Googling and ARMS sentiment across economic phases and horizons: insights into Brazilian crises Open Access

Financial globalization and liberalization in recent decades have significantly increased the integration of global stock markets. While this interconnectedness has attracted substantial foreign investment, it has also exposed national economies, especially those of emerging markets, to greater vulnerability from global shocks. These dynamics have contributed to amplified price volatility and an increase in the frequency and severity of financial crises, often exacerbated by institutional and structural weaknesses inherent in less developed economies.

Thus, understanding the causes and mechanisms of financial crises is a critical challenge. Two main theoretical frameworks have emerged to explain the crisis dynamics. The fundamentalist approach emphasizes the role of macroeconomic and financial indicators in determining asset prices, whereas behavioral finance highlights how cognitive biases, investor sentiment, and irrational behavior can lead to market inefficiencies and dislocations.

Most existing studies have emphasized fundamental determinants such as stock market performance (Mishkin & White, 2002; Bai, Qin, & Zhang, 2021), liquidity (Næs et al., 2011; Brito, 2024), and volatility (Aggarwal, Inclan, & Leal, 1999; Ben Yaala & Henchiri, 2025). In parallel, a growing body of literature has investigated investor sentiment as a behavioral driver of market dislocations (Zouaoui, Nouyrigat, & Beer, 2011). Recent findings underscore this role: optimism measured via Google Trends and Twitter has predicted speculative bubbles (Carosia, da Silva, & Coelho, 2025); pessimism, combined with low liquidity, has heightened crash risk (Nguyen & Nguyen, 2024a, b); machine learning models identify negative sentiment as a robust crisis predictor (Karasan, Alp, & Weber, 2025); and sentiment contagion has been shown to elevate systemic risk (Cao, He, & Jiao, 2025). These insights align with earlier theoretical work suggesting that investors may form stochastic, biased beliefs, leading prices to deviate from their fundamentals (De Long et al., 1990; Kumar & Lee, 2006; Lee et al., 1991).

Investor sentiment is also closely intertwined with market cycles; optimism generally dominates during expansions, while pessimism increases during contractions. These shifts manifest across different investment horizons (short-, medium-, and long-term) (Forero-Laverde, 2018). Despite these advances, there are several gaps in the literature. First, much of the research has concentrated on developed markets, leaving emerging economies—particularly Latin America—understudied. Second, few analyses have systematically investigated how investor sentiment interacts with market cycles across different investment horizons. Third, studies tend to focus on either direct sentiment indicators (e.g. search engine data) or indirect proxies (e.g. market-based indices) without integrating both within a unified framework.

Brazil provides an ideal context for addressing these gaps. As Latin America’s largest economy, Brazil faces complex challenges from global shocks (such as the 2008 financial crisis and COVID-19 pandemic) and domestic instability, including political uncertainty and fiscal imbalances. The increase in retail investor participation and digital engagement further amplifies the role of sentiment in market dynamics.

This study aims to bridge these gaps by examining the determinants of the financial crises in Brazil. It investigates how market returns, liquidity, and volatility, combined with both optimistic and pessimistic investor sentiment, influence crisis probability across expansion and contraction phases. Integrating direct sentiment indicators (Google Trends) and indirect proxies (ARMS Index) provides a comprehensive view of the behavioral and fundamental forces driving the crisis dynamics.

This study makes several important contributions to the existing literature. Theoretically, it bridges behavioral finance, sentiment analysis, and macroeconomic indicators to deepen our understanding of financial crises. Methodologically, it innovatively compares direct sentiment indicators (e.g. Google Trends) with indirect proxies (e.g. the ARMS Index), employing a probit model that incorporates market cyclical phases through the local bull-bear indicator (Forero-Laverde, 2018). Practically, this study provides effective tools for timely risk assessment and early crisis detection, enabling market participants to respond proactively to emerging threats. Socially, this study aims to enhance financial stability by providing actionable insights for policymakers and investors. Specifically, it offers policymakers an empirical basis for integrating behavioral indicators into macroprudential frameworks, enabling improved surveillance, greater market transparency, and more responsive tools to manage systemic risk.

The remainder of this paper is structured as follows. Section 2 reviews the literature, Section 3 outlines the methodology, and Section 4 describes the data. Section 5 presents the results and analysis. Section 6 discusses the findings and concludes the study.

Previous studies have extensively examined fundamental factors such as stock market performance, volatility, and liquidity as crisis indicators. More recently, investor sentiment has emerged as a critical behavioral factor that influences financial markets.

A significant body of research links stock market performance to the onset of crises, in particular, declining stock returns. For instance, Mishkin & White (2002) argue that a sharp decline in stock prices, often around 20%, can signal an impending crisis, a finding based on events such as the stock market crashes of 1929 and October 1987. Similarly, Patel & Sarkar (1998) characterize a crisis as a substantial drop in share prices relative to the historical peaks.

Expanding on this, Zouaoui et al. (2011) empirically demonstrate that year-on-year stock market performance is negatively correlated with crisis risk in stock markets across 15 European countries and the United States. Their findings suggest that higher returns from the previous year reduce the probability of crises because strong performance typically reflects market stability.

More recently, Bai et al. (2021) examined stock price crashes in emerging markets and identified both firm- and market-level factors that contribute to sudden declines in stock prices. Their study highlights the vulnerability of markets such as Brazil, India, and Indonesia to crash risks, and underscores the importance of market dynamics in shaping these outcomes.

Given the consensus in the literature, we propose the following hypothesis for the Brazilian market.

Empirical evidence strongly links stock market crashes to heightened volatility. For instance, Fang (2001), using the daily closing prices of all companies listed on the Taiwan Stock Exchange between January 1995 and December 1998 and employing Autoregressive Conditional Heteroskedasticity (order 3) with conditional variance in the mean equation model (ARCH(3)-M), observed a marked increase in stock return volatility during the 1997–1998 Asian financial crisis. This period of heightened volatility coincides with a significant decline in stock performance.

Choudhry (1996) used Generalized Autoregressive Conditional Heteroskedasticity with conditional variance in the mean equation model (GARCH-M) on monthly data (1976–1994) from six emerging markets and found that volatility shifted before and after the 1987 crash, with variations across markets influenced by various factors.

Similarly, Aggarwal et al. (1999) compare volatility across emerging and developed stock markets during the 1987 crash. Their findings showed that both the decline in stock prices and the surge in volatility were more pronounced in emerging markets than in developed markets.

Ben Yaala and Henchiri (2025b) extended this line of inquiry by investigating the Tunisian market. Their results showed that explosive speculative bubbles are closely associated with sharp increases in volatility, reinforcing the argument that volatility is a defining feature of unstable and crisis-prone financial environments.

Recent contributions have further underscored the relevance of volatility in crisis prediction using advanced modeling techniques. Rodriguez-Nieto and Mollick (2021) examined the United States financial crisis and its spillover effects on stock returns, market volatility, and credit risk across the Americas. Their findings emphasize the interconnectedness of volatility dynamics and crisis transmission in both developed and Latin American economies. Similarly, Tabash, Chalissery, Nishad, and Al-Absy (2024) investigate the impact of market shocks on stock volatility in both emerging and developed markets, confirming that volatility intensifies significantly during turbulent periods and is a critical variable for monitoring systemic risk.

Based on these observations, we propose the following hypothesis:

Market liquidity is a pivotal concern for investors as it directly influences portfolio performance (Amihud, 2002; Amihud & Mendelson, 1986). An illiquid asset typically incurs higher transaction costs, which can significantly increase the risk of substantial loss. Several studies explore the dynamics of market liquidity during crisis periods, revealing its crucial role in market stability.

Amihud, Mendelson, and Wood (1990) were among the pioneers identifying market liquidity as a contributing factor to market downturns. They argue that the stock market crash of 1987 was partly driven by a widespread decline in investors’ expectations regarding liquidity conditions. Similarly, Rösch & Kaserer (2014) enhance our understanding of market liquidity behavior during periods of financial distress by analyzing a sample of German companies. Their findings indicate that liquidity deteriorated during the global financial crisis, highlighting a strong correlation between market risk and liquidity levels.

Moreover, Christoffersen et al. (2016) emphasize the significance of market trading frictions in shaping index return patterns, suggesting that fluctuations in perceived crash risk are closely linked to investors’ fears regarding market illiquidity.

Recent evidence confirms these dynamics across diverse markets. Nguyen and Nguyen (2024a, b) find that low liquidity significantly raises stock price crash risk in Vietnamese firms, especially those with concentrated ownership. Similarly, Brito (2024) observed that the Covid-19 pandemic intensified return instability and liquidity constraints in Brazil, illustrating how liquidity shortages can exacerbate crisis effects in emerging markets.

Given these insights, we hypothesize that:

From a behavioral finance perspective, uninformed investors—or “noise traders”—can drive asset prices away from fundamental values due to irrational beliefs and emotions. Early work by De Long and Shleifer (1991) argued that overly optimistic sentiment contributed to overvaluation ahead of the 1929 crash. Zouaoui et al. (2011) found that rising investor optimism in Europe increased the probability of a crisis, while Pan (2020) showed that optimism heightens both the likelihood and severity of market bubbles. Carosia et al. (2025) used a deep learning model that leveraged sentiment signals from Twitter, Google Trends, and financial news in Brazil and concluded that optimism plays a key role in bubble formation. In the Middle East and North Africa (MENA) region, Ben Yaala and Henchiri (2024) applied a Nonlinear AutoRegressive model with exogenous inputs (NARX), demonstrating that both excessive optimism and pessimism can predict crashes.

Wu, Cai, and Zhang (2021) observed that pessimistic sentiment increases crash risk in China, while Alnafea & Chebbi (2021), using survey data from Saudi Arabia, showed that strong negative investor emotions promote managerial opacity, thereby heightening crash likelihood. Nguyen and Nguyen (2024a, b) employed text mining on financial media in the Asia-Pacific markets and confirmed the crash-predictive power of negative sentiment. Karasan et al. (2025) applied machine learning models, specifically eXtreme Gradient Boosting (XGBoost) and Long Short-Term Memory (LSTM) networks, to narrative sentiment data, finding that pessimistic signals are robust predictors of crash events. Similarly, Cao et al. (2025) develop a sentiment connectedness index to show how negative sentiment propagates across markets, amplifying systemic risk. Teng et al. (2022) proposed a heliobiological sentiment approach that links biologically driven mood shifts to an increased crash frequency. Carosia et al. (2025) also reported that, in Latin America, pessimistic sentiment extracted from online data was more predictive of crashes than optimism.

Finally, Daniel et al. (1998) and Veronesi (1999) link investor sentiment to market overreactions, with sentiment influencing asset overvaluation during booms and undervaluation during busts. Lu & Lai (2012) further found that sentiment varies by market phase: optimism tends to increase market participation in expansions, whereas pessimism reduces it during contractions.

Based on this, two hypotheses are proposed:

Although global research has linked investor sentiment, market fundamentals, and financial crises, Brazil’s stock market has unique traits that justify its focus. As Latin America’s largest economy, Brazil is highly exposed to global commodity cycles, political instability, and macroeconomic volatility, creating conditions distinct from other emerging and developed markets (Grigoryev & Starodubtseva, 2021). Domestic shocks, such as the 2014–2016 recession, Dilma Rousseff’s impeachment, and the COVID-19 pandemic, have further shaped investor behavior in ways that are not fully captured by global models.

Moreover, Brazil’s growing retail investor base and media-driven sentiment amplify behavioral effects, increasing vulnerability to liquidity shocks and speculative bubbles (Carosia et al., 2025; Brito, 2024). Despite this, empirical studies on investor sentiment in Brazil, especially those combining direct and indirect measures across cycles and horizons using probit models, are limited. This study fills this gap by examining investor sentiment in Brazil using comprehensive sentiment measures and probit models to predict crises.

This section outlines the selected model, provides a detailed description of the variables, and explains the methods used for crisis detection and for dating the Expansion and Contraction phases across the three time horizons. The model specifications adopted for the analysis were also presented.

To explain the risk of crisis occurrence, we select a limited dependent regression model (specifically, a probit model). The Probit model links a qualitative endogenous variable (crisis or calm period) to a set of exogenous variables:

Formally, the probit model is as follows:

With:

F: Cumulative distribution function of the standard normal distribution

X_i: Vector of exogenous variables

After presenting the general framework of the model, we describe all variables included in the analysis.

The CRISIS variable is a binary variable that appears as an endogenous variable in the model. It has the following two values.

The explanatory variables of the model include fundamental variables, namely stock market returns, liquidity, and volatility, as well as behavioral variables, such as investor optimism and pessimism.

To capture price acceleration, we included a representative measure of the Brazilian stock market’s year-on-year performance in the model. This is calculated as the logarithm of the ratio of the closing price at time t divided by the closing price at time t – n.

With:

R_t: The return of the index on day (t).

P_t: The price of the index on day (t).

P_t−n: Price of index on day (t−n).

n: A stock market year

We focus on market depth measured using Amihud’s (2002) illiquidity ratio, which captures the price impact of trading volume. This ratio is calculated by dividing the absolute daily return of the index by its daily trading volume. To address fluctuations in the illiquidity series, we apply the natural logarithm of this measure following Hadhri and Ftiti (2019). A higher ratio indicates higher market liquidity.

With:

R_t: Daily index return calculated as the logarithm of the closing price on day t divided by the closing price on day t–1.

V_t: Trading volume on day t.

To calculate the volatility of the returns, we use the Generalized Autoregressive Conditional Heteroskedasticity ((GARCH) (1,1)) model developed by Bollerslev (1986). The GARCH (1,1) process can be expressed as follows:

With:

$σt2$⁠: Conditional variance of returns.

εt∶ Residuals

ω, α, and β: Parameters satisfying ω > 0, α ≥ 0, β ≥ 0, and α+ β < 1 for covariance stationarity.

Before the estimation, we ensured that the data satisfied the necessary assumptions for GARCH modeling:

1. Stationarity of the return series:

We conducted an Augmented Dickey-Fuller (ADF) test under three specifications: with intercept, with trend and intercept, and without intercept. In all cases, the null hypothesis of a unit root is rejected at the 1% significance level, confirming that the return series is stationary.

1. Existence of conditional heteroskedasticity:

To detect volatility clustering, we apply the ARCH LM test (lag = 1) to the residuals from the mean equation. The results show a significant ARCH effect, confirming time-varying variance and supporting the use of GARCH modeling.

1. Covariance stationarity of the GARCH(1,1) process:

The estimated GARCH(1,1) parameters were: ω = 0.011379, α = 0.072737 and β = 0.808777

All the coefficients are positive and statistically significant. Additionally, the sum α+β = 0.881514 < 1 confirms that the conditional variance process is covariance stationary.

The results are summarized in Table 1.

To measure optimistic and pessimistic investor sentiment, we use two different measures: an indirect measure (ARMS index) and a direct measure derived from Google Trends.

To measure investor sentiment, we select the ARMS index, a market performance measure based on the ratio of advancing/declining stocks and their associated volumes. The ARMS index was calculated using the following formula:

Indeed, when the trading volume of advancing securities increases, the ARMS index falls below one, indicating optimistic investor sentiment. Conversely, when the trading volume of declining securities increases, the ARMS index rises above 1, reflecting pessimistic investor sentiments.

The second measure of optimistic and pessimistic investor sentiment is derived from Google Trends search volumes, normalized between 0 and 100. Twenty positive and 20 negative economic-related terms from the Harvard IV-4 and Lasswell dictionaries were analyzed. The positive words include profit, beneficiary, euphoria, purchase, gain, wealth, savings, profitability, productivity, gain, worth, buyout, success, contribute, increase, entrepreneur, subsidy, and benefit. Negative words included crisis, depression, recession, decline, loss, bankruptcy, unemployment, poverty, deficit, liquidation, depreciation, debtor, inflation, default, cost, expensive, fall, costly, expense, and tough.

To ensure the accuracy and contextual relevance of this sentiment measure, all Google Trends terms were filtered to reflect search activities that originated specifically from Brazil. This location-based filtering ensures that the sentiment index captures domestic investor sentiment rather than global search patterns.

Only economy-related studies were considered. Following Da, Engelberg, and Gao (2011), seasonal effects were removed via regression and standardized residuals were obtained. Twenty terms (10 positive and 10 negative) most correlated with crises were selected. Finally, principal component analysis was applied to construct the sentiment indices (Da, Engelberg, & Gao, 2015; Petit et al., 2019).

In this study, we identify stock market crashes in Brazil using the CMAX method (Patel & Sarkar, 1998), which captures deviations from historical peaks. This approach offers several advantages: it is objective, transparent, and replicable; it effectively captures investor panic through sharp price declines; and it precisely identifies the start, trough, and recovery dates of crises, allowing for a complete and consistent timeline. CMAX also supports cross-market comparisons through statistical thresholds (e.g. 1.5 standard deviations below the average).

Alternative methods, such as the 20% peak-to-trough rule (Mishkin & White, 2002), GARCH-based volatility spikes, maximum drawdown measures, and market stress indices (Bekaert, Hoerova, & Duca, 2013) —are valid, but less suited for sentiment-focused analysis. Given its strengths, CMAX is particularly appropriate for our study.

The CMAX indicator is defined as:

With: P_it is the stock market index at time t.

A stock market crisis is identified when the CMAX value for country i at time t falls below the average CMAX for that country minus 1.5 standard deviations, which serves as the threshold level.

The indicator representing the stock market crisis in country i at time t, Ci,t, is as follows:

Following Ben Yaala and Henchiri (2023, 2025a), we define the key crisis dimensions as follows:

1. The beginning of the crisis (peak) was the day on which the index reached its highest point before exceeding the critical level.

2. The trough date is when the index hits its lowest point during the crisis.

3. The recovery date is when the index regains its pre-crisis maximum.

4. Crisis duration is the time between the crisis start and the recovery.

5. The magnitude represents the maximum loss observed, calculated as the percentage change in the index between the peak and trough.

The methodology for dating the expansion and contraction phases of stock markets, as proposed by Forero-Laverde (2018), involves three indicators representing different time horizons: short-term (1–30 days), medium-term (2–6 months), and long-term (7–12 months). These indicators are based on index returns, calculated as follows:

With:

P_t: index closing price on date t

P_t-n: index closing price on date t−n.

N: the different time horizons over which returns are calculated.

Forero-Laverde (2018) suggested that each return series should account for both its mean and volatility. Therefore, the standardized return series is obtained using the following equation:

With:

µ: Average on date t corresponding to each return series, r_n

σ_t,n: standard deviation at date t corresponding to each return series r_n

The temporal variability of the average was obtained using an exponentially weighted moving average equation.

In our case, we assumed a time window of 40 observations.

To compute the moving average for the fortieth day, observations from days 1 to 40 were used. Shifting the window forward by one day, observations from days 2 to 41 yielded average for day 41. This process was continued until final observation. Notably, this measure assigns greater weight to recent data.

Regarding the dispersion measure, Forero-Laverde (2018) used the conditional standard deviation obtained from the GARCH(1,1) model, as follows:

With:

h_t: Conditional standard deviation

δ: A strictly positive parameter.

α and β: Positive parameters and their sums must be strictly less than one.

Having calculated the 20 standardized yield series, we now need to construct three matrices:

D(short): composed of 5 five vectors of standardized yield d_t,n, where N = 1, 5, 10, 15, and 20.

D(medium) is composed of five standardized yield vectors d_t,n, where N = 40, 60, 80, 100, and 120.

D(long): composed of six standardized yield vectors d_t,n, where N = 140, 160, 180, 200, 220, and 240.

Generally speaking, the local bull-bear indicator (LBBI) is defined as follows:

With:

where ω represents the weight vector.

The weight vector was obtained using factor analysis proposed by Tsay (2005).

Admittedly, factor analysis, a purely statistical technique, aims to reduce the dimensions of large datasets. Therefore, it must be applied to each of the already composed matrices.

The output weights of the factor analysis are called “Factor Loadings.” They are resized so that their sums are equal to unity.

Finally, the local bull-bear indicator for the three time horizons takes the following form.

The beginning and end dates of the Expansion and Contraction phases were defined based on the LBBI as follows:

1. The Expansion phase begins when LBBI exceeds 0.5 standard deviations and ends when it falls below −0.5 standard deviations.

2. The Contraction phase begins when LBBI falls below −0.5 standard deviations and ends when it exceeds 0.5 standard deviations.

To identify the factors influencing crisis risk, we propose three models that incorporate investor sentiment across different time horizons.

Model 1 (short-term sentiment impact):

Pr(CRISIS_t = 1) = f(α₁+β_1,1(RETURN)_t+β_1,2(LIQUIDITY)_t+β_1,3(VOLATILITY)_t+

β_1,4(OPTIMISM)_t*(DUM_EXPCT)_t + β_1,5(PESSIMISM)_t *(DUM_CONTCT)_t+є_1,t)

where sentiment is considered in the short-term expansion (OPTIMISM × DUM_EXPCT) and contraction (PESSIMISM × DUM_CONTCT) phases.

Model 2 (medium-term sentiment impact):

Pr(CRISIS_t = 1) = f(α₂+β_2,1(RETURN)_t+β_2,2(LIQUIDITY)_t+β_2,3(VOLATILITY)_t+

β_2,4(OPTIMISM)_t*(DUM_EXPMT)_t + β_2,5(PESSIMISM)_t *(DUM_CONTMT)_t+є_2,t)

where sentiment is incorporated into the medium-term expansion (OPTIMISM × DUM_EXPMT) and contraction phases (PESSIMISM × DUM_CONTMT).

Model 3 (long-term sentiment impact):

Pr(CRISIS_t = 1) = f(α₃+β_3,1(RETURN)_t+β_3,2(LIQUIDITY)_t+β_3,3(VOLATILITY)_t+

β_3,4(OPTIMISM)_t*(DUM_EXPLT)_t + β_3,5(PESSIMISM)_t *(DUM_CONTLT)_t+є_3,t)

where sentiment is accounted for in the long-term expansion (OPTIMISM × DUM_EXPLT) and contraction (PESSIMISM × DUM_CONTLT) phases.

Each model estimates the probability of a crisis based on the interaction between the market fundamentals and investor sentiment. To ensure robustness, the models were estimated separately using sentiment measures derived from the ARMS Index and Google Trends.

To evaluate the performance of the estimated probit models, we compared the predicted probabilities with the actual stock market crisis occurrences, presenting the four outcomes in Table 2. Types C and D represent correct signals for crises and stability, respectively, while Type A errors occur when the model fails to detect actual crises and Type B errors occur when non-crises are incorrectly identified as crises. To improve the accuracy, minimizing Type A and B errors is crucial for maximizing correct predictions. Additionally, a probability threshold is set to signal impending crises, with lower thresholds increasing the number of predicted crises and raising false alarms. Following Boucher (2004) and Coudert & Gex (2008), the estimation results are presented at the 25% and 50% thresholds.

The sample consists of both fundamental data (returns, liquidity, and volatility) and behavioral data (investor sentiment: optimism and pessimism) covering the period from January 2, 2004, to May 30, 2025, at a daily frequency. Data sources vary depending on the type of measurement.

1. Returns, volatility, and liquidity are derived from the BOVESPA stock index, which represents the Brazilian stock market. Liquidity is calculated based on the daily trading volume.

2. The ARMS indicator, used as an indirect measure of investor sentiment, is calculated using the closing prices and trading volumes of companies listed on the BOVESPA index, with data obtained from Datastream.

3. The direct sentiment measure was constructed by analyzing the frequency of positive and negative search terms on Google Trends.

We present the results of crisis detection, as well as the identified Expansion, and Contraction phases for the three horizons, along with the estimation results of the probit models and a diagnostic assessment of model performance.

Using the CMAX approach, two major crises were identified in the Brazilian stock market, between 2004 and 2025. The first began on 20/05/2008, reached its trough on 27/10/2008, and recovered on 11/09/2017, with a total magnitude of 59.96%. Although initially triggered by the 2008 Global Financial Crisis, the unusually prolonged recovery, lasting over eight years—was largely driven by domestic disruptions. These included the 2014–2016 economic recession, the Lava Jato (Car Wash) corruption investigation, and the political upheaval surrounding the 2016 impeachment of President Dilma Rousseff. Such Brazil-specific events deepened market uncertainty and significantly delayed normalization.

The second crisis, from 23/01/2020 to 07/01/2021, with a 46.82% decline, was initiated by the global shock of the COVID-19 pandemic. However, its severity in Brazil has been intensified by internal challenges, including conflicting responses between federal and state authorities, institutional frictions, and fiscal uncertainty. These local dynamics undermined investor confidence and shaped both the depth of the downturn and the pace of recovery, even as the global markets began to stabilize.

These findings confirm that the CMAX methodology is sensitive not only to global shocks, but also to Brazil-specific crises, including political turmoil, fiscal instability, and domestic economic mismanagement. Thus, the identified crisis periods reflect both international contagion and local vulnerabilities, supporting the contextual validity of our crisis detection approach.

Table 3 provides the details of each identified crisis.

The different phases of short-, medium-, and long-term expansions and contractions identified in the Brazilian stock market are available upon request. These phases vary in duration, with longer time horizons corresponding to extended periods of expansion or contraction.

We systematically analyze the influence of fundamental variables alongside optimistic and pessimistic investor sentiment across short-, medium-, and long-term stock market cycle phases, as identified using the ARMS index and Google Trends data, on the risk of stock market crises in Brazil.

The analysis, using three models with McFadden R² values of 60%, 59%, and 59%, shows strong robustness and good model fit, supported by significant maximum likelihood probabilities. The RETURN variable consistently has negative coefficients (−5.451039, −5.367026, and −5.265531), all significant at the 1% level, confirming that declining stock prices precede market crises, consistent with studies by Mishkin & White (2002), Patel & Sarkar (1998), and more recently, Bai et al. (2021).

Regarding market liquidity, the negative and statistically significant coefficients across all the models support our hypothesis that higher liquidity reduces crisis risk. Liquidity encourages block formation, enhances investor intervention (Edmans et al., 2013) and improves price informativeness (Chordia et al., 2008), making it harder for managers to manipulate stock prices and thus reducing crisis risk. This is in line with the views of Amihud et al. (1990) and Rösch & Kaserer (2014), who demonstrate the role of illiquidity in weakening market stability, and Nguyen and Nguyen (2024a, b), who confirm this phenomenon in Vietnamese firms.

Volatility significantly increases crisis risk as higher price fluctuations introduce uncertainty and information asymmetry. Both informed and uninformed investors reduce stock holdings in response to volatility, thereby triggering crises. This aligns with the findings of Fang (2001) and Aggarwal et al. (1999), who link volatility to market instability. Choudhry (1996) and Ben Yaala and Henchiri (2025b) show a strong association between volatility and financial crises in both developing and developed markets.

Our study also finds that investor sentiment, particularly the ARMS index, plays a key role in explaining stock market crises. Both optimistic and pessimistic sentiments contribute to mispricing and increase crisis risk, consistent with previous studies that highlight the impact of sentiment on market instability and bubble formation (Zouaoui et al., 2011; De Long & Shleifer, 1991; Pan, 2020; Wu et al., 2021; Carosia et al., 2025; Karasan et al., 2025; Alnafea & Chebbi, 2021).

Finally, the influence of sentiment on crises is stronger in the short-to medium-term, driven by demand shocks from noise traders. Over longer horizons, these effects diminish, as arbitrage opportunities increase.

Notably, the constant term remains statistically significant across all models, which may indicate that some relevant explanatory variables, such as macroeconomic shocks, political risk, and cross-market contagion, are not fully accounted for. This opens promising directions for future research aimed at refining model specifications and capturing the multifaceted nature of the crisis dynamics.

The estimation results of the three probit models incorporating the fundamental variables and indirect sentiment measure (ARMS) in the Brazilian context are summarized in Table 4.

The three models exhibit a good overall fit, with McFadden R² values of 62%, 60%, and 60% and significant maximum likelihood statistics. The results for RETURN, LIQUIDITY, and VOLATILITY remain consistent with the initial estimations using the indirect sentiment measure (ARMS index). Stock market returns and liquidity continue to reduce the likelihood of crises, whereas volatility increases the probability of crisis. Investor sentiment, both optimistic and pessimistic, during the Expansion and Contraction phases heightens the risk of stock market crises in Brazil. The effect of sentiment is stronger in the short and medium terms, and diminishes over longer horizons. Notably, direct sentiment measures based on Google Trends data explain crisis risk more effectively than the ARMS index does. The strong relationship between online search activities and market movements underscores the importance of sentiment in stock market dynamics.

The continued statistical significance of the constant term even after incorporating the direct sentiment indicator suggests that certain influential variables may still be omitted. Future models could benefit from integrating broader structural or behavioral factors to improve predictive accuracy.

These results are detailed in Table 5.

The performance analysis of the double estimation of the models, each time incorporating a measure of sentiment across time horizons, shows high percentages of correctly predicted stock market crises alongside low false alarm rates (Type B errors) at significance levels of 50% and 25%. These results support the validity of the estimated model.

Table 6 lists the detailed performance metrics of the models.

This study provides a comprehensive analysis of stock market crises in Brazil by integrating both traditional and behavioral finance perspectives. It examines the role of fundamental factors—past stock returns, liquidity (measured by the Amihud ratio), and volatility (modeled using the GARCH model)–alongside investor sentiment, captured through the ARMS indicator and Google Trends search volume, across different time horizons.

These findings provided several important insights. First, past stock returns significantly contribute to crisis formation because price acceleration increases the risk of future market corrections. Second, liquidity plays a stabilizing role by enhancing market efficiency and reducing mispricing, thus lowering the probability of crises. Third, heightened volatility amplifies uncertainty and information asymmetry, which can reduce investor confidence and trigger a sharp decline.

Most notably, investor sentiment significantly influences the crisis dynamics. Optimism during expansionary phases and pessimism during contractions both increase the likelihood of crises, particularly in the short and medium term, while their influence diminishes in the long run, as fundamental forces reassert themselves. This reinforces the importance of investor psychology in market stability and highlights the predictive power of Google Trends data in crisis anticipation.

Although the models were estimated using historical data, their strong predictive accuracy and low false alarm rates suggest considerable potential for real-time implementation. Continuous updating of these indicators enables the models to function as early warning systems to anticipate market distress and initiate preventive actions. Investors and regulators can benefit from real-time monitoring, allowing for timely portfolio rebalancing, stress testing, and intervention strategies to reduce the severity of impending crises.

The implications of this research are yet to be determined. Theoretically, it bridges the gap between efficient market theory and behavioral finance by demonstrating how sentiment interacts with fundamentals to shape crisis dynamics. Methodologically, it offers a robust framework that combines the CMAX approach for crisis detection, Forero-Laverde’s (2018) method for identifying expansion and contraction phases, and probit regression for estimating crisis probabilities.

Practically, this study offers actionable insights to financial analysts, investors, and portfolio managers. Google Trends proves to be a cost-effective and timely sentiment proxy, enabling market participants to track the behavioral shifts that often precede market turmoil. Integrating this tool into existing risk management systems can enhance decision making by detecting instability early and guiding investment adjustments accordingly.

For policymakers, this study provides an empirical foundation for incorporating behavioral indicators into macroprudential frameworks. By identifying both fundamental and sentiment-driven crisis triggers, regulators can enhance surveillance mechanisms, increase market transparency, and deploy more responsive tools to contain systemic risks. For example, authorities can set sentiment-based thresholds to trigger closer market inspections or integrate sentiment indices into macro-financial stress testing tools. Search-based sentiment measures introduce an innovative dimension to traditional oversight, reinforcing the need for dynamic and adaptive regulatory approaches.

In the educational domain, this study enriches the teaching of market dynamics by offering an integrative perspective that blends quantitative and behavioral approaches. This provides a practical reference for students, educators, and professionals aiming to understand and forecast financial instability using a combination of theoretical models and real-world data.

The societal implications are also significant. Market crises often have far-reaching consequences, including job losses, the erosion of household wealth, and deteriorating consumer confidence. Enhancing the timeliness and accuracy of crisis detection supports broader economic and financial wellbeing. Furthermore, the findings highlight the importance of financial literacy in curbing emotionally driven market responses and promoting more informed and rational investment behavior.

Nonetheless, this study has some limitations that suggest directions for future research. First, it relies on a single crisis definition based on the CMAX methodology. Future studies could assess the robustness of these findings using alternative crisis criteria, such as fixed-percentage price declines (e.g. 20%), volatility spikes, or market stress indices. Second, the focus on aggregate market indices may obscure heterogeneous dynamics at the firm- or sector-level. More granular analyses using firm- or industry-specific data can yield deeper insights. Third, the presence of significant constant terms in the probit models may indicate omitted variables such as macroeconomic shocks, political events, or institutional factors. Incorporating these dimensions could further strengthen the explanatory power and policy relevance of future studies.

This study did not involve human participants, animals, or sensitive personal data.

The data supporting the findings of this study are available from the corresponding author upon reasonable request.

Sirine Ben Yaala – Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing; Jamel Eddine Henchiri – Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Project administration, Resources, Software, Supervision, Validation, Visualization, Writing – original draft, Writing – review & editing.