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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