxon signed-rank tests with Holm correction for multiple comparisons confirmed that the improvements over GSPHAR are statistically significant for most proxies, with p-values as low as 0.006 for mean squared error on realized semivolatility.

The advantage becomes even more pronounced at the 22-day horizon, where the signature block, computed from the full look-back segment aligned with the long target, can encode nonlinear interactions that linear lag aggregation cannot. Sig-GSPHAR improved on GSPHAR in 26 of 29 markets for realized variance and in all 29 markets for four of the five proxies under mean absolute error. Holm-adjusted p-values fell to the order of 10 to the minus 6 for mean squared error and 10 to the minus 8 for mean absolute error, among the strongest statistical evidence reported in this literature. The result suggests that the longer the forecasting horizon, the more valuable it becomes to represent the shape of the volatility path rather than just its coarse averages.

Perhaps the most scientifically interesting part of the paper is its honest diagnosis of when signatures fail. The aggregate advantage of the new model comes almost entirely from calm days: on the 95 percent of test days with ordinary volatility levels, Sig-GSPHAR is more accurate, while on the top 5 percent of extreme days it slightly under-predicts true spikes, with a median forecast-to-realized ratio of 0.62 versus 0.68 for GSPHAR. The two markets where the new model loses to its predecessor, Finland’s OMXHPI and Denmark’s OMXC20, are precisely the most heavy-tailed in the panel, with sample kurtosis of 259 and 89 respectively. For OMXHPI, just ten days account for 43 percent of the entire out-of-sample squared error, so a small difference on a handful of high-leverage days determines the headline number. The authors trace this behavior to the graph-HAR backbone rather than the signature branch itself, and suggest jump-aware loss functions or variance-stabilized log domains as remedies.

Two robustness analyses strengthen the practical case. First, a rolling-window re-estimation of the spillover network shows that the dominant transmission structure is highly persistent: in normal periods the Spearman rank correlation between rolling and static net-spillover vectors is about 0.81, and even during the COVID-19 shock, when the correlation drops to roughly 0.56, total connectedness stays high and the set of top net-transmitters is largely preserved. Because the model uses the graph only through the magnetic-Laplacian spectral basis, which depends on the dominant structure rather than fragile individual edges, a static graph estimated once on the training data remains adequate. Second, the authors equip their point forecasts with distribution-free conformal prediction intervals using a volatility-normalized score. Both Sig-GSPHAR and GSPHAR achieve near-nominal coverage, but at matched coverage the new model produces intervals that are 7 to 11 percent narrower across all five proxies, translating its point-forecast gains into sharper, more informative uncertainty bands that widen during turbulence and tighten in calm markets.

The broader significance of the work lies in demonstrating that ideas from stochastic analysis can be fused productively with graph machine learning in a domain as noisy and adversarial as financial volatility. Rather than replacing interpretable econometrics with opaque deep networks, Sig-GSPHAR keeps the HAR skeleton, adds a mathematically principled nonlinear feature layer, and aligns everything in a single spectral representation governed by the physics of market spillovers. The authors point to time-varying spillover graphs and robust training losses as natural next steps, but the core message stands: when the goal is anticipating how turbulence propagates through a globally connected financial system, the shape of the recent past matters as much as its average, and rough path theory provides exactly the language needed to describe that shape.

Subject of Research: Multivariate realized volatility forecasting using path signatures and directed graph spectral methods

Article Title: Signature-enhanced graph spectral HAR for multivariate realized volatility forecasting

Article References: Guo, Z., Han, A., Wang, C., & Gao, J. (2026). Signature-enhanced graph spectral HAR for multivariate realized volatility forecasting. Applied Intelligence, 56(14), Article 406. https://doi.org/10.1007/s10489-026-07445-1

Image Credits: AI Generated

DOI: 10.1007/s10489-026-07445-1

Keywords: realized volatility, path signatures, rough path theory, graph signal processing, HAR model, magnetic Laplacian, Diebold-Yilmaz spillover, volatility forecasting, conformal prediction, financial econometrics, machine learning, spillover networks