The research, conducted by Oumaima Abouzaid and Faouzi Boussedra of Université Chouaib Doukkali in El Jadida, Morocco, begins from a diagnosis that will resonate with anyone who watched economic predictions collapse during recent crises. Traditional econometric tools—ARIMA models, Vector Autoregressions, Dynamic Stochastic General Equilibrium frameworks—rest on assumptions of parameter stability and largely linear relationships. When structural breaks occur, meaning fundamental shifts in the statistical properties governing economic variables, those assumptions fail. Parameters estimated under one regime become biased in the next, statistical inference weakens, and forecast errors balloon precisely when accurate predictions matter most.

To confront this instability, the authors built their framework around a sequence of complementary techniques. First, Bai–Perron structural break analysis detects endogenous breakpoints in the data without requiring prior assumptions about when changes occur. Second, Markov-Switching models identify latent economic regimes—expansionary and recessionary states with distinct statistical properties—whose labels are then fed into the forecasting engine as additional state-dependent features. Only after this regime-aware preparation do the machine learning models take over, trained on data that explicitly encode the economy’s shifting character rather than pretending it never changes.

The centerpiece of the predictive architecture is Double Machine Learning, or DML, a causal inference framework that integrates machine learning algorithms into econometric estimation while preserving valid statistical inference in high-dimensional settings. DML relies on orthogonalization and sample-splitting procedures to estimate causal effects while controlling for large numbers of confounding variables, reducing sensitivity to overfitting and omitted variable bias. Because macroeconomic time series exhibit serial dependence and volatility clustering, the authors adapted the standard approach by using block cross-fitting—partitioning observations into contiguous time blocks rather than random splits—and by computing heteroskedasticity and autocorrelation consistent standard errors with Newey–West corrections. Alongside DML, the framework employs Causal Forests, which extend Random Forest methods to estimate heterogeneous treatment effects across different economic regimes, recognizing that the same policy variable may exert very different influences in calm periods than in crises.

The empirical analysis drew on a monthly macroeconomic dataset spanning January 2000 to March 2025, yielding 303 observations per variable. The dataset combined indicators from the Federal Reserve Economic Data service, the International Monetary Fund, the OECD, the World Bank, and the Economic Policy Uncertainty database. The target variable was inflation, measured as year-over-year Consumer Price Index growth, with explanatory variables including GDP growth, unemployment, the federal funds rate, the dollar exchange rate index, Brent oil prices, M2 money supply growth, the VIX volatility index, and the Economic Policy Uncertainty index. Missing observations, which made up less than 2.3 percent of the data, were imputed using Kalman smoothing, and extreme outliers were winsorized at the first and ninety-ninth percentiles. The data were split chronologically into training, validation, and test subsets to avoid look-ahead bias, with rolling-window cross-validation used for tuning.

The results were striking. Across root mean squared error, mean absolute error, and mean absolute percentage error, the DML framework outperformed every benchmark, including conventional Vector Autoregressions, time-varying parameter VARs, Random Forests, XGBoost, and Long Short-Term Memory neural networks. The DML model achieved an RMSE of 1.01, compared with 1.58 for the standard VAR and 1.12 for the LSTM network. The gap widened during crises. Averaged across the 2008 financial crisis, the COVID-19 shock, and the 2022 inflation surge, the DML framework posted an RMSE of 1.49, against 2.55 for the VAR and 1.70 for the LSTM. The pandemic period proved the hardest test for all models, reflecting unprecedented volatility and nonlinear disruption, yet the causal framework remained the most resilient throughout. Robustness checks with alternative data splits and samples excluding individual crisis episodes confirmed that the results were not artifacts of any particular configuration.

Beyond raw predictive accuracy, the causal estimates offered economically meaningful insights into what drives inflation. Oil prices exerted the strongest positive causal effect, at 0.52, underscoring the dominance of energy price transmission during supply-side shocks. Money supply growth followed at 0.41, suggesting that expansionary liquidity conditions amplify inflationary pressure, while exchange rate depreciation contributed 0.31 through imported inflation channels. Economic Policy Uncertainty and financial volatility added positive effects of 0.24 and 0.18 respectively, indicating that uncertainty shocks and financial stress worsen price instability. Interest rate shocks, by contrast, showed a significant negative effect of −0.38, consistent with conventional monetary transmission theory in which higher policy rates dampen aggregate demand. SHAP-based explainability analysis then revealed how these influences shift across regimes: monetary variables dominate predictions in stable periods, while uncertainty indicators and financial volatility become far more influential during crises.

The framework’s most unconventional element is its blockchain layer, which the authors are careful to distinguish from the predictive engine itself. Blockchain here is not a forecasting tool and was not evaluated with performance metrics. Instead, it functions as a decentralized governance infrastructure. After preprocessing, each dataset version receives a cryptographic fingerprint using the SHA-256 hashing algorithm, and only that hash plus descriptive metadata is recorded on a distributed ledger. Smart contracts validate metadata consistency before new records are appended, and the ledger tracks model training events, hyperparameter configurations, software versions, random seeds, prediction outputs, and even the SHAP explanations attached to each forecast. Because any modification to the underlying data produces a different hash, tampering becomes immediately detectable, and every forecast can be traced back to the exact dataset and model version that produced it.

The authors’ comparative assessment suggests the governance gains are substantial: auditability, traceability, reproducibility, and tamper resistance all improve markedly relative to conventional centralized pipelines, where data revisions and model updates may go partially undocumented. The architecture could also strengthen coordination among central banks, finance ministries, statistical agencies, and international organizations by giving them a shared, transparent validation protocol. The authors acknowledge real trade-offs, however. Cryptographic hashing, smart-contract execution, and network synchronization impose computational overhead, scalability challenges emerge with many participating nodes, and consortium governance demands careful rules for access control and consensus. They also emphasize that the governance benefits described are architectural capabilities rather than experimentally validated performance improvements, since blockchain-specific metrics such as latency and throughput were not empirically tested.

The study’s implications reach well beyond academic benchmarking. As financial systems digitalize and central banks explore Central Bank Digital Currencies, the demand for forecasting systems that are simultaneously accurate, interpretable, and institutionally trustworthy will only grow. By demonstrating that causal machine learning can outperform both classical econometrics and black-box deep learning under structural instability—and that blockchain can wrap such systems in an auditable, tamper-resistant governance shell—the research sketches a plausible blueprint for the next generation of policy-grade economic intelligence. Future work, the authors suggest, will implement the governance layer on a permissioned blockchain platform and explore integrations with decentralized oracles, federated learning, and transformer-based models. If the vision holds, the economies of the future may be forecast not by opaque algorithms or brittle equations, but by transparent, decentralized systems whose every prediction can be verified, explained, and trusted.

Subject of Research: A blockchain-enabled causal machine learning framework for explainable macroeconomic forecasting under structural instability

Article Title: Decentralized blockchain governance for explainable causal AI in macroeconomic forecasting

Article References: Abouzaid, O., & Boussedra, F. (2026). Decentralized blockchain governance for explainable causal AI in macroeconomic forecasting. Frontiers in Blockchain, 9, Article 1883639. https://doi.org/10.3389/fbloc.2026.1883639

Image Credits: AI Generated

DOI: 10.3389/fbloc.2026.1883639

Keywords: blockchain, causal machine learning, Double Machine Learning, macroeconomic forecasting, explainable AI, SHAP, structural breaks, inflation, economic uncertainty, smart contracts, data governance, monetary policy

The research, published in Frontiers in Forests and Global Change, examines Austria, Brazil, Canada, China, Finland, France, Germany, Sweden, and the United States over the period from 1961 to 2022, using 62 annual observations per country drawn from the Global Footprint Network. The team, led by İlkay Güler of Ankara Haci Bayram Veli University together with colleagues from Bingöl University, Arkin University of Creative Arts and Design, Tarsus University, and Artvin Coruh University, focused on a measure called forest ecological balance, or FEB. This indicator is calculated as forest biocapacity minus the forest product footprint, capturing both the supply side, meaning the regenerative capacity of a nation’s forests, and the demand side, meaning the pressure that annual consumption of forest products places on those forests.

The choice of indicator matters. Most previous work on the stochastic properties of environmental indicators has concentrated on carbon dioxide emissions or aggregate ecological footprint, leaving forest-specific conditions comparatively underexplored. Forests underpin the United Nations’ Sustainable Development Goal 15, Life on Land, but they also feed into goals on food security, clean water, and climate action. Roughly 1.6 billion people depend directly or indirectly on forests for their livelihoods, and forest resources can account for around 22 percent of household income in some tropical developing countries. Understanding whether damage to these systems fades away or lingers is therefore far more than an academic exercise.

The statistical logic at the heart of the study is deceptively simple. If an environmental indicator is stationary, it fluctuates around a constant mean, and the effects of any shock, whether a policy change, a drought, or a market disruption, eventually dissipate as the series returns toward its long-term equilibrium. If the series is non-stationary, containing what statisticians call a unit root, shocks can have permanent consequences, and the system may drift to a new state rather than recover. For policymakers, this distinction determines whether an intervention produces a temporary correction or a lasting transformation, and whether uniform international frameworks can plausibly deliver comparable outcomes across different national contexts.

To probe these properties, the researchers applied two complementary tests. The conventional KPSS test, introduced by Kwiatkowski and colleagues in 1992, treats stationarity as the null hypothesis and decomposes a series into a deterministic trend, a random walk, and a stationary error term. Its weakness is that it ignores structural breaks, which can bias results toward rejecting stationarity. The Fourier KPSS test addresses this by incorporating sine and cosine functions that flexibly capture smooth, unknown, and multiple structural changes in the data. When the trigonometric terms prove statistically significant, the Fourier version provides the more reliable reading. Lag lengths in both tests were selected automatically using the Newey-West bandwidth with a Bartlett kernel to handle serial correlation and heteroskedasticity in the residuals.

The second pillar of the methodology is the maximal overlap discrete wavelet transform, or MODWT, which splits each country’s forest ecological balance series into short-term components spanning two to eight years, medium-term components spanning eight to thirty-two years, and long-term components beyond thirty-two years. The team used the Daubechies Least Asymmetric filter of length eight, known as LA8, together with a reflection boundary condition to preserve sample size and minimize information loss at the edges of the data. The authors preferred MODWT over the classical discrete wavelet transform because it is phase-independent, accommodates arbitrary data lengths, and retains outlying observations, making it better suited to relatively short annual samples.

The headline results reveal striking heterogeneity. For the original, undecomposed series, the conventional KPSS test found non-stationarity in every country, but the Fourier KPSS test, after accounting for smooth structural changes, identified stationary behavior in China, Germany, and the United States. The remaining six countries, Austria, Brazil, Canada, Finland, France, and Sweden, showed non-stationary dynamics, meaning shocks there may leave more persistent marks. The authors attribute China’s apparent stability to roughly three decades of large-scale reforestation and ecological restoration programs, Germany’s to long-standing institutionalized sustainable forest management aligned with European Union environmental goals, and the United States’ to pioneering anti-pollution policies, advanced forest monitoring systems including the Forest Inventory and Analysis program, and the ecosystem services approach.

The frequency-domain analysis adds a crucial layer of nuance. In the short run, most countries displayed non-stationary behavior, with only Finland and France showing mean-reverting dynamics, suggesting that short-term disturbances in those two countries dissipate more rapidly. In the medium run, the picture changed dramatically: both KPSS and Fourier KPSS tests supported stationarity for all nine countries once structural breaks were considered, indicating that medium-term forest ecological balance is generally resistant to persistent shocks regardless of national governance differences. The long run was the most heterogeneous of all. Fourier KPSS results flagged persistent, non-stationary behavior in China and Finland, while the other seven countries, Austria, Brazil, Canada, France, Germany, Sweden, and the United States, exhibited stationary long-run components where policy shocks would prove only temporary.

These findings carry a pointed message for forest policy. Because persistence varies by both country and time horizon, uniform forest-policy frameworks are unlikely to generate comparable outcomes across major forest-producing economies. The authors recommend short-term measures such as enforcing existing forest laws, cracking down on illegal logging, deploying rangers, drones, and satellite monitoring, and rapid reforestation, alongside long-term strategies including restoration of degraded areas, institutional capacity building, and conservation incentives. Country-specific recommendations range from Brazil’s need for stricter enforcement against illegal logging and protection of Indigenous land rights, to Canada’s focus on wildfire prevention and Indigenous co-governance, to Sweden’s push to reduce intensive clear-cutting in sensitive areas. The authors caution that their evidence concerns temporal persistence rather than causal effects, and that stationarity alone should not be read as proof of ecological resilience. Still, by showing that the same forest indicator can behave differently at different frequencies, the study offers an empirical foundation for forest management strategies tailored to both the nation and the timescale, a combination that one-size-fits-all policy has long overlooked.

Subject of Research: Frequency-dependent persistence of forest ecological balance in major forest product-producing countries

Article Title: Assessing forest ecological sustainability through wavelet decomposition and stationarity tests: a comparative analysis of major forest product producers

Article References: Güler, İ., Naimoğlu, M., Özbek, S., Adalı, Z., & Şimşek, O. (2026). Assessing forest ecological sustainability through wavelet decomposition and stationarity tests: a comparative analysis of major forest product producers. Frontiers in Forests and Global Change, 9, Article 1622811. https://doi.org/10.3389/ffgc.2026.1622811

Image Credits: AI Generated

DOI: 10.3389/ffgc.2026.1622811

Keywords: forest ecological balance, wavelet decomposition, stationarity tests, Fourier KPSS, forest biocapacity, ecological footprint, forest sustainability, MODWT, forest policy, structural breaks, timber production, mean reversion

The mathematical core of the framework deserves closer attention, because it is the piecewise least squares cost function that gives the analysis its power to locate transitions precisely. In essence, the algorithm evaluates every possible way of splitting the 56-quarter series into segments and, for each candidate split, measures how well a simple mean-based model fits the data within each segment. The configuration that minimizes the total squared deviation across all segments is retained as the best description of the series’ internal structure. Binary Segmentation then applies this logic recursively: it first finds the single most important break in the entire series, then repeats the search independently on the data to the left and to the right of that break, continuing until no further split meaningfully improves the fit. This recursive character is what allows the method to uncover a hierarchy of transitions rather than imposing a predetermined number of regimes, and it explains why the five detected breakpoints fall where they do—each one marks the location where the mean level of the Z″-score series shifts in a way that cannot be explained by random quarter-to-quarter fluctuation.

A subtlety of this approach, and one the authors handle with deliberate care, concerns the statistical validity of breaks that are found by searching. When a researcher scans many candidate locations for a break, the ordinary critical values of a classical Chow test no longer apply, because the test does not account for the fact that the break location was itself chosen to maximize evidence of instability. The supremum-Wald statistic addresses this by aggregating the Wald test across all candidate breakpoints and evaluating the maximum against distributional thresholds that incorporate the search itself. The reported value of 38.61, which exceeds the 1% asymptotic critical value, therefore carries more weight than an isolated Chow test would: it certifies that at least one genuine structural break exists in the series, not merely an artifact of data mining. This distinction between endogenous detection and exogenous assumption is what separates the study from earlier work that simply assumed break dates based on known corporate events.

The six regimes that emerge from the analysis trace a coherent narrative arc when read in sequence. The opening phase, with a mean Z″-score of 1.58, sits in what the Altman framework classifies as a zone of moderate vulnerability—above the distress threshold but well short of the safe region, a position typical of capital-intensive operators whose heavy asset bases and leverage keep scores compressed. The second phase’s transitory peak of 2.42 is notable precisely because it was temporary: the firm’s financial profile briefly strengthened before beginning the long decline that would define the following decade. From there the trajectory is essentially monotonic downward—0.60 in the transition phase, −0.29 at structural distress onset, −1.40 during accelerated deterioration, and finally −2.52 in severe terminal distress. The negative territory in the later phases is particularly meaningful, since under the Z″-score construction such values place a firm deep inside the distress zone, where historical misclassification rates are lowest and the indicator’s discriminative power is strongest.

The timing of the first persistent distress signal, identified at 2015Q2 under the market-value specification, is arguably the study’s most consequential empirical finding. A warning horizon of nearly a decade before the February 2025 filing substantially exceeds the anticipatory windows reported in prior retrospective studies of corporate failure, which typically document lead times of one to four years. Several features of the case help explain this extended horizon. Capital-intensive telecommunications firms carry enormous fixed assets and long-dated obligations, so financial deterioration accumulates gradually through successive quarters rather than arriving as a single shock. The regime structure detected in the data—with the transition-to-distress phase beginning in 2018 and the structural onset phase following—suggests a staircase pattern of decline, in which each deterioration step became the new baseline from which the next step descended. A monitoring framework sensitive to such mean shifts can flag the process early, whereas threshold-based classification would only sound the alarm once the score crossed a fixed boundary, potentially years into the decline.

The sensitivity analysis comparing market-value and book-value specifications of the Z″-score adds an important layer of methodological reassurance. The Altman Z″ model, developed for private and non-manufacturing firms, can in principle be computed with equity measured at market value or at book value, and the choice is known to affect both the level of the score and its volatility. The authors find that the five breakpoints remain stable across both specifications, indicating that the regime structure is a property of the underlying financial dynamics rather than an artifact of one particular accounting convention. At the same time, they are careful to note that the specific score levels and distress-zone classifications reported in the study pertain to the market-value specification adopted as primary. This honest separation between what is robust—the timing and number of structural breaks—and what is specification-dependent—the absolute score values—models a standard of transparency that applied distress research has not always met, and the authors position this systematic test as filling a gap in the prior applied literature.

The regional context strengthens the case for generalizability. The Latin American telecommunications sector has produced a series of high-profile insolvencies sharing the same structural anatomy: OI S. A. in Brazil, whose USD 19 billion bankruptcy protection filing in 2016 was preceded by accounting distress signals identifiable years earlier; NII Holdings, which restructured USD 4.35 billion in senior unsecured notes through Chapter 11 in 2014–2015; and WOM Chile, which sought Chapter 11 protection in April 2024 carrying USD 1.05 billion in debt. These operators, like Telefónica del Perú, combined high capital intensity with currency-mismatched debt and operated under strict regulatory regimes—OSIPTEL in Peru, ANATEL in Brazil, and Subtel in Chile—that constrained pricing power and limited financial flexibility. The convergence of these conditions across national borders suggests that the regime-shifting pattern documented for the Peruvian case is not an idiosyncratic curiosity but a recurring signature of distress in the sector, and that a replicable monitoring framework calibrated on one case could plausibly be transferred to comparable firms.

For practitioners, the implications cut across several constituencies. Creditors holding bondholder or supplier claims could in principle integrate change-point monitoring into their surveillance of exposure, using detected breakpoints as triggers for covenant review or renegotiation rather than waiting for payment defaults. Regulators overseeing concession-based utilities might adopt regime detection as a complement to periodic financial reporting requirements, since a statistically confirmed shift in the mean of a distress indicator provides an objective, reproducible signal that is harder to dismiss than qualitative warnings. Investors in listed emerging-market firms, where analyst coverage is thinner and information asymmetries are wider than in developed markets, stand to benefit from a method that extracts structure from public quarterly data without requiring privileged access. The framework’s reliance on standard accounting inputs—working capital, retained earnings, earnings before interest and taxes, market capitalization, and sales—means it can be implemented with data that is already disclosed, lowering the barrier to adoption.

Several limitations nonetheless bound the interpretation of the findings. The analysis rests on a single firm, and while the case offers the considerable advantage of a formally observable ex post validation event—the February 2025 insolvency filing—generalization to other firms, sectors, and jurisdictions requires further empirical application. The Z″-score itself, though well validated, is an accounting-based construct whose inputs can be shaped by managerial discretion, reclassifications, and inflation accounting in high-inflation environments. Change-point detection identifies when the mean of a series shifts but does not by itself identify the economic causes of the shift; interpreting the 2018Q2 or 2020Q4 breakpoints, for example, requires supplementary institutional knowledge about competitive dynamics, regulatory decisions, and ownership changes. The authors also note that the anticipatory horizon of 2015Q2 emerges from the longitudinal depth of the analysis—a fourteen-year window of 56 quarterly observations—and shorter series would mechanically shorten the detectable lead time.

These caveats notwithstanding, the study’s contribution lies in demonstrating that the integration of two mature methodologies—accounting-based distress scoring and structural break detection—yields insights neither can deliver alone. The Z″-score provides an economically interpretable index whose movements track the anatomy of financial deterioration, while Binary Segmentation supplies the statistical machinery to determine objectively when the trajectory changed character. Applied to a case with a known terminal event, the combination shows that the path to insolvency was neither invisible nor abrupt: it was a sequence of six regimes, each statistically distinguishable, unfolding over more than a decade. For capital-intensive firms in emerging markets—where distress tends to be cumulative, regulatory constraints bind, and formal risk assessment mechanisms often arrive too late—the framework offers a replicable mathematical template for turning scattered quarterly observations into an early, structured, and statistically defensible account of where a firm stands in its trajectory toward—or away from—financial distress.

Subject of Research: Change-point detection applied to the Altman Z″-score to identify structural financial distress regimes in a capital-intensive Peruvian telecommunications firm

Article Title: Change-point analysis of Altman Z″-score dynamics: structural regime detection in a capital-intensive emerging market firm

Article References: Bazán-Ramírez, W., Prudencio-Vidal, J. A., Mejía-Osorio, A. G., Gutiérrez-Gómez, E., Palomino-Malpartida, Y. G., Bazán-Ramírez, A., & Bello-Bernal, M. Á. (2026). Change-point analysis of Altman Z″-score dynamics: structural regime detection in a capital-intensive emerging market firm. Frontiers in Applied Mathematics and Statistics, 12, Article 1955286. https://doi.org/10.3389/fams.2026.1955286

Image Credits: AI Generated

DOI: 10.3389/fams.2026.1955286

Keywords: Altman Z″-score, change-point detection, Binary Segmentation, financial distress, structural breaks, emerging markets, telecommunications, insolvency risk, Telefónica del Perú, early warning systems, quantitative finance, Peru

The methodological architecture of the study is what gives its findings their weight. Rather than relying on a single regression model, Salami combines Ordinary Least Squares estimation with Newey–West heteroskedasticity and autocorrelation-consistent standard errors, a correction that ensures the statistical conclusions remain robust even when the data exhibit the volatility typical of developing economies. On top of this baseline, the analysis layers time-series threshold regression, which allows the inflation–growth relationship to shift abruptly at a critical value, and smooth transition regression, which instead models a gradual change in the relationship as inflation rises. The two approaches are complementary: threshold models capture sharp regime changes, while smooth transition models capture softer, more continuous adjustments. Comparing their results provides a way to test whether the inflation–growth link truly behaves differently at different levels of inflation, or whether any apparent shift is a statistical artifact.

The headline result is that inflation is negatively and statistically significantly associated with real GDP growth in Nigeria, and that the magnitude of this association varies across inflation regimes. The threshold model identifies the critical value at 12.22 percent, and, notably, the inflation coefficient is negative both below and above that line. This is an important nuance. Some countries exhibit a benign zone of low inflation where the relationship is positive or neutral, turning negative only at higher rates. In Nigeria’s case, the data suggest that inflation is already a burden even at moderate levels, and that crossing the 12.22 percent mark changes the intensity of the damage rather than its direction. For a country that has experienced inflation rates well into double digits in recent years, this finding implies that the economy has been operating on the wrong side of the threshold for extended periods.

Rigorous science demands sensitivity analysis, and the study delivers one that addresses a subtle data problem. The trade-openness series used in the analysis required a completion procedure for its three boundary observations, and any such imputation could in principle distort the estimated threshold. To check this, the author re-estimated the model excluding those three boundary observations. The result was reassuring: the 12.22 percent threshold survived intact, and the regime-specific coefficients were closely comparable to the baseline estimates. This means the central finding is not materially driven by the data-completion procedure, a conclusion that substantially strengthens confidence in the threshold estimate. In empirical macroeconomics, where results can hinge on small sample choices, this kind of robustness check is the difference between a suggestive correlation and a defensible policy benchmark.

The smooth transition model tells a more cautious story. It identifies a transition location of approximately 11.50 percent, remarkably close to the threshold estimate, but its transition parameters are not statistically significant. In practical terms, this means the evidence for a gradual, smooth adjustment of the inflation–growth relationship is weaker than the evidence for a discrete regime shift. The convergence of the two models on a similar location, around 11.5 to 12.2 percent, is itself informative, suggesting that something real happens to Nigerian growth dynamics as inflation approaches the low teens. But the statistical weakness of the transition parameters means the threshold model remains the more reliable guide, and policymakers should treat the smooth transition results as corroborating rather than independently conclusive.

Inflation does not operate in a vacuum, and the study’s treatment of Nigeria’s external and fiscal environment is one of its most valuable contributions. Exchange-rate depreciation and international Brent crude oil-price shocks are both negatively associated with growth in the baseline specification, a result that reflects Nigeria’s well-known vulnerabilities as an oil-dependent economy with a currency sensitive to external pressures. Intriguingly, however, the independent statistical significance of these external variables weakens once nonlinear inflation dynamics are incorporated into the model. This suggests that part of the damage inflicted by oil shocks and currency depreciation may operate through their effect on inflation itself, which then transmits to growth. In other words, inflation may be the channel through which Nigeria’s external shocks do much of their harm, making price stability not merely one policy goal among many but a central defensive mechanism.

Perhaps the most policy-relevant finding concerns the interaction between inflation and fiscal conditions. The study finds a positive and statistically significant interaction between inflation and the fiscal balance, indicating that improved fiscal positions can attenuate, though not eliminate, the adverse association between inflation and growth. The mechanism is intuitive: when a government’s budget is healthier, it is better able to cushion households and firms against price shocks, avoid inflationary deficit financing, and maintain public investment that supports productive capacity. The crucial caveat is the word attenuate. Sound fiscal management softens the blow of inflation but cannot substitute for monetary control of prices. The finding underscores the study’s overarching conclusion that Nigeria’s growth stability depends on coordinated monetary, fiscal, and exchange-rate policies rather than on any single lever pulled in isolation.

The temporal dimension of the analysis reveals how Nigeria’s macroeconomic history is written into the data. Structural-break tests identify breaks in 2016, 2020, and 2023, corresponding to the country’s recession, the COVID-19-related economic disruption, and the exchange-rate liberalisation reforms respectively. These are not abstract statistical artifacts but recognizable chapters in Nigeria’s recent economic narrative. The 2016 recession followed the collapse of oil prices and foreign-exchange shortages; the 2020 break captures the pandemic’s simultaneous supply and demand shocks; and the 2023 break reflects the liberalisation measures that reshaped the currency regime. That the econometric tests independently detect these episodes lends credibility to the modeling framework, while also reminding analysts that parameter stability cannot be assumed in an economy subject to such repeated structural upheaval.

Complementary evidence comes from quantile regression, which examines how the inflation–growth relationship varies across the distribution of growth outcomes rather than only at the mean, and from machine-learning techniques applied in an explicitly exploratory role. Random Forest and XGBoost models were assessed using chronologically ordered hold-out validation, a demanding test that trains models on earlier data and evaluates them on later periods. The results indicated limited temporal generalisation, meaning the machine-learning models struggled to predict growth in unseen future periods. Consequently, their feature-importance and SHAP outputs are interpreted as exploratory nonlinear evidence rather than independent predictive or causal confirmation. This is a methodologically honest stance. Machine-learning tools can reveal complex interaction patterns that linear models miss, but without demonstrated out-of-sample predictive power, their outputs cannot be elevated to causal claims. The study’s willingness to constrain its own machine-learning findings is a model of restraint in a field often tempted by algorithmic overreach.

Taken together, the findings paint a coherent and sobering picture of Nigeria’s post-shock macroeconomic environment. The inflation–growth relationship is negative, regime-sensitive, and conditioned by fiscal and external circumstances. Trade openness is positively associated with growth, offering a rare bright spot, while broad money growth exhibits a negative baseline relationship, though these effects vary across specifications. Parameter-stability diagnostics, including CUSUM and CUSUMSQ tests, confirm that the baseline model’s coefficients and residual variance remain within statistical bounds, indicating no systematic instability that would undermine the estimates. For Nigerian policymakers, the practical message is clear: keeping inflation below the estimated 12.22 percent threshold, strengthening fiscal balances to buffer the inflation–growth nexus, and managing exchange-rate and oil-price exposures through coordinated policy are not competing objectives but interlocking requirements. For economists studying other emerging economies, the study offers a template for combining classical threshold econometrics with modern machine-learning diagnostics while respecting the limits of each. As global inflation pressures persist, the Nigerian experience serves as a reminder that the cost of letting prices drift upward is not abstract; it is measured in forgone growth, and the price of that mistake becomes steeper with every percentage point past the line.

Subject of Research: The nonlinear threshold relationship between inflation and economic growth in Nigeria

Article Title: Inflation threshold, fiscal conditions and growth stability in Nigeria’s post-shock macroeconomic environment

Article References: Salami, R. A. (2026). Inflation threshold, fiscal conditions and growth stability in Nigeria’s post-shock macroeconomic environment. Discover Sustainability. https://doi.org/10.1007/s43621-026-04682-9

Image Credits: AI Generated

DOI: 10.1007/s43621-026-04682-9

Keywords: inflation, economic growth, Nigeria, inflation threshold, fiscal balance, exchange rate, oil prices, threshold regression, quantile regression, machine learning, macroeconomics, structural breaks