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

1 Introduction

The detection of structural breaks in financial time series and the longitudinal monitoring of corporate financial distress represent two methodologically mature yet rarely integrated areas of quantitative finance. Financial indicators in capital-intensive firms frequently exhibit non-stationary dynamics reflecting underlying regime transitions—discrete shifts in mean behavior that static, threshold-based classification approaches cannot capture. This limitation is particularly pronounced in emerging market contexts, where financial deterioration tends to be gradual and cumulative rather than abrupt, and where the absence of longitudinal, regime-sensitive monitoring frameworks leaves creditors, regulators, and investors without systematic tools for early risk identification. The present study addresses this gap by proposing an integrated framework that combines the Altman Z″-Score—a well-established accounting-based distress indicator—with Binary Segmentation change-point detection using a least squares cost function, providing a replicable mathematical approach to examining corporate financial distress as a dynamic regime-shifting process.

Telefónica del Perú S. A. A. is a publicly listed telecommunications operator that entered the Peruvian market through a major privatization transaction in the 1990s and operated under the ownership of Telefónica de España for more than three decades. However, despite this prolonged presence, the financial trajectory of the Peruvian subsidiary evidenced a progressive and cumulative deterioration that led to the submission of a restructuring request under the Ordinary Insolvency Procedure (Procedimiento Concursal Ordinario, PCO) before the National Institute for the Defense of Competition and the Protection of Intellectual Property (Instituto Nacional de Defensa de la Competencia y de la Protección de la Propiedad Intelectual, Indecopi) in February 2025—driven by the company’s inability to service its financial liabilities, primarily fiscal obligations and bondholder debt, within the framework of the General Insolvency Law (1)—coinciding with the exit of Telefónica de España from the Peruvian market as the company transferred its equity stake to an Argentine business group, under whose ownership it was renamed Integratel Perú S. A. A. This case represents a singular instance of prolonged corporate insolvency risk in a capital-intensive listed firm (2, 3): a formally documented insolvency event involving bondholder obligations, fiscal liabilities, and supplier debt amounting to several hundreds of millions of US dollars (4)—in which persistent signals of financial deterioration were observable prior to the insolvency event, yet no formal risk assessment mechanism identified the trajectory before the institutional event materialized. This constitutes a unique empirical opportunity to examine how accounting-based risk indicators behave longitudinally in the Latin American telecommunications sector.

The selection of Telefónica del Perú S. A. A. as the unit of analysis is justified on grounds that extend beyond the local context. The Latin American telecommunications sector has experienced a documented pattern of financial distress and formal insolvency proceedings among capital-intensive operators: OI S. A.—a publicly listed firm on the Brazilian stock exchange B3 (Bolsa, Brasil, Balcão) under the ticker OIBR3—filed for USD 19 billion bankruptcy protection in 2016 (5), with prior academic evidence confirming that accounting-based distress signals were identifiable years before the formal event (6); and NII Holdings, Inc.—listed on the NASDAQ stock exchange under the ticker NIHD—which operated under the Nextel brand across Latin America, underwent Chapter 11 reorganization in 2014–2015, restructuring USD 4.35 billion in senior unsecured notes (7). More recently, WOM Chile filed for Chapter 11 bankruptcy protection in the United States in April 2024 with USD 1.05 billion in debt (8). These cases share structural conditions with Telefónica del Perú: high capital intensity, currency-mismatched debt, and strict regulatory frameworks—including OSIPTEL (Organismo Supervisor de Inversión Privada en Telecomunicaciones) in Peru, ANATEL (Agência Nacional de Telecomunicações) in Brazil, and Subtel (Subsecretaría de Telecomunicaciones) in Chile—that constrain pricing power and limit financial flexibility. This regional pattern of distress conditions justifies the selection of Telefónica del Perú as a representative case for the longitudinal monitoring framework proposed in this study.

The telecommunications sector in Latin America provides a particularly relevant setting for distress analysis because operators share common structural characteristics including high leverage, spectrum investment requirements, regulatory constraints, and long-term infrastructure commitments. These features make individual distress episodes less idiosyncratic and more representative of sector-wide financial fragility patterns, strengthening the external validity of single-firm longitudinal analyses.

The financial deterioration documented in this study may also be interpreted through the lens of agency theory (9): as Telefónica del Perú’s Z″-Score deteriorated progressively, bondholders activated early repayment clauses—with financial obligations totaling approximately USD 305 million due in 2025 alone, including approximately USD 188 million in bond maturities (4)—ultimately transferring control from shareholders to creditors in the concursal proceeding. From a theoretical standpoint, this longitudinal design allows the study to document distress signals nearly a decade before the formal insolvency event, illustrating how regime-based monitoring can characterize deterioration trajectories over horizons longer than those typically examined in retrospective early warning studies.

The literature on financial distress prediction originates in the pioneering work of (10), who demonstrated that individual accounting ratios carry predictive information about solvency conditions several years prior to failure—establishing the empirical foundations for using accounting information as an early warning signal. Building on this, (11) developed the first multivariate bankruptcy prediction model integrating five financial ratios into a single synthetic index—the Z-Score—which introduced a structured three-zone risk classification framework and substantially outperformed univariate approaches. Subsequent adaptations extended the model’s applicability: (12) introduced the Z′-Score for private manufacturing firms, and (13) developed the Z″-Score for non-manufacturing firms—both listed and unlisted—establishing classification thresholds of 1.10 and 2.60 through discriminant analysis. (2) consolidate the Z″-Score as the standard tool for capital-intensive regulated industries, including utilities and telecommunications, while (14) further documents its dissemination in emerging market contexts. The Z″-Score thresholds (Z″ < 1.10: distress zone; 1.10 ≤ Z″ ≤ 2.60: grey zone; Z″ > 2.60: safe zone) have been widely adopted across diverse sectors and institutional contexts—including healthcare, banking, supply chain management, and public sector firms (15, 16)—as well as in Latin American non-manufacturing firms directly comparable to the present study (17, 18), reflecting well-recognized advantages in interpretability, methodological consistency, and inter-study comparability (19, 20).

In emerging markets—characterized by lower capital market depth, higher macroeconomic volatility, and more pronounced information asymmetries—accounting-based models retain a central role in corporate solvency analysis. The Z″-Score has been applied across capital-intensive telecommunications firms listed in emerging markets, where financial deterioration typically manifests gradually (21–23). Evidence from other capital-intensive sectors reinforces this utility: (24) document persistent deterioration signals in the European airline industry, and (25) demonstrate predictive capacity in mining firms on the Johannesburg Stock Exchange. Despite recognized limitations regarding generalizability (26, 27), recent evidence confirms the model’s informative capacity across emerging market firms in sectors characterized by high capital intensity (28), Latin American non-manufacturing contexts (17, 18), and diverse firm life cycles (29). Despite advances in machine learning approaches achieving classification accuracies exceeding 93% (30), the Z″-Score remains the benchmark model in applied literature due to its parsimony, economic interpretability, and methodological transparency (3)—qualities particularly valuable in longitudinal studies where the interest lies in tracking deterioration trajectories rather than maximizing short-term predictive accuracy.

The detection of structural breaks in financial time series constitutes a well-established methodological area in empirical finance. The foundational framework for multiple structural break detection was formalized by (31), who proposed simultaneous estimation of multiple breakpoints through least squares minimization. Binary Segmentation has emerged as a computationally efficient method for segmenting time series into statistically homogeneous intervals (32), with recent contributions confirming its practical applicability to real-world financial time series (33). Despite the extensive literature on financial distress prediction, the application of structural break detection to accounting-based distress indicators remains underexplored—particularly in emerging market contexts where financial deterioration tends to be gradual and cumulative. Existing studies predominantly adopt cross-sectional classification designs that do not capture the temporal dynamics through which insolvency risk accumulates over multi-year horizons, a limitation especially pronounced for capital-intensive telecommunications firms in Latin America where regulatory constraints, infrastructure investment cycles, and ownership transitions compound financial fragility over extended periods.

This case raises several relevant questions from the perspective of corporate risk management and financial distress analysis: Can change-point detection methods effectively segment financial time series into statistically homogeneous regimes that are temporally consistent with corporate insolvency events? To what extent does the integration of structural break econometric techniques enrich the dynamic interpretation of accounting-based financial indicators? Can the Altman Z″-Score identify financial deterioration prior to its formal institutional recognition in a telecommunications firm listed in an emerging market? And does the model show longitudinal coherence in capturing the trajectory of financial fragility in capital-intensive and highly regulated service firms? Addressing these questions requires moving beyond static, cross-sectional approaches, adopting dynamic frameworks capable of tracking prolonged trajectories of insolvency risk accumulation in capital-intensive firms.

Existing empirical evidence presents two complementary gaps. On the one hand, a risk assessment gap: studies on financial distress in telecommunications predominantly employ static or short-term approaches, without systematically examining the longitudinal dynamics of insolvency risk accumulation or its link to formal institutional events (21, 23). On the other hand, a geographical gap: the Latin American telecommunications sector remains sparsely documented in the international literature on corporate insolvency risk and financial distress prediction, despite its relevance as an emerging market context characterized by high capital intensity and strict regulation (19, 28). No prior study explicitly links the longitudinal trajectory of the Z″-Score in a Latin American telecommunications firm with a formally observable insolvency proceeding, which reinforces the pertinence of the present work.

This integration offers a perspective that combines two typically separate analytical traditions: threshold-based financial ratio classification, which provides a static, period-by-period diagnosis, and change-point detection, most commonly applied to market-based or macroeconomic series. By applying this combination to a single firm’s longitudinal accounting-based indicator, the present study identifies not merely whether financial ratios indicate distress at a given point in time, but when and how the underlying pattern of accounting information shifts between structurally distinct regimes Table 1.

Table 1. Quarterly classification according to Altman Z″-score zones.

The observation corresponding to 2012Q2 (Z″ = 0.97) represents an isolated entry into the distress zone, with an immediate return to the grey zone in the following quarter. Persistent and uninterrupted financial distress begins from 2015Q2 onwards.

Within this framework, the Altman Z″-Score emerges as a methodologically appropriate tool for this type of analysis. Developed as an adaptation of the original Z-Score for non-manufacturing and emerging market contexts (13), it combines parsimony, interpretability, and empirical robustness—qualities that recent literature identifies as key advantages of the Z-Score over more complex machine learning approaches (3), making it particularly suitable for credit risk monitoring and early warning applications in financial institutions, regulatory bodies, and institutional investors. To the best of our knowledge, this is the first study to document the complete trajectory of the indicator in a Latin American telecommunications firm across 56 consecutive quarters, explicitly linking the identified structural regimes with a formally observable insolvency event. This study applies the Altman Z″-Score to Telefónica del Perú using quarterly financial data for the period 2011Q1–2024Q4, and complements this analysis with Binary Segmentation change-point detection (32), implemented within the multiple structural break framework of (31), to identify endogenous regime transitions in the indicator’s trajectory.

The results show that financial deterioration was observable beginning in 2015Q2—preceding the filing of the insolvency restructuring request by nearly a decade—suggesting consistency between the Z″-Score’s trajectory and the subsequent institutional outcome, illustrating its monitoring potential for prolonged corporate fragility. The resulting Z″-Score levels and corresponding distress-zone classifications are specific to the market-value specification adopted as primary in this study, as detailed in Section 4.4. This study contributes to the literature in five main ways. First, it demonstrates that Binary Segmentation change-point detection methods (32) can effectively segment financial time series into regimes internally homogeneous in mean level, providing a structured basis for the retrospective identification and longitudinal monitoring of structural financial deterioration. Second, it shows that integrating structural break econometric techniques with accounting-based indicators substantially enriches the dynamic interpretation of financial distress indicators, enabling the identification of regime transitions that static cross-sectional approaches cannot capture. Third, it provides longitudinal evidence of temporal consistency between the Altman Z″-Score trajectory and the subsequent risk event—evidence that is particularly compelling given the ex post observability of that event—with direct implications for creditors, bondholders, pension funds, and regulatory bodies engaged in corporate risk monitoring. Fourth, it provides a longitudinal analysis of 56 consecutive quarterly observations (2011Q1–2024Q4) showing that accounting-based distress indicators, when examined through a structural break lens, reveal trajectories of financial fragility in capital-intensive and highly regulated service firms—suggesting a methodological pathway applicable to comparable firms in emerging markets. Fifth, it demonstrates through a systematic sensitivity analysis that the identified structural regimes are robust to the specification of the Z″-Score’s market-based component, addressing a methodological gap not explicitly tested in prior applied literature.

2 Materials and methods

2.1 Study design and scope

This study adopts a longitudinal time-series analytical design, aimed at assessing the ex post temporal consistency between the Altman Z″-Score trajectory and financial distress in a telecommunications company listed in an emerging market. Moving beyond descriptive or cross-sectional approaches, the analysis focuses on examining the Z″-Score’s monitoring potential for financial deterioration by contrasting its temporal evolution against a formal institutional crisis event.

The research is developed as an applied empirical single-case study, using Telefónica del Perú S. A. A. as the unit of analysis. While the study does not seek population-wide statistical inference, the methodological design prioritizes procedural replicability. Thus, the empirical strategy can be applied to other non-manufacturing, capital-intensive firms subject to similar regulatory frameworks in emerging markets.

The methodological objective is not to maximize short-term classificatory accuracy metrics, but rather to assess the utility of the Z″-Score as a tool for continuous financial risk monitoring through the analysis of longitudinal financial time series. The integration of structural break detection techniques enables the identification of statistically differentiated regimes in the indicator’s temporal trajectory, allowing for the documentation of medium and long-term deterioration trajectories relevant to corporate risk management and decision-making for regulators, creditors, and market participants. The selection of Telefónica del Perú S. A. A. as the unit of analysis is justified by three criteria: the availability of 56 consecutive quarters of audited public financial data; the existence of a formally documented insolvency event—the PCO filed before Indecopi in February 2025—that serves as an observable ex post validation benchmark; and the firm’s status as the largest historically listed telecommunications operator in Peru—a capital-intensive, highly regulated sector representative of the emerging market context in which this type of longitudinal distress analysis is most needed.

The analytical pipeline proceeds in two conceptually distinct stages. First, quarterly financial-statement data are transformed into a single accounting-based indicator—the Altman Z″-Score—following the operationalization detailed in Section 2.4. Second, the resulting 56-quarter time series is analyzed as a whole using change-point detection: rather than classifying each quarter independently, the algorithm identifies dates at which the series’ average level shifts, partitioning the full trajectory into a small number of internally homogeneous phases. Sections 2.4 through 2.6 detail, respectively, how each stage is implemented and validated.

2.2 Unit of analysis, time horizon, and validation event

The unit of analysis is Telefónica del Perú, a telecommunications operator listed on the Lima Stock Exchange (Bolsa de Valores de Lima) that operates in a highly regulated environment characterized by significant fixed capital investment requirements.

The analysis period comprises 56 consecutive quarters, from 2011Q1 to 2024Q4. This timeframe captures a complete financial performance cycle, covering phases of relative stability, gradual decline, and severe financial stress prior to the crisis event. This temporal breadth is appropriate for analyzing cumulative financial distress processes, which are typical of regulated service providers.

The validation event corresponds to the formal submission of a PCO request before Indecopi in February 2025. This institutional milestone is considered an observable event of severe financial distress and is used as an ex post reference to evaluate whether the Z″-Score emitted early warning signals.

2.3 Data sources and nature

The information used is derived from (unconsolidated) individual quarterly financial statements, expressed in thousands of Peruvian Soles (PEN). These were obtained from the Securities Market and Collective Funds Information System (SIMV), managed by the Superintendency of the Securities Market of Peru (Superintendencia del Mercado de Valores), available via its official platform (34). All data come from publicly accessible reports, ensuring traceability and reproducibility.

The use of individual financial statements reflects a methodological decision to isolate the operational and financial risk of the local legal entity, thereby avoiding distortions stemming from subsidiaries or the corporate group’s international operations. As a result, the Z″-Score reflects the financial situation relevant to local creditors, suppliers, and authorities.

Data are maintained in the original currency (PEN) without inflationary adjustments or exchange rate conversions. This decision is consistent with the relative nature of the ratios comprising the Z″-Score and preserves intertemporal comparability. Table 2 documents the exact construction of each Z″-Score component, together with the corporate actions affecting shares outstanding throughout the sample period.

Table 2. Documentation of Z″-Score data construction and corporate actions affecting shares outstanding.

All financial statements are individual (unconsolidated) quarterly statements, audited annually and reviewed quarterly, and publicly disclosed through the SMV platform (34). No missing values were identified across the 56 quarterly observations comprising the sample. Market Value of Equity was computed using the number of shares outstanding at the end of each quarter, consistent with standard practice in Z″-Score applications. Share price data correspond to the closing price on the last trading day of each quarter, obtained from (35).

2.4 Operationalization of the Altman Z″-score

Financial distress is operationalized through an adaptation of the Altman Z″-Score model (13), originally formulated for non-manufacturing firms in emerging markets, in which market value of equity is used in X4 in place of the book value specified in the original formulation, as detailed below. The index is calculated according to Equation 1:

Z ″ = 6.56 X 1 + 3.26 X 2 + 6.72 X 3 + 1.05 X 4 (1)

where:

X 1 = Working Capital / Total Assets

X 2 = Retained Earnings / Total Assets

X 3 = EBIT / Total Assets

X 4 = Market Value of Equity / Total Liabilities

The classification of financial conditions follows the conventional threshold criteria of the Altman Z″-Score model. Specifically, values below 1.10 indicate financial distress, values between 1.10 and 2.60 correspond to a grey zone, and values above 2.60 indicate financial stability (2, 13, 16, 20).

The Market Value of Equity is calculated as the product of the quarterly closing share price and the total number of shares outstanding at the end of each period. Historical prices were obtained from (35), while the accounting data were sourced from the financial statements published in the SIMV.

This specification combines accounting indicators with market information, allowing for the integration of both historical financial performance and investor expectations regarding the firm’s future viability.

The emerging-market constant (+3.25) introduced in Altman’s Emerging Market Scoring (EMS) methodology (19) was not incorporated in the present analysis. This constant standardizes the Z″-Score so that a score at or below zero corresponds to a D-rated (default) bond, serving the specific purpose of mapping the indicator to bond-rating equivalents. As the present study focuses on regime-based distress monitoring rather than bond-rating classification, the classification thresholds applied here (1.10 and 2.60) correspond to the Z″-Score specification without this constant (13), consistent with prior empirical applications to listed firms in emerging markets (21, 25).

The market value of equity was used in X4. While the Z″-Score was originally calibrated using book value of equity (13, 19), the use of market value in X4 appears recurrently in applied studies of publicly listed firms across different sectors and emerging markets, including insurance in Jordan (36), supply chain in Spain (16), telecommunications in Indonesia (21) and mining in South Africa (25), although none of these studies explicitly justifies this specification choice. Altman (19) explicitly contemplates this substitution within the EMS process as a comparative rather than exclusive procedure, using the divergence between book and market-value scores to adjust the final assessment. Following this comparative logic, market value is adopted as the primary specification in the present study. Compared to book value, market value yields a systematically less severe reading of financial distress in the early years of the sample: under book value, the firm enters the distress zone (Z″ < 1.10) in the very first quarter of the study period (2011Q1), whereas under market value the firm remains predominantly in the moderate-vulnerability/grey zone throughout 2011–2014—with only one isolated quarter (2012Q2) briefly entering the distress zone before an immediate return to the grey zone—and with mean values 0.97 points higher than under book value during this period. Market value is therefore the more conservative specification, providing a more credible baseline against which the subsequent progressive deterioration can be documented, rather than an artificially inflated distress signal from the outset. Both specifications converge to identical structural breakpoints, confirming that the timing of the regime transitions central to this study is not an artifact of this specification choice.

2.5 Financial distress classification criteria

Financial risk classification is performed using the operational thresholds commonly employed in empirical applications of the Z″-Score:These cut-off points are interpreted as standardized empirical criteria, widely used in the applied literature, and facilitate both intertemporal and cross-study comparability (2, 13, 15). In the present analysis, the thresholds are used for diagnostic and longitudinal monitoring purposes, rather than as mechanical binary decision rules.

• Z ″ < 1.10: financial distress zone,
• 1.10 ≤ Z ″ ≤ 2.60: grey zone or warning zone,
• Z ″ > 2.60: financial safety zone.

2.6 Analysis strategy

The empirical strategy is structured into three complementary components:

2.6.1 Temporal trajectory analysis

The quarterly evolution of the Z″-Score throughout the study period is evaluated, identifying patterns of financial deterioration, stabilization, or recovery, as well as transitions between classification zones and potential structural shifts in the indicator’s dynamics.

In plain terms, the structural break analysis that follows addresses three questions in sequence: how many structural breaks are present in the series (assessed via the Bayesian Information Criterion), where exactly these breaks are located and whether their timing is statistically defensible (assessed via Chow tests and a supremum-Wald test), and whether the resulting phases are internally well-behaved rather than artifacts of the estimation method (assessed via trend, stationarity, and autocorrelation diagnostics). Each of these questions is addressed in turn below.

Change point detection methods provide a well-established framework for identifying structural changes in time series by segmenting them into statistically homogeneous regimes. These approaches can be formally understood as the combination of a cost function, a search method, and a constraint on the number of change points (32). Formally, given a signal y = (y₁, …, y_n), the objective is to find the partition that minimizes the total cost, as shown in Equation 2:

τ ̂ 1 , … , τ ̂ K = arg min τ 1 , … , τ K ∑ k = 0 K V ( y τ k + 1 : τ k + 1 ) (2)

where V ( y a : b ) = ∑ t = a b ∥ y t − y ↼ a : b ∥ 2

is the cost function, K is the number of breakpoints, and τ ̂ 1 < τ ̂ 2 <. < τ ̂ K are the estimated change-point positions.

Within this framework, to identify endogenous transitions in the mean behavior of the Z″-Score, a Binary Segmentation algorithm with a least squares (L2) cost function was implemented in Python (32), following the theoretical framework of multiple structural break detection established by (31). The number of breaks (k = 5) was selected based on the Bayesian Information Criterion (BIC), computed across specifications k = 1 to k = 6. The BIC reached its global minimum at k = 5 (BIC = −34.828), although the improvement over k = 4 (BIC = −33.211) is modest (ΔBIC = 1.6; see Table 3); according to the interpretive scale of (37), a BIC difference in this range (0 to 2) does not constitute meaningful evidence favoring one model over another. Both specifications are therefore reported: the breakpoints under k = 4 coincide with four of the five breakpoints identified under k = 5 (2014Q3, 2018Q2, 2020Q4, and 2022Q1), differing only in the absence of the 2013Q2 breakpoint, so that the substantive interpretation of the regime structure is materially unaffected by this choice.

Table 3. Bayesian information criterion (BIC) profile for k = 1 to 6 breakpoints—Binary Segmentation with L2 cost function.

BIC = n × log(RSS/n) + 2(k + 1) × log(n), where n = 56 quarterly observations and k = number of breakpoints. RSS = residual sum of squares. The optimal specification k = 5 (BIC = −34.828) is highlighted. BIC worsens at k = 6, confirming k = 5 as the global minimum.

It is acknowledged that the Z″-Score series exhibits a significant downward linear trend (R² = 0.852); the L2 cost function identifies transitions in the mean trajectory of the series—including its trend component—which is consistent with the study’s objective of characterizing longitudinal regimes of cumulative financial deterioration rather than isolating trend-free fluctuations. To assess whether the identified regimes reflect genuine discrete transitions rather than a smooth trend discretized into steps, Binary Segmentation was additionally applied using a linear cost function that fits a local trend within each segment rather than a constant mean. Four of the five breakpoints are identical under both specifications, with only the first breakpoint differing marginally (2013Q2 under the L2 model versus 2012Q1 under the linear model). Furthermore, within-phase trend analysis shows that slope coefficients are statistically non-significant at the 5% level in five of the six identified phases, although Phase 3 and Phase 6 yield borderline p-values (p = 0.051 and p = 0.062, respectively) that approach conventional significance thresholds; only Phase 5 shows a clearly significant within-phase trend (p = 0.034; see Table 4). This pattern indicates that the detected regimes are internally homogeneous in mean rather than artifacts of a continuously discretized trend.

Table 4. Robustness check: L2 vs. linear (trend-based) cost function, and within-phase trend analysis.

Panel A compares breakpoints identified by Binary Segmentation under the standard L2 (mean-shift) cost function versus a linear cost function that fits a local trend within each segment, both estimated for k = 5. Panel B reports OLS slope coefficients and p-values for a linear trend estimated within each of the six phases identified under the L2 specification. Non-significant within-phase slopes (p > 0.05) indicate that phases are internally homogeneous in mean rather than artifacts of a continuously discretized trend.

Stationarity (ADF, KPSS) and autocorrelation (Ljung-Box) diagnostics were additionally computed for each phase (Table 5). For the four phases with ten or more observations (Phases 1, 3, 4, and 6), ADF and KPSS results are jointly consistent with stationarity only in Phase 3, with Phases 1 and 4 showing borderline ADF results (p = 0.055 and p = 0.059, respectively) and Phase 6 showing contradictory evidence between the two tests (ADF p = 0.856 provides no support for stationarity, against a marginal KPSS p = 0.073). For Phase 2 and Phase 5 (n = 5 each), stationarity tests have insufficient statistical power to yield conclusive results, a well-known property of these tests in small samples rather than a limitation of the present analysis. The Ljung-Box test shows no significant autocorrelation in any of the six phases (p > 0.05 in all cases), including Phase 2 and Phase 5.

Table 5. Within-phase stationarity and autocorrelation diagnostics.

ADF = Augmented Dickey-Fuller test (H₀: unit root / non-stationary); KPSS = Kwiatkowski-Phillips-Schmidt-Shin test (H₀: stationary); Ljung-Box tests for residual autocorrelation (H₀: no autocorrelation), evaluated at lag 2 for all phases given sample size constraints. ¹For Phase 2 and Phase 5 (n = 5 each), ADF and KPSS results are not reported, as these tests have insufficient statistical power to yield conclusive results at this sample size—a well-known property of unit-root tests in small samples rather than a limitation specific to the present analysis. The Ljung-Box test, which does not share this power constraint at short lags, shows no significant autocorrelation in any of the six phases (p > 0.05 in all cases).

As an additional robustness check, the Binary Segmentation procedure was re-estimated after excluding the 2024Q3 observation (Z = −4.36), which is visibly extreme relative to adjacent quarters. The resulting five breakpoints are identical to those obtained with the full sample (2013Q2, 2014Q3, 2018Q2, 2020Q4, and 2022Q1), confirming that the identified regime structure is not driven by this single outlying observation.

Because these five breakpoints were selected endogenously—at the locations where the Binary Segmentation cost function is minimized—standard critical values for tests conducted at these specific dates are not strictly applicable, as they do not account for the search over candidate break locations. With this caveat in mind, the statistical distinctness of all adjacent phases was assessed through independent-samples t-tests, which yielded significant mean differences across all phase pairs (p < 0.05 in all cases), providing a supporting descriptive diagnostic consistent with the identified segmentation. As a further supporting diagnostic, Chow tests were additionally computed at each of the five endogenous breakpoints (p < 0.01 in all cases; see Table 6).

Table 6. Chow test results at endogenous breakpoints identified by Binary Segmentation (k = 5).

The Chow test assesses the null hypothesis of parameter stability across the identified breakpoint against the alternative of a structural break. F-statistics were computed using ordinary least squares regression with a linear trend. df = degrees of freedom. All five tests yield p < 0.01. Because these dates were selected endogenously, these results are presented as descriptive diagnostics rather than independent formal validation of each individual breakpoint (see Section 2.6).

To formally address this, a supremum-Wald test (38) was performed, computing the Chow F-statistic at every candidate breakpoint within a 15% trimmed range (39 candidate quarters, 2013Q2–2022Q4) and evaluating the maximum of this statistic against Andrews’ asymptotic critical values for unknown change-point location. The resulting statistic (sup-Wald = 38.61, attained at 2014Q4) substantially exceeds the corresponding 5 and 1% asymptotic critical values for two restricted parameters under 15% trimming (11.79 and 15.51, respectively), confirming the presence of at least one genuine structural break in the series independently of the specific breakpoint locations selected by the Binary Segmentation algorithm. This test establishes structural instability in the series overall rather than independently validating each of the five specific breakpoints; the t-test and Chow-test statistics reported above should accordingly be interpreted as descriptive diagnostics rather than formal validation of each individual date, with the reliability of the five endogenously detected breakpoints instead supported by their consistency across the sensitivity analyses reported in Table 4 and Figure 1.

The procedure identified five endogenous breakpoints located at 2013Q2, 2014Q3, 2018Q2, 2020Q4, and 2022Q1, delimiting six structurally differentiated regimes characterized by different mean levels of the indicator.

2.6.2 Persistence analysis in the distress zone

Continuous episodes of values below 1.10 are identified and interpreted as signals of structural financial deterioration. The duration of these episodes is used as an indicator of the severity and reversibility of the distress.

2.6.3 Ex-post validation via institutional event

The trajectory of the Z″-Score is contrasted with the insolvency proceedings initiated in 2025, evaluating the temporal consistency between the indicator’s trajectory and the crisis event.

This approach views the Z″-Score as a continuous monitoring tool focused on interpreting risk trajectories rather than specific point predictions of bankruptcy.

2.7 Methodological scope and limitations

This study adopts a deliberately parsimonious methodological design, centered on the application of the Altman Z″-Score using the adapted specification described in Section 2.4, without coefficient re-estimation or local calibrations. The objective is to preserve interpretability, transparency, and intertemporal and inter-study comparability, qualities that are highly valued in applied financial analysis and regulatory contexts.

Furthermore, the study does not incorporate comparisons with alternative models or machine learning-based approaches, as the goal is not to maximize short-term predictive accuracy metrics. Instead, it aims to document the Z″-Score’s ability to capture medium and long-term financial deterioration trajectories through an accessible, replicable, and methodologically consistent approach applicable to other capital-intensive service companies listed in emerging markets under comparable regulatory frameworks.

2.8 Use of artificial intelligence tools

Artificial intelligence tools, specifically Claude (Anthropic, claude.ai) and SciSpace (scispace.com), were used during the preparation of this manuscript to support the revision of academic writing style, English grammar, consistency checking across sections, and reference verification. No artificial intelligence tool was used for data collection, analysis, or interpretation of results. All analytical procedures were conducted exclusively by the authors using Python and standard statistical methods.

3 Results

3.1 Quarterly evolution of the Altman Z″-score (2011–2024)

Figure 2 presents the quarterly trajectory of the Altman Z″-Score estimated for Telefónica del Perú S. A. A. during the period 2011Q1–2024Q4, covering a total of 56 consecutive observations. The evidence reveals a markedly non-stationary pattern and a process of progressive deterioration that manifests in differentiated phases.

In the initial period (2011–2014), the indicator remained predominantly within the gray zone, with values close to the upper threshold of financial stability. This evolution suggests that, although the entity did not exhibit immediate signs of insolvency, it did present a structurally vulnerable financial profile.

However, from 2015Q2, a clear and persistent turning point emerges: the Z″-Score begins a sustained and uninterrupted downward trajectory, crossing the threshold associated with severe financial distress (Z″ < 1.10) and remaining below it for the remainder of the analysed period. This behavior is consistent with cumulative structural weakening.

3.2 Quarterly classification by financial risk zones

To systematize the interpretation of the indicator, each quarterly observation was classified into three regimes: safe zone, gray zone, and financial distress zone.

The evidence shows that Telefónica del Perú remained mainly in the gray zone during the initial stage, reflecting a state of moderate warning. However, since 2015Q2, a persistent and uninterrupted transition toward values below the critical threshold (Z″ < 1.10) is identified, consolidating a prolonged financial distress regime that extends to the end of the analysed period.

This finding is particularly relevant because it confirms that the deterioration did not emerge as a sudden shock, but rather as a gradual and cumulative process.

3.3 Decomposition of the Z″-score: accounting sub-index vs. market-based component

Given that component X₄ of the model explicitly incorporates market information (market value of equity to total liabilities), a decomposition of the Altman Z″-Score into its accounting sub-index (6.56·X1 + 3.26·X2 + 6.72·X3) and the market-based component (1.05·X4) was conducted to assess the relative contribution of each to the overall trajectory.

Figure 3 presents both the full Z″-Score and the accounting sub-index together. The accounting sub-index—which excludes X4 entirely—mirrors the full Z″-Score trajectory throughout the study period, confirming that the structural deterioration documented in this study is driven primarily by accounting fundamentals: liquidity (X1), cumulative profitability (X2), and operating efficiency (X3). The market-based component (X4) contributed positively to the Z″-Score only during 2011–2014, when market capitalization remained relatively high. From 2015Q2 onwards, its contribution became negligible, and from 2018 both series are virtually identical.

This decomposition directly addresses the concern that the inclusion of market value in X4 may introduce circularity into the analysis: the progressive and persistent deterioration of the Z″-Score is fundamentally an accounting phenomenon, not a market artifact. The five structural breakpoints identified by Binary Segmentation coincide with inflection points in both series, confirming that the identified regime transitions are robust to the X4 specification.

3.4 Identification of structural breaks in the Z″-score dynamics

To assess whether the evolution of the Z″-Score responded to discrete transitions in its mean behavior, a Binary Segmentation algorithm with a least squares cost function was applied in Python (32), following the structural break detection framework of (31).

The algorithm identified five endogenous breakpoints, located at 2013Q2, 2014Q3, 2018Q2, 2020Q4, and 2022Q1, delimiting six structurally differentiated regimes characterized by successive phases of increasing financial fragility. The statistical distinctness of all adjacent phases was assessed through independent-samples t-tests, which yielded significant mean differences across all phase pairs (p < 0.05 in all cases).

Before presenting the phase segmentation, Figure 4 illustrates the complete Z″-Score series incorporating the estimated breaks visually, allowing for a clear observation of the structural transitions between regimes.

Below, Table 7 summarizes the descriptive statistics of the Z″-Score within each structural regime. These values are empirically grounded in the observed statistics for each subsample delimited by the detected breaks (mean, dispersion, and extremes), constituting direct quantitative evidence of the progressive shift toward severe distress.

Table 7. Descriptive statistics of the Z″-Score by identified structural regime.

Classification thresholds: Z″ < 1.10 (distress zone), 1.10 ≤ Z″ ≤ 2.60 (grey zone), Z″ > 2.60 (safe zone) (19, 20). Breakpoints were estimated using a Binary Segmentation algorithm with a least squares cost function in Python (32), following the methodological framework of (31). The number of breakpoints (k = 5) was selected based on the Bayesian Information Criterion (BIC), which reached its minimum at k = 5 (BIC = −34.828). Independent-samples t-tests showing significant mean differences between all adjacent phases (p < 0.05 in all cases) are reported as a descriptive diagnostic consistent with this segmentation, rather than as independent confirmation of the BIC-based selection, since these tests compare means of segments constructed specifically to separate them. Breakpoints indicate the last observation of each regime; phases begin in the quarter immediately following each breakpoint (e.g., Phase 3 begins in 2014Q4, the quarter following the second breakpoint at 2014Q3).

Following a transitory stability peak in Phase 2, the remaining phases show a consistent and progressive decline in mean Z″-Score values, as detailed in Table 7.

Collectively, this evidence shows that the Z″-Score not only captures contemporary levels of financial fragility but also allows for the identification of structurally differentiated regimes of cumulative deterioration.

3.5 Ex post contrast with the ordinary insolvency proceeding of 2025

Finally, this section contrasts the estimated trajectory of the Altman Z″-Score with the formal institutional event observed in February 2025, when Telefónica del Perú submitted a request to enter the PCO before Indecopi.

The results show that the firm exhibited persistent signals of financial distress from mid-2015 onwards, prior to the filing of the insolvency restructuring request. This ex post temporal consistency between the indicator’s trajectory and the eventual insolvency proceeding illustrates the monitoring potential of the Z″-Score for prolonged processes of corporate fragility.

It should be noted that the denomination Integratel Perú S. A. A. corresponds to a corporate stage subsequent to the initiation of the insolvency proceeding. Therefore, the 2011–2024 series must be interpreted under the economic and financial continuity of Telefónica del Perú, avoiding retrospective relabeling.

Accordingly, the findings suggest consistency with the hypothesis that the insolvency outcome observed in 2025 was preceded by a prolonged and financially identifiable deterioration.

4 Discussion

4.1 Financial distress as a dynamic process: longitudinal evidence from the Z″-score

The results obtained confirm that the financial distress of Telefónica del Perú does not manifest as a discrete event, but rather as a gradual process observable in the quarterly trajectory of the Altman Z″-Score. This evidence is consistent with the classic argument that accounting indicators can function as early signals of corporate deterioration, several years before institutional episodes of insolvency or formal restructuring materialize.

Indeed, the approach pioneered by (10)—who examined financial ratios over a five-year window preceding failure, demonstrating their predictive capacity—was subsequently consolidated by (11, 12) through a multivariate index capable of simultaneously capturing liquidity, profitability, and leverage. The present study extends this horizon substantially: distress signals were observable from 2015Q2, nearly a decade before the filing of the insolvency restructuring request in February 2025—suggesting that longitudinal, regime-based monitoring can capture deterioration trajectories beyond those identified in the original early warning literature. The resulting Z″-Score levels and distress-zone classifications are specific to the market-value specification adopted as primary in this study, as detailed in Section 4.4. Consequently, the systematic decline in the Z″-Score observed in this study is consistent with the original function of the model: to identify trajectories of fragility prior to bankruptcy or severe distress.

Recent evidence also supports the usefulness of the Z″-Score as an early warning tool in diverse sectors—including regulated industries and telecommunications—confirming that deterioration often takes persistent and structural forms, not merely transitory ones (21, 23). In the Latin American telecommunications context specifically, Santana Sediyama et al. (6) documented anticipatory distress signals in Grupo OI (Brazil) up to four years before its 2016 insolvency proceeding, using an accounting-based prediction model—a finding consistent with the gradual nature of financial deterioration identified in the present study, though over a substantially longer horizon. More broadly, recent empirical evidence confirms that financial distress risk constitutes a persistent and measurable dimension of corporate vulnerability across international markets and different firm life cycles (29).

4.2 Identification of structural regimes in the Altman Z″-score trajectory

The Altman Z″-Score is widely used as a quantitative indicator of the level of financial distress based on accounting ratios. In many empirical applications, its interpretation is based on observed values in specific periods, allowing for the classification of a firm’s degree of financial fragility at a given point in time (2, 20).

However, when extensive time series are available, it is relevant to assess whether the evolution of the indicator responds to stable behavior or whether it exhibits structural changes in its dynamics. In this study, using quarterly data for the period 2011Q1–2024Q4, the existence of statistical transitions in the mean level of the Z″-Score was explicitly examined.

For this purpose, a Binary Segmentation algorithm with a least squares cost function (32) was applied, within the structural break detection framework of (31). This approach allows for the estimation of multiple change points without imposing predetermined dates, delimiting differentiated regimes within the trajectory of the indicator.

The results identified five endogenous breakpoints, located at 2013Q2, 2014Q3, 2018Q2, 2020Q4, and 2022Q1. These breakpoints delimit six structurally differentiated phases in the evolution of financial distress, suggesting that the deterioration of Telefónica del Perú did not follow a uniform pattern throughout the analysis period, but rather was organized into temporally differentiated regimes of increasing fragility—consistent with independent-samples t-tests confirming statistically significant mean differences between all adjacent phases (p < 0.05 in all cases), reported as a supporting descriptive diagnostic in Section 2.6.

Figure 4 presents the complete Z″-Score trajectory visually incorporating the estimated breaks, while Table 7 summarizes the descriptive statistics corresponding to each identified regime. From a time series analysis perspective, the identification of these regime transitions demonstrates that the Z″-Score exhibits the non-stationary dynamics characteristic of financial indicators subject to structural change, supporting the methodological rationale for combining accounting-based scoring models with change-point detection algorithms.

4.3 Quantitative evidence of differentiated regimes of financial deterioration

A central element of the evidence obtained is that the trajectory of the Altman Z″-Score can be decomposed into structurally differentiated phases, which reflect a progressive and persistent displacement toward conditions of severe financial distress. In this regard, the descriptive statistics estimated within each subsample delimited by the structural breaks allow the magnitude of deterioration across regimes to be quantified, offering a richer dynamic interpretation than the static classification based solely on point-in-time values of the indicator.

As summarized in Table 7, the six identified regimes reflect a phase of moderate vulnerability (Phase 1), followed by a transitory stability peak in Phase 2 (2013Q3–2014Q3), which registers the highest mean Z″-Score of the entire series (2.42). After this peak, the trajectory shifted decisively and irreversibly toward distress, with mean Z″-Score values declining to −2.52 in Phase 6—a deterioration trajectory spanning nearly 14 years of continuous and progressive financial fragility from that point onward.

This staggered pattern is consistent with international evidence documenting that the Z″-Score tends to deteriorate gradually prior to episodes of insolvency or institutional restructuring, particularly in capital-intensive and highly regulated industries such as the telecommunications sector. Applied studies in comparable contexts have shown convergent dynamics, in which deterioration consolidates in stages before reaching critical levels (22, 23).

Likewise, recent research underscores that one of the main strengths of the Altman model lies in its ability to capture prolonged processes of financial weakening, functioning as an early warning system even outside the original industrial context for which it was designed (24, 25). The identification of differentiated regimes provides additional evidence that corporate distress can be understood not as a uniform linear phenomenon, but as a sequence of structural phases of cumulative fragility, empirically observable in high-frequency series.

Decomposing the Z″-Score into its four underlying components (X1, working capital to total assets; X2, retained earnings to total assets; X3, EBIT to total assets; and X4, market value of equity to total liabilities) clarifies the specific financial mechanisms driving each transition. The improvement observed in Phase 2 was driven predominantly by X4, which rose sharply while the accounting components (X1, X2, and X3) remained comparatively stable—consistent with the market-based, rather than fundamentals-based, nature of this transitory peak. The subsequent decline into Phase 3 was dominated by a sharp reversal in X4, alongside a deterioration in X1, marking the onset of the sustained downward trajectory. From Phase 4 onward, the deterioration became increasingly rooted in accounting fundamentals rather than market valuation: X2 declined markedly across Phases 4 and 5, reflecting eroding cumulative profitability, while X1 recorded its steepest deterioration in the transition to Phase 6, consistent with a terminal collapse in liquidity. This component-level pattern indicates a shift over time from a market-driven signal in the early phases to a fundamentally-driven deterioration in the later phases, reinforcing the decomposition evidence presented in Section 3.3 and Figure 3.

4.4 Limitations

This study presents three main limitations that should be considered when interpreting its findings. First, the analysis is based on a single case study—Telefónica del Perú S. A. A.—which limits the direct statistical generalization of results to other firms in the telecommunications sector or to different institutional contexts. The absence of a formal control group of non-distressed comparable firms represents a recognized limitation of the present design. A sustained distress signal spanning approximately forty consecutive quarters does not, by itself, discriminate between a firm that will ultimately enter formal insolvency and one that will remain in prolonged distress without doing so; the present study cannot quantify this discriminatory cost, as doing so would require a comparative sample of firms exhibiting similarly extended distress trajectories with divergent outcomes. The Z″-Score trajectories reported in prior studies of comparable capital-intensive firms (21–25) were not designed as a control group and do not provide a basis for estimating this cost. This limitation notwithstanding, the single-case design reflects a deliberate selection criterion grounded in established case study methodology (39, 40): the firm constitutes a critical case (40) selected not for statistical inference but for its unique combination of empirical properties—56 consecutive quarters of audited public data, a formally documented insolvency event serving as an observable ex post validation benchmark, and structural conditions—high capital intensity, emerging market regulatory environment, and accounting-based distress signals observable prior to the formal insolvency event—shared with comparable Latin American telecommunications operators (5–8). As Flyvbjerg (40) has demonstrated, one can generalize on the basis of a single critical case when the case is chosen for its strategic properties rather than its statistical representativeness. In this sense, the analytical objective is not to generalize statistical parameters across a population, but to demonstrate the internal validity and procedural replicability of the proposed framework (39). Second, the structural breaks identified using the Binary Segmentation algorithm (32) represent statistical transitions in the mean behavior of the series and should not be interpreted as causal events driving financial deterioration, but rather as delimiters of structurally differentiated regimes whose analytical value lies in characterizing the temporal dynamics of distress, not in explaining the mechanisms that generate it. Third, the use of market value of equity in X4—rather than book value, as originally specified in the Z″-Score calibration (13, 19)—constitutes a methodological adaptation common in the applied literature but not formally justified therein (16, 21, 25, 36). A sensitivity analysis using book value of equity in X4 is reported in Figure 1. While the timing of the five structural breakpoints is identical under both specifications—confirming that the regime transitions identified in this study are not an artifact of the X4 specification—the absolute Z″-Score levels differ substantially between the two, which in turn shifts the corresponding distress-zone classification for several quarters. Readers comparing these results with studies applying the original book-value formulation should therefore interpret the absolute Z″-Score values with this distinction in mind, while noting that the timing and structure of the identified regimes remain unaffected. These thresholds are retained without modification to preserve comparability with the broader Z″-Score literature and across the two specifications compared in this study, rather than representing thresholds independently re-validated for the market-value adaptation; the resulting zone classifications (distress, grey, and safe zones) should accordingly be understood as descriptive rather than as formally validated categorizations for this specification.

4.5 Comparison with the literature: generalizability, sectoral validity, and known limitations

While multiple studies have documented the predictive capacity of the Altman model in specific sectors, it is also recognized that its performance may vary according to institutional context, market structure, and estimation period.

For example, (26, 27) caution that classical models may face classification errors when transferred across decades or jurisdictions, which requires interpretive caution and contextual adjustments. However, recent research in emerging markets has shown that, despite these limitations, the Z″-Score remains a widely used and empirically informative tool when applied as a dynamic indicator rather than as a rigid threshold (18, 19). Consistently, (41) confirm that the financial ratios embedded in the Altman Z″-Score—particularly profitability and solvency indicators—retain significant predictive content for 500 listed Vietnamese firms over a ten-year panel (2012–2021), even when static threshold-based classification shows context-dependent limitations. This is precisely the condition that motivates the longitudinal regime-detection approach adopted in the present study.

This study also contributes methodologically to the applied literature on the Z″-Score: while some studies apply market value of equity in X4 for publicly listed firms (16, 21, 25, 36), none explicitly test whether this specification choice affects the resulting distress classification or regime detection outcomes. By systematically comparing both specifications (Figure 1) and demonstrating that the identified structural breakpoints are robust to this choice, the present study provides methodological evidence supporting the reliability of change-point detection frameworks applied to accounting-based distress indicators, regardless of the specific equity valuation used.

Beyond this methodological contribution, the present study also advances the substantive literature by showing that, in a Peruvian case from the telecommunications sector, the Z″-Score not only maintains descriptive capacity but also reveals differentiated structural phases that are temporally consistent with subsequent institutional deterioration—extending prior evidence from comparable Latin American telecommunications cases (6) through a substantially longer anticipation horizon and a more rigorous structural break detection framework.

More broadly, these findings contribute to the applied mathematical finance literature on structural change detection by demonstrating that accounting-based financial indicators, when treated as time series subject to formal change-point analysis rather than as discrete cross-sectional ratios, can reveal structurally distinct regimes of deterioration that static, single-period assessment would not detect. This extends the applicability of structural break methodologies—predominantly developed for macroeconomic and market-based series—to firm-level, accounting-derived indicators, framing financial-statement information not merely as input to static classification but as the basis for a continuous, mathematically formalized monitoring process capable of tracking how a firm’s financial condition evolves across regimes over multi-year horizons.

4.6 Ex post implication regarding the 2025 insolvency event: temporal consistency of diagnosis without causal inference

As documented in Sections 3.4 and 3.5, the trajectory of the Altman Z″-Score is consistent with the interpretation that the financial deterioration of Telefónica del Perú did not reflect a transitory episode, but rather a prolonged and cumulative process of structural fragility organized across six structurally differentiated regimes (delimited by breakpoints at 2013Q2, 2014Q3, 2018Q2, 2020Q4, and 2022Q1). The formal insolvency recognition in 2025 should therefore be interpreted as the institutional outcome of this multi-phase deterioration process, rather than as the consequence of an isolated shock in the immediately preceding years. In this regard, the behavior of the Altman Z″-Score is consistent with its original purpose as an early warning system based on accounting ratios, particularly relevant for firms undergoing extended processes of financial weakening (2, 12).

Nevertheless, it is essential to emphasize that the structural breaks estimated through the Binary Segmentation algorithm represent statistical transitions in the mean behavior of the series, and do not constitute evidence of direct causal relationships with respect to the insolvency event. Their analytical value lies in demonstrating that financial distress can be organized into structurally distinguishable and quantifiable regimes, reinforcing the temporal consistency of the diagnosis, without attributing ex post causal relationships.

Consequently, the contrast between the identified regimes and the 2025 insolvency event should be understood as an ex post empirical validation of the Z″-Score’s ability to capture persistent trajectories of cumulative fragility prior to their institutional formalization, without mechanically attributing the structural breaks as triggers of the insolvency proceeding.

4.7 Contributions and academic projection

The integration of the Altman Z″-Score indicator with Binary Segmentation change-point detection (32), following the methodological framework of (31), provides an analytical framework for examining financial distress as a dynamic process characterized by regime changes. This approach expands the traditional interpretation of the Altman model (11, 12), based mainly on the static classification of firms, enabling the analysis of persistent financial deterioration trajectories in emerging market contexts. Furthermore, the progressive transfer of control from shareholders to creditors is broadly consistent with agency theory arguments concerning conflicts of interest in highly leveraged firms (9), wherein the deterioration of financial indicators such as the Z″-Score generates escalating agency costs between equity and debt holders.

5 Conclusion

The findings provide direct answers to the four research questions posed in the introduction. First, Binary Segmentation change-point detection methods (32) effectively segmented the Z″-Score time series into six regimes internally homogeneous in mean level—delimited by five endogenous breakpoints at 2013Q2, 2014Q3, 2018Q2, 2020Q4, and 2022Q1, selected via the Bayesian Information Criterion (BIC = −34.828 at k = 5), with independent-samples t-tests providing a supporting descriptive diagnostic (p < 0.05 in all adjacent phase comparisons)—providing a structured quantitative basis for the longitudinal monitoring of structural financial deterioration. Second, the integration of structural break techniques with the Altman Z″-Score substantially enriched the dynamic interpretation of the indicator, enabling the identification of regime transitions that static cross-sectional approaches cannot capture. Third, the financial deterioration of Telefónica del Perú was identifiable several years before the formal insolvency proceedings, with persistent insolvency risk signals observable from the second quarter of 2015—illustrating the Z″-Score’s monitoring potential as an ex post consistent corporate risk indicator. The resulting Z″-Score levels and distress-zone classifications are specific to the market-value specification adopted as primary in this study. Fourth, the Altman Z″-Score showed longitudinal coherence in capturing the prolonged trajectory of financial fragility in a capital-intensive and highly regulated service firm across 56 consecutive quarterly observations, suggesting its methodological relevance in emerging market contexts beyond the manufacturing settings for which it was originally designed.

The findings show that the trajectory of the Z″-Score can be decomposed into six structurally differentiated phases, delimited by the five identified breakpoints. The six phases reflect a systematic and progressive displacement from moderate vulnerability (Phase 1) through a transitory stability peak (Phase 2), distress transition (Phase 3), structural distress onset (Phase 4), accelerated deterioration (Phase 5), to severe terminal distress (Phase 6), as detailed in Table 7. Taken together, this sequence confirms that corporate insolvency risk did not reflect a transitory episode but rather a cumulative risk accumulation process observable prior to the filing of the insolvency restructuring request in February 2025—a finding with direct relevance for financial risk management and early warning system design.

From a financial risk management standpoint, the findings carry relevant implications for different actors within the financial system. For credit analysts, risk managers, and financial institutions, the study demonstrates that simple accounting-based indicators such as the Z″-Score can register persistent distress signals substantially before formal insolvency events—in this case, nearly a decade prior to the PCO filing, a horizon considerably longer than those typically examined in the retrospective early warning literature (10)—without requiring complex models or high-frequency data, making it a cost-effective tool for corporate credit risk monitoring. Practitioners applying this approach should note that specific Z″-Score levels and distress-zone classifications depend on whether market or book value of equity is used in X4. For regulators and supervisory bodies, the evidence suggests that longitudinal monitoring of the Z″-Score in capital-intensive service firms represents a potential complementary monitoring indicator for the supervision of systemic financial risk in strategic sectors. For bondholders, creditors, suppliers, pension funds, and other stakeholders, the results demonstrate that persistent signals of financial deterioration were identifiable in the accounting record long before the company’s formal acknowledgment of its inability to service financial obligations (1), reinforcing the utility of integrating longitudinal distress indicators into credit evaluation and investment risk management in emerging markets. This finding is broadly consistent with agency theory arguments (9): the progressive deterioration of the Z″-Score documented in this study reflects the type of escalating agency costs between shareholders and debt holders that creditors and bondholders should monitor in highly leveraged firms.

Finally, the results open avenues for future research. First, replicating the analysis across other Latin American telecommunications firms would allow for an evaluation of the generalizability of the findings beyond the single case studied. Second, extending the component-level decomposition presented in this study (Section 4.3) to additional cases would allow for comparative analysis of which specific financial dimensions—liquidity, profitability, leverage, or market value—drive each regime transition across different firms and sectors. Third, incorporating macroeconomic variables—such as exchange rates, inflation, or regulatory changes—as covariates in the structural analysis could help clarify the external mechanisms underlying the identified transitions. Finally, extending the methodological framework to other capital-intensive and highly regulated sectors in emerging markets—such as utilities, mining, or aviation—would allow for an evaluation of the replicability of the proposed analytical framework in comparable institutional contexts, and could contribute to the development of sector-specific insolvency risk monitoring systems for regulatory and credit risk management purposes.

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Footnotes

Edited by: Svetlozar Rachev, Texas Tech University, United States

Reviewed by: Lersak Phothong, Mahasarakham University, Thailand

Luis David Lara Rodríguez, Universidad Popular Autónoma del Estado de Puebla, Mexico

Nela Safelia, Jambi University, Indonesia