Do Weather Variables Affect the Stock Companies in the Same Way as Fundamental Variables? GARCH-Based Modelling on the Case of Banks Listed on the Warsaw Stock Exchange

1. Introduction

While initially seeking to validate the efficient market hypothesis-EMH [1], scholars progressively identified systematic valuation deviations known as market anomalies [2,3,4]. These irregularities span calendar-related patterns [5], momentum behaviours, and fundamental discrepancies [6]. Recently, attention has shifted toward distortions driven by meteorological variables, such as temperature, cloudiness, humidity, wind dynamics, precipitation, and sun exposure [7,8,9]. By altering human emotional states [10,11], these factors can significantly impact investor cognition and decision-making [6,9].

While day-to-day weather fluctuations have always been a natural element influencing human routines, the context of global climate change fundamentally amplifies their significance. Amid escalating global warming, it is imperative to conceptualize the increasing frequency and intensity of these meteorological anomalies not merely as transient behavioural disruptors, but as physical climate risks that jeopardize systemic financial stability [12,13]. For European financial equities, such threats negatively predict bank stock returns [14] and amplify market volatility through complex, nonlinear, and asymmetric mechanisms [15]. This vulnerability is particularly critical for the banking sector in Central and Eastern Europe (CEE), including Poland. These jurisdictions remain highly exposed to physical climate hazards while simultaneously exhibiting the lowest adaptation readiness within the European Union [16].

Current literature state highlights that weather variables affect market volatility, trading volume, and liquidity more consistently than average daily returns [17,18]. Despite these findings, empirical investigations dedicated to the stock exchanges in the CEE region (in which Poland has a significant share) remain limited. Moreover, prior research predominantly focused on aggregate market indices [19,20], rather than individual sectors, which may affect weather conditions in various ways. Furthermore, the literature lacks a direct comparative analysis evaluating the explanatory dominance of daily weather variables against fundamental variables for CEE financial institutions, in which banks listed on the Warsaw Stock Exchange (WSE) play a significant role. Most regional evidence either relies on lower-frequency monthly datasets such as recent GARCH-type modelling applications extending systemic risk (CRISK) measures with physical climate shocks for Polish banks [21] or entirely neglects daily-level ARCH-type modelling of bank shares [22]. Consequently, this study attempts to meet this substantial research gap.

The primary objective of this paper is to evaluate how specific weather variables compare against fundamental variables in shaping the daily returns and changes of trading volume of the individual stock companies included in the WIG-BANKING sectoral index listed on the WSE between 2020 and 2025. Focusing specifically on this index is methodologically justified, as these entities account for approximately 35–40% of the total trading volume on the WSE, making it a systemically representative benchmark [21,23]. Rather than detailing individual parameters at this stage, the analysis broadly contrasts weather variables against established fundamental variables.

In this context, the Polish financial market serves as a highly suitable proxy for the wider CEE banking industry. The selected 2020-2025 timeframe is distinguished by heightened instability and severe market fluctuations across international financial systems [24]. This turbulence amplifies the role of market sentiment, underscoring the critical need to decipher modern investor decision-making amidst substantial information asymmetry [25,26]. In the light of these dynamics, the paper poses the following central research question: Do weather variables provide explanatory information beyond firm-specific and market-wide financial variables?

The layout of this paper is structured as follows: Section 2 reviews the relevant literature. Section 3 outlines the data and methodology applied in the study. Section 4 presents the empirical results, Section 5 provides the discussion, and Section 6 concludes the paper and highlights directions for future research.

2. Literature Review: Valuation of Physical Climate Risks and Financial Fundamentals in the Banking Sector

2.1. Weather Anomalies and Investor Behaviour

The strategic importance of behavioural finance lies in its ability to decipher how exogenous environmental variables influence investors' decision-making processes. Traditional paradigms emphasize the impact of daily temperature, rainfall, and cloud cover on emotional states, risk appetite, and trading volumes. Systematic reviews confirm that temperature remains the most extensively documented driver capable of disrupting classical asset pricing [11]. Foundational studies demonstrate that morning sunshine strongly and positively correlates with daily market returns, a phenomenon attributed to the psychological misattribution of upbeat moods to optimistic economic prospects [6]. However, this linear "sunshine-returns" relationship has faced empirical pushback. Comprehensive assessments of localized trading reveal that while extreme physical impediments (e.g. blizzards) can paralyze market liquidity and reduce trading volume by over 17%, ordinary variations in cloud cover yield negligible linear impacts on actual equity returns [27]. This divergence is particularly pronounced in emerging markets, where adverse weather and Seasonal Affective Disorder (SAD) systematically degrade market liquidity and depress turnover rather than directly altering stock returns [17,28].

Pioneering psychological and intraday analyses clarify this mechanism, demonstrating that meteorological fluctuations have their primary influence not by boosting positive emotions, but by directly exacerbating negative affect, physical tiredness, and cognitive distraction [10]. For instance, extreme heatwaves significantly depress daily trading volumes on the French stock market by escalating indoor investor fatigue, bad mood, and cognitive distraction [18]. Furthermore, experimental evidence demonstrates that the clinical depression associated with SAD causally induces profound financial risk aversion, prompting individuals to systematically shun risky equities during darker winter months [29]. This specific seasonal distortion is rigorously validated within Central and South-Eastern European (CEE/SEE) exchanges, where reduced daylight heightens local investors' risk aversion, thereby driving up expected market returns while maintaining a muted, or even negative, effect on volatility [22]. This dampened volatility aligns with broader international evidence showing that mood-depressing variables systematically suppress market variance as pessimistic investors slip into apathy and withdraw from active trading [30]. Ultimately, these behavioural mechanisms are best explained by the salience theory, which posits that market participants disproportionately adjust their strategies in response to extreme weather shocks (e.g., severe humidity), driving market distortions almost entirely through sentiment deterioration rather than fundamental corporate declines [31]. These weather-driven emotional adjustments operate in parallel with broader informational channels on the WSE, where news sentiment—specifically during periods of geopolitical and macroeconomic tension—significantly shapes aggregate short-term investment decisions and retail investor behaviour [32]. Crucially, these psychological aspects of weather perception now form the cognitive foundation for a modern approach to physical environmental risks within the ESG paradigm, translating severe daily weather anomalies into tangible factors that destabilize the financial ecosystem [33]. These psychological transmission channels, initially framed merely as short-term mood effects, have increasingly been reinterpreted as mechanisms through which sudden, extreme weather fluctuations manifest as deeper, systemic market vulnerabilities.

2.2. From Weather Anomalies to Physical Environmental Risk

The shift from viewing daily weather anomalies merely as psychological distractors to treating severe meteorological extremes as systemic financial risks has gained significant momentum in recent literature. This evolution catalysed the emergence of modern environmental finance. It is a discipline situated at the intersection of environmental and financial economics, which systematically re-evaluates how acute weather hazards shape cross-sectional equity returns [12]. Fundamental to understanding this process is the dichotomy between transition risk, which stems from the economic costs of shifting to a more sustainable economy, and physical risk, which directly encompasses destructive meteorological threats such as severe floods, droughts, and heatwaves [33].

Capturing the precise financial impact of physical climate risk remains methodologically challenging due to its inherent non-linearity and geographical complexities. Aggregating these risks on a global scale often obscures the true impact of meteorological extremes. For instance, comprehensive panel analyses across 54 countries reveal that broad firm-level physical risk metrics frequently remain statistically insignificant, underscoring the market's historical inefficiency in pricing tangible environmental threats without highly localized data [34]. However, advanced high-frequency evaluations demonstrate that when accurately measured, extreme weather shocks have an immediate, severe negative impact on European stock market returns, although this adverse dependence progressively reverses into a positive association over longer horizons due to market learning and adaptive portfolio reallocations [14]. This immediate vulnerability is particularly acute for institutions with spatially concentrated physical assets. Indeed, recent evidence leveraging granular geospatial data of European bank branches confirms that equity markets actively price in localized physical hazard exposures (such as floods, landslides, and heatwaves), significantly penalizing vulnerable institutions during regulatory environmental stress tests [35]. This spatial and structural exposure of financial institutions necessitates a closer examination of how severe meteorological shocks directly impair core banking fundamentals and systemic stability.

2.3. Weather Shocks, Bank Fundamentals and Systemic Stability

Traditional financial ratios and macroeconomic stability provide a baseline for assessing the impact of meteorological shocks on institutional market value. In CEE markets, fundamentals such as GDP growth and inflation strictly dictate long-term market equilibriums but exhibit negligible explanatory power over short-term daily return deviations [36]. Consequently, metrics like Return on Equity (ROE) and the Price-to-Book Value (P/BV) ratio cannot be analysed in isolation from environmental risks. Severe meteorological events, such as extreme precipitation or thermal anomalies in the CEE region, directly depreciate loan collateral, eroding book value and escalating credit risk. This mechanism is corroborated by European banking data, showing that chronic temperature anomalies and indirect transition risks (e.g., Scope 3 emissions) severely deteriorate bank-level financial stability measured by Z-scores and amplify systemic volatility [13]. Furthermore, robust ESG engagement acts as a crucial "reputation insurance" that significantly dampens this climate-induced volatility during crises [37], whereas corporate financial constraints and frictions structurally amplify firm-level stock return volatility in highly vulnerable countries [38].

Beyond individual balance sheets, severe weather shocks cascade through the broader financial system, fundamentally altering contagion dynamics. Advanced network topology models applied to emerging markets reveal that temperature deviations now sit at the core of systemic risk contagion, with the banking sector uniquely vulnerable to heatwaves that trigger credit delinquency cascades [39]. This sensitivity is grounded in foundational Delta Conditional Value at Risk (ΔCoVaR) evaluations—which measure the systemic risk contribution of an individual financial institution to the entire system—demonstrating that isolated temperature anomalies have a highly nonlinear impact on institutional tail risk, whereby positive hot shocks drastically escalate systemic vulnerability, whereas cold shocks surprisingly suppress interconnected market losses [40]. The devastating magnitude of these cascading failures is explicitly quantified by advanced climate stress-tests, which prove that initial weather shocks are drastically amplified by subsequent rounds of endogenous interbank distress and overlapping portfolio fire-sales [41]. Ultimately, proving that systemic vulnerability extends far beyond direct loan exposures, this necessity to contrast stable fundamentals with sudden weather-induced volatility forms the natural methodological transition to ARCH/GARCH-class models. The need to contrast relatively stable fundamental valuations with sudden, weather-induced volatility spikes therefore leads directly to the methodological preference for GARCH-family models capable of capturing asymmetry, clustering, and non-linear dynamics.

2.4. The CEE and Polish Context

Poland, as the region’s largest capital market, serves as a highly representative proxy for CEE dynamics. The unique vulnerability of this region stems from its heavy reliance on fossil fuels and structural economic imbalances. While developed Western European financial institutions easily absorb major physical climate disasters through robust risk-sharing mechanisms with only moderate equity responses [42], CEE jurisdictions face a starkly different reality. Recent unsupervised clustering analyses classify Poland and other CEE nations (e.g., Romania, Bulgaria) among the most exposed to physical climate risks and the least prepared in terms of climate policy implementation and adaptation readiness [16]. This macro-level vulnerability directly translates into institutional fragility. Environmentally augmented systemic risk models (E-CoVaR and E-SRISK) explicitly rank Polish and Romanian banking institutions at the very bottom of the European resilience hierarchy [43]. The mechanics of this fragility are deeply rooted in asymmetric macro-financial transmission channels, where extreme weather shocks systematically exacerbate existing economic imbalances and degrade aggregate financial soundness under high underlying stress [44]. Consequently, local banking systems are highly susceptible to the ripple effects of natural hazards, triggering profound proactive adjustments in credit supply. CEE banks immediately tighten borrowing conditions and raise interest spreads for firms situated in high-risk areas following extreme weather events, even if those enterprises suffered no direct physical damage [45].

Despite this pronounced structural exposure, the evolution of environmental finance from simple weather correlations to advanced text-based models [33,46] has largely bypassed sectoral analyses in transition economies. Early empirical investigations into CEE stock exchanges primarily analysed broad aggregate indices, often concluding that systematic weather effects on returns were negligible or entirely overshadowed by global market dynamics [19,20,47]. Crucially, contemporary investigations exploring weather anomalies specifically on the Polish capital market remain exceptionally scarce, limited to only a handful of recent studies. Within this extremely narrow body of literature, the work by Tarczyński et al. [48,49] presents the impact of weather variables on the securities listed on the WSE. It successfully isolated the local energy sector and demonstrated how weather variables significantly impact market activity when evaluated through advanced econometric frameworks. Even when specific meteorological distortions are successfully detected in other regional exchanges, such as evidence from the Romanian equity market confirming that temperature and air pressure systematically escalate market volatility despite having no direct impact on stock returns [8], these findings remain restricted to broad national benchmarks rather than isolating vulnerable financial sectors. This muted historical response is consistent with broader international evidence revealing that, over the past three decades (1995–2024), extreme weather events have generally had a limited aggregate impact on global stock markets compared to the overwhelming market disruptions caused by traditional systemic financial crises [50]. Despite this pronounced structural exposure and the methodological advances outlined above, a critical research gap remains regarding the comparative role of daily weather variables versus traditional fundamental metrics in the CEE banking sector.

2.5. Research Gap and Contribution

The identified research gap points to a critical lack of studies directly comparing weather variables against typical fundamentals indicators, which is noticeable in the case of CEE stock exchanges (particularly in the case of WSE). Furthermore, it seems extremely important to address this issue in the context of the above-average uncertainty in global financial markets observed over the past few years [51]. The 2020-2025 period is defined by compounding macroeconomic shocks like the COVID-19 pandemic, the war in Ukraine and Gaza Strip, and severe energy crises. They triggered unprecedented, asymmetric volatility spillovers across global financial markets [24]. The immediate severity of the pandemic precipitated a rapid flight to safe-haven assets and induced massive cross-country volatility, heavily driven by social media sentiment and further destabilized by unconventional policies such as unlimited quantitative easing [25]. Within the Polish financial market, geopolitical and natural disaster uncertainties similarly Granger-caused significant structural disruptions [52]. Consequently, European banking equities exhibited profoundly asymmetric volatility and an exacerbated sensitivity to market fear [53], severely deviating from the EMH and rendering traditional asset pricing models based on predictable returns entirely insufficient [4].

Based on the identified literature gaps [54,55,56], the following two main hypotheses are formulated to guide the empirical investigation:

MH1: Weather variables have a statistically significant effect on the daily returns of banks listed on the WSE, comparable to the explanatory power of fundamental variables.

MH2: Weather variables have a statistically significant effect on the daily changes of trading volume of banks listed on the WSE, comparable to the explanatory power of fundamental variables.

Uncovering weather-induced market distortions that challenge the EMH carries profound practical value. Ultimately, such insights help investors and institutions to critically reassess and adapt their portfolio allocations to weather variables as short-term manifestations of environmental conditions [15,33].

Crucially, such extreme macro-financial turbulence can temporarily mask the true valuation of environmental threats. This masking phenomenon is robustly explained by the 'investor distraction hypothesis' under which severe market panic overwhelms limited investor attention, severely weakening the transmission of environmental systemic risk [57]. Furthermore, pandemic-induced lockdowns physically isolated retail investors from outdoor meteorological anomalies, temporarily neutralizing traditional behavioural transmission channels, save for pervasive variables like atmospheric pressure [58]. Despite the acute structural exposure of transition economies to these overlapping shocks, comprehensive reviews confirm a glaring scarcity of rigorous empirical evidence concerning physical environmental risks in highly vulnerable emerging markets, as the vast majority of research remains concentrated on developed economies. By explicitly isolating the banking sector of a profoundly exposed CEE economy and subjecting it to advanced GARCH-family conditional variance evaluations, the present study directly answers the academic call to evaluate how severe, compounding weather variables can affect the financial stability in under-researched, lower-readiness jurisdictions [59].

3. Materials and Methods

To verify MH1 and MH2, it was necessary to obtain three types of data. The first was the quotations of banks listed on the WSE grouped in the WIG-BANKING sectoral index. It is a sub-sector index and its portfolio includes WIG constituents belonging to the ‘banking’ sector. Weightings in the index are the same as in the WIG index portfolio. WIG-BANKING index base date is December 31, 1998 [23]. This index groups thirteen companies (as at the beginning of 2026) such as: PKO, PEKAO, ERSTE (Santander Bank Polska S.A. was acquired by Erste Group Bank AG in January 2026, which obtained a 49% controlling stake. The bank was subsequently rebranded as Erste Bank Polska S.A.; however, Santander Bank Polska is retained as the entity name in this study because the observation period ends in 2025. In this study, in order to avoid confusion arising from the similar names of two separate banks (Banco Santander and Santander Bank Polska S.A.), it was decided to use the new name (Erste Bank Polska S.A.) for the latter, which is currently in use), MBANK, ING, ALIOR, MILLENIUM, BNP, HANDLOWY, UNICREDIT, BOS, SANTANDER, GETIN. For these companies, daily share prices and trading volumes were collected from 2020 to 2025 [60] to calculate logarithmic daily returns and changes of the trading volume. They played the role of dependent variables in the GARCH models, because they can reflect the general investors’ sentiments [61].

The second type of data needed in this study was daily weather data. They have been downloaded from the Institute of Meteorology and Water Management National Research Institute in Poland [62]. The approach used in previous research was to download weather data from the closest meteorological station for the main location of the analysed companies [48,49]. A similar approach was used in this study, as the first part of the research. Because two of the banks investigated were foreign-owned (UNICREDIT & SANTANDER), their headquarters in Poland (WARSAW) were adopted as the main locations. Therefore, the closest locations of the meteorological stations (with their individual numbers provided by the IMGW) for each company were as follows:

• PKO - WARSZAWA-FILTRY (252200230),
• PEKAO - WARSZAWA-BIELANY (252200150),
• ERSTE - WARSZAWA-FILTRY (252200230),
• MBANK - WARSZAWA-FILTRY (252200230),
• ING - KATOWICE (350190560),
• ALIOR - WARSZAWA (352200375),
• MILLENIUM - WARSZAWA-FILTRY (252200230),
• BNP - WARSZAWA-FILTRY (252200230),
• HANDLOWY - WARSZAWA-OBSERWATORIUM (252210160),
• UNICREDIT - WARSZAWA-OBSERWATORIUM (252210160),
• BOS - WARSZAWA-FILTRY (252200230),
• SANTANDER - WROCLAW-OGROD BOTANICZNY (251170280),
• GETIN - WROCLAW-OGROD BOTANICZNY (251170280).

For each of the above-mentioned locations, daily data (as the part of the conditional mean equation) were downloaded from IMGW for the period 2020-2025 regarding:

• average temperature in °C (tm),
• relative humidity in % (rh),
• water vapor pressure in % (vapp),
• average cloud cover in % (cloud_cover),
• average wind speed in km/h (wind_speed),
• average air pressure in hPa (ppp),
• sum of falls in mm (prcp),
• sunshine duration in hours (sunshine),
• time of rainfall in hours (ra_time),
• time of snowfall in hours (sn_time).

In addition to the approach used in previous studies [10,48,49,63], which was based on the nominal values of daily weather data for the meteorological stations assigned to individual companies, the authors of this study decided to apply modified, original research procedure. It utilises the difference between the daily data of the specified weather variables and their long-term average, estimated for individual months based on data from the period 1991–2019 [62]. This made it possible to estimate certain types of weather anomalies (Ar), which may have a greater impact on decisions made by investors in financial markets than the nominal values of individual weather variables [9,64]. The availability of long-term average IMGW data enabled the calculation of the following variables, which were implemented in the second part of the study:

• average temperature deviation in °C (tmAr),
• relative humidity deviation in % (rhAr),
• water vapor pressure deviation in % (vappAr),
• average wind speed deviation in km/h (wind_speedAr),
• average air pressure deviation in hPa (pppAr),
• sum of falls deviation in mm (prcpAr),
• sunshine duration deviation in hours (sunshineAr).

Moreover, the following independent variables were included (in both approaches) in the models as control variables (all daily). They consist of a combination of fundamental indicators for individual banks and also fundamental variables designed to assess overall sentiment in the financial market and its impact on the market valuation [65] of the investigated banks listed on the WSE. All of these data have been downloaded from the Stooq.com historical database [60]. Control variables also include two variables responsible for typical calendar anomalies (day of the week/month), which have been frequently observed in financial markets in recent years as factors influencing investor decisions [3,51]. The full set of control variables to the conditional mean equation is listed in Table 1.

The relationships between the weather variables and the logarithmic returns/changes of trading volume of the WIG-BANKING companies are estimated using GARCH models. This approach is more appropriate than conventional multiple linear regression for examining the impact of weather variables on stock returns because financial time series typically exhibit volatility clustering with time-varying conditional variance (periods of high volatility) and leptokurtosis (fat-tailed distributions). These characteristics violate the homoscedasticity assumption underlying ordinary least squares (OLS) regression, potentially leading to inefficient parameter estimates and biased statistical inference [66]. The methodological necessity of employing this framework is confirmed by recent systematic literature reviews, which conclusively demonstrate the superiority of asymmetric GARCH configurations (such as EGARCH) over traditional OLS regressions in accurately capturing the complex, non-linear sensitivity of returns to exogenous environmental shocks [67]. Direct empirical comparisons powerfully reinforce this necessity. On the example of recent research, analyses of the German stock market reveal that applying traditional OLS models to weather data generates entirely different and often spurious anomaly results when compared to Glosten-Jagannathan-Runkle GARCH (GJR-GARCH) model specifications. This emphasizes that violating the econometric assumptions of heteroskedasticity leads to fundamentally flawed conclusions regarding environmental market distortions [9]. This profound methodological sensitivity is also explicitly confirmed within the WSE. Evaluations of Polish energy equities demonstrate that static OLS and Feasible Generalized Least Squares (FGLS) regressions completely fail to capture behavioral anomalies. Only advanced asymmetric GARCH specifications (e.g., EGARCH, TS-GARCH) successfully reveal that mood-depressing variables like cloudiness and low atmospheric pressure systematically dictate stock returns and trading volumes [48].

The justification for addressing these non-linearities stems from the fact that weather variables tend to act as negative market shocks, triggering distinct asymmetric and leverage effects [68]. Applications of GARCH models (such as exponential GARCH-EGARCH) reveal that extreme weather events create more severe volatility spikes than positive market news, although the ultimate magnitude of these anomalies is often moderated by the underlying efficiency of the specific market [56]. Empirical evidence demonstrates that while daily meteorological fluctuations fail to significantly alter actual stock returns in highly developed exchanges, they systematically and profoundly escalate time-varying market volatility across all assessed markets regardless of their foundational efficiency, validating the use of threshold GARCH (TGARCH) and EGARCH frameworks [55]. Furthermore, recent empirical applications of GARCH models confirm that specific daily meteorological data, notably high temperatures combined with high humidity, significantly amplify market volatility and uncertainty, making this econometric approach essential for accurate short-term risk assessment [69]. Consequently, the framework of GARCH models enables a more reliable assessment of whether weather variables affect stock returns directly or indirectly through changes in return and trading volume [7]. In particular, it seems appropriate to use those GARCH models which take into account the asymmetry in market reactions to positive and negative data, as well as the aforementioned leverage effect, both of which may occur in the event of sudden weather shocks [56,70]. These arguments were also confirmed by the data used in this study. The ADF stationarity tests [71], the ARCH effect [72], and the autocorrelation of residuals [73] unequivocally indicated the need to use GARCH models instead of classical OLS to verify the impact of weather factors on the daily rates of return and changes of trading volume generated by companies included in the WIG-BANKING index. It was therefore decided to use the three models described below.

The first of them was the classic symmetric GARCH (p,q) model, which assumes that conditional variance depends linearly on squared residuals and their own lagged values [74]. In all of the GARCH-type models p symbolises the lag orders of the ARCH component (ϵ_t-1²) and q symbolises the lag orders of the GARCH component (σ_t−j²). Classic GARCH model has been calculated based on the following formula (1):

σ_t² = ω +∑ α_iϵ_t-1² +∑ β_jσ_t−j²

(1)

Where:

σ_t² - conditional variance at day t,

ω - baseline constant variance intercept (ω > 0),

α_i - parameter which measures the short-run impact (ARCH effect) of volatility shocks from period t-P,

β_j - parameter which measures the persistence (GARCH effect) of volatility from period t- Q.

To ensure the conditional variance is always positive and stationary, the model requires ω > 0, α_i ≥ 0, and β_j ≥ 0. The stationarity condition, that the sum of all parameters α_i and β_j will always be <1 for stationarity.

The next model was Exponential GARCH (EGARCH (p,q)), which captures the empirical tendency for negative shocks to increase volatility more than positive shocks of equal magnitude (the leverage effect). It drops the non-negativity constraints on parameters by modelling the natural logarithm of variance [75]. Moreover, it simulates the phenomenon of grouping variances [76]. The use of a GARCH model that incorporates the leverage effect is particularly important in the event of negative market shocks, which occurred with particular frequency between 2020 and 2025 [77]. It has been calculated based on the formula (2):

ln (σ_t²) = ω + ∑ α_i │ϵ_t−1/σ_t−1│+ ∑ γk (ϵ_t−k/σ_t−k) ₊ ∑ β_j ln (σ_t-j²)

(2)

Where:

γk – asymmetry (leverage) parameter evaluates the direction of the market shock. If it is < 0, negative news increases volatility more than positive news.

The last model was Glosten-Jagannathan-Runkle GARCH (GJR-GARCH (p,q)), which also indicate volatility clustering, handle leptokurtic returns, and account for the leverage effect [78], what is extremely important in the adopted research period and for indicated weather variables. It handles asymmetric shocks and improves the accuracy of volatility modelling [79]. It has been calculated based on the formula (3):

σ_t² = ω +∑ α_iϵ_t-1² +∑ γ_kI_t-kϵ_t-k²+ ∑ β_jσ_t−j²

(3)

Where:

{0 ifϵ_t-k≥μ}

I_t-k = {1ifϵ_t-k<μ}

To ensure stationarity, the model requires ω > 0 ∑α_i +∑ β_j + ½ ∑ γk < 1_.

All models were calculated using GRETL. Each model was based on the Student t-distribution using the outer product of the gradient (OPG), which estimates the covariance matrix [80] based on the gradients of the logarithm of the likelihood function. Various combinations of lags (between 0,0 and 2,2) were used to construct these GARCH models. To address the issue of multiple testing arising from the large number of estimated coefficients, the statistical significance of the weather-related variables was additionally evaluated using the Benjamini & Hochberg false discovery rate [81] . The next section presents those with the best fits using the Akaike information criterion (AIC) [82] and the Bayesian Schwarz information criterion (BIC) [83].

4. Results

This section shows the results of the research procedure presented above, which examined the impact of weather variables on the daily returns and changes of trading volume of banks listed on the WSE during the 2020-2025 period. As mentioned earlier, the analysis of the influence of weather variables was carried out using the daily returns and logarithmic change of the trading volume of bank shares as the dependent variable. Table 2, Table 3, Table 4 and Table 5 present the results of calculations using three different GARCH models with varying combinations of lags. As indicated in the previous section, this study employed two research approaches, each of which required separate calculations. In Table 2 and Table 3, the nominal values of the weather data were used for calculations. In contrast, Table 4 and Table 5 are based on the difference between daily readings and the long-term average calculated for each month from the period 1991–2019 [62]. Based on the previously identified AIC and BIC criteria, the models with the best fit were selected for each of the thirteen analysed banks. In Table 2, Table 3, Table 4 and Table 5, only the statistically significant variables (at least p-value < 0.1) have been presented.

The empirical results presented in the Table 2, Table 3, Table 4 and Table 5 offer comprehensive insights into the daily returns and changes of trading volume of companies grouped in the WIG-BANKING sectoral index during the 2020-2025 period. By examining both daily logarithmic stock returns and changes of trading volume under two different approaches (nominal weather variables & weather anomalies understood as deviations from historical monthly averages) the empirical findings reveal a hierarchy of determinants the stock market parameters of banks listed on the WSE. Across all estimated GARCH-type models for both dependent variables fundamental variables demonstrate overwhelmingly frequency of statistically significant associations compared to fundamental indicators of individual banks and weather variables. This impact is particularly evident in the STOXX600 index, which tracks the daily returns of 600 securities across 17 European countries representing nearly 90% of the underlying investable market [84]. Both for the nominal and deviation approaches, STOXX600 is statistically significant for almost all evaluated banks (p-value<0.01), yielding robust positive coefficients predominantly above 1.0 (e.g., ALIOR: 1.24, PEKAO: 1.17, Santander: 1.18, MBANK: 1.14, PKO: 1.07). This underscores that Polish banking companies behave as high-beta, cyclical assets deeply integrated into the broader European financial ecosystem [21].

Second most important independent variable is EURPLN, which represents daily returns of the EUR/PLN rates. It demonstrates strong statistical significance across 11 out of 13 banks for daily returns in the nominal approach and 12 out of 13 banks in the deviation approach (p-value<0.01). The coefficients are systematically negative (e.g., MILLENNIUM: -1.62, MBANK: -1.47, ALIOR: -1.39, PEKAO: -1.34, PKO: -1.18). A depreciation of the Polish Zloty (PLN) against the Euro (EUR) triggers immediate downward pressure on domestic bank valuations, capturing sovereign risk perceptions and systemic capital flow shifts [85]. A key fundamental variable that has been shown to be statistically significant in many models is the GOLD variable, which represents the daily returns on the “safe-haven” asset. It exhibits a statistically significant negative relationship with stock returns for 7 banks (e.g., MILLENNIUM: -0.19, SANTANDER: -0.14, PEKAO: -0.13), which is consistent with the findings of previous studies [86]. It is extremely interesting that these variables had a significant impact on the daily returns of stocks companies included in the WIG-BANKING index, while their impact on the daily change of trading volume was far less noticeable.

From the perspective of this paper, however, the most important aspect was to verify whether weather variables could influence the dependent variables analysed for banks listed on the WSE. Therefore, we decided to provide a summary aimed at identifying whether, and if so, which - weather variables affected daily logarithmic returns/changes of trading volume of the 13 banks under investigation. Table 6 below shows in how many models the individual variables included in the calculations were statistically significant in their impact on the dependent variable. Table 6 has been also divided into two parts, reflecting the two distinct approaches used in this study (nominal values of weather variables/difference between the values of weather variables and long-term monthly averages).

Based on the first approach using nominal weather variables, it should be noted that their impact on both daily logarithmic returns and changes of trading volume of shares of individual companies included in the WIG-BANKING index was relatively rare. It is worth mentioning only a two weather variables that showed statistical significance in more than three models. Among them is the cloud_cover variable, which had a negative (weak) impact on returns (e.g., ERSTE, mBANK, BOŚ, with a p-value < 0.05), lending minor support to classical "cloudiness/sunlight" behavioural theories where overcast skies induce mild pessimistic sentiment among traders [87]. Furthermore, the snowfall duration variable (sn_time) exhibits a significant negative effect on the daily change of trading volume across 4 out of 13 banks including ALIOR, MILLENNIUM, UNICREDIT, BOŚ (p-value < 0.1). Extended snowfall physically or cognitively suppresses market participation, reducing overall turnover [17]. These isolated occurrences and the lack of a consistent trend in the results indicate that the impact of nominal weather conditions on the returns and volume changes of banks listed on the WSE was weak and unstable.

However, implementing weather variables deviations/anomalies (Ar) in the second approach significantly increases the frequency of statistical significance across GARCH-type models. This is particularly evident in the case of the variable representing atmospheric pressure (ppp). It emerges as the most prevalent significant weather variable, influencing returns positively in 5 out of 13 banks (mBANK, MILLENNIUM, BNP, BOŚ, UNICREDIT; p-value<0.1). For these banks, unusually high barometric pressure relative to seasonal norms can be reflected as a behavioural channel documented in previous literature [88]. Also, tmAr and rhAr display a positive impact on the returns of banks listed on the WSE (PKO, PEKAO, ERSTE, ALIOR, and GETIN; p-value<0.1). They thus indicate that monthly temperature and humidity readings, higher than the monthly averages can affect short-term investment decisions, as has already been noted in studies conducted in other markets [89,90,91].

Similarly, among models that used changes of trading volume as the dependent variable, weather variables were significantly more likely to be statistically significant when using an approach based on deviations from the average. prcpAr variable emerges as a prominent inhibitor of trading activity, statistically significant in 5 out of 13 banks (PEKAO, ERSTE, HANDLOWY, GETIN; p-value< 0.1). Negative coefficients (e.g., PEKAO: -0.0093, ERSTE: -0.0076, HANDLOWY: -0.0117) indicate that abnormal, heavy rainfall relative to seasonal averages discourages active trading, leading to lower liquidity on the financial market [92]. Similarly to returns, a statistically significant positive effect of the tmAr variable can also be observed with regard to changes of trading volume, which affects the volume in 4 out of 13 banks (mBANK, MILLENNIUM, BOŚ, UNICREDIT; p-value<0.1).

Concluding, the empirical evidence confirms that the individual stocks of companies included in the WIG-BANKING sectoral index in 2020-2025 are primarily driven by fundamental variables (STOXX600, EURPLN, GOLD) more than weather variables. The research conducted therefore do not allow for the fully acceptance of the research hypotheses proposed above (MH1 and MH2).

Nevertheless, the results obtained allow to draw an interesting conclusion. Introducing weather anomalies (understood as the difference between the values of weather variables and long-term monthly averages) significantly improves model diagnostics compared to traditional nominal values of weather variables. This may suggest that weather variables (such as temperature, cloud cover, humidity, etc.) may not have a clear impact on investor behaviour, however significant deviations from their average values may affect investor sentiment, as can be seen in this study [42,68].

5. Discussion

While the empirical evidence does not support the premise that weather variables have a greater impact than fundamental variables, it reveals a heterogeneous, secondary role for weather anomalies in shaping daily returns and changes of trading volume of banks listed on the WSE. Weather variables, when operationalized as localized deviations rather than nominal metrics, appeared statistically significant in several GARCH specifications. However, their capacity to explain daily return and changes of trading volume is fundamentally subordinated to the dominant influence of fundamental variables such as the EUR/PLN exchange rate and the STOXX Europe 600 index. This clear hierarchy of determinants indicates that investors exhibit a highly selective cognitive processing of environmental cues, reacting almost exclusively to unusual conditions relative to seasonal norms.

The findings of this study demonstrate a clear hierarchy of determinants, with fundamental variables exhibiting overwhelming frequency of statistically significant associations of the stock returns and trading volumes of WSE-listed banks compared to daily weather variables and individual bank fundamentals. This pattern is most vividly illustrated by the STOXX Europe 600 index, which was statistically significant with robust positive coefficients exceeding 1.0 for almost all analysed banks, including ALIOR (1.24), PEKAO (1.17), SANTANDER (1.18), mBANK (1.14), and PKO (1.07) in the nominal model. This finding confirms that Polish banks behave as high-beta, cyclical assets deeply integrated into the wider European financial system [67]. This deep regional integration is highly consistent with the cointegration analyses of CEE markets by Ligocká [36], who highlights that fundamental variables dictate long-term market equilibriums, even if their short-term predictive power over daily return variations remains strictly limited.

Furthermore, the EUR/PLN exchange rate was highly significant across nearly all models, displaying systematic negative coefficients. A depreciation of the Polish Zloty (PLN) against the Euro (EUR) triggers an immediate downward valuation of domestic bank stocks, capturing sovereign risk perceptions and systemic capital outflows [85]. This aligns closely with domestic foreign exchange dynamics during extreme macro-financial stress, where the initial shock of the COVID-19 pandemic induced severe volatility and systemic depreciation of the Polish Zloty against major global currencies, notably the Euro [93]. The negative relationship between bank returns and gold returns across seven banks (e.g., MILLENNIUM, SANTANDER, PEKAO) further demonstrates safe-haven capital reallocations during periods of heightened market fear, a phenomenon well-documented in international finance [24]. These findings imply that while daily weather variations do influence investor psychology, they operate as supplementary "noise" against the powerful, fundamental variables that dictate CEE financial valuations, as represented by the long-term macroeconomic equilibriums documented on regional exchanges [36] and the baseline market determinants identified in behavioural studies [9].

A crucial contribution of this study is the comparison between nominal weather readings and weather anomalies (second approach—Ar). While these anomalies are defined in this research as deviations from 30-year monthly historical averages, prior studies have similarly operationalized short-term weather deviations to filter out seasonal patterns [69]. While nominal weather variables exhibited weak and unstable effects on returns, the GARCH-type estimations reveal that incorporating monthly weather deviations (anomalies) significantly increases the frequency of statistical significance across the models. This pattern lends robust empirical support to the salience theory of choice under risk, demonstrating that behavioural mood-transmission channels are activated by cognitive surprise rather than absolute atmospheric levels. Consequently, while daily weather shocks do inject transient "noise" into the market, they function as micro-level behavioral perturbations that operate strictly within the boundaries set by dominant fundamental variables [94].

In particular, barometric pressure anomalies (pppAr) emerged as the most prevalent weather determinant, influencing returns across five systemically important banks: mBANK, MILLENNIUM, BNP, BOŚ, and UNICREDIT. High barometric pressure relative to seasonal averages acts as a subtle psychological booster, improving collective market sentiment and leading to short-term upward pressure on stock returns for mBank, Millennium, BNP, and BOŚ [9,48]. Similarly, positive temperature (tmAr) and relative humidity (rhAr) anomalies exhibited positive effects on daily bank returns. This suggests that warmer and more humid conditions than seasonally expected act as positive sentiment drivers in Poland's temperate climate, helping investors achieve above-average returns in the short term, a behaviour previously observed in the Polish energy sector [48,49]. On the other hand, in nominal models, daily cloud cover (cloud_cover) had a weak negative impact on returns for ERSTE, mBANK, and BOŚ. This provides minor support for classical weather-behavioural theories where overcast skies and reduced sunlight induce mild pessimistic sentiment and risk aversion [87].

The analysis of changes of trading volume validates the behavioural transmission channel, revealing that weather anomalies can disrupt slightly market participation [18]. In the case of changes of trading volume estimations, abnormal heavy precipitation (prcpAr) relative to seasonal averages emerged as a prominent inhibitor of trading activity, yielding statistically significant negative coefficients for PEKAO, ERSTE, HANDLOWY, and GETIN. Heavy rainfall dampens the willingness of investors to engage in active trading, directly depressing market liquidity. This pattern is consistent with evidence from order-driven markets, where weather-induced poor moods systematically restrict liquidity and market turnover rather than asset returns [17]. In contrast, positive temperature deviations (tmAr) promoted trading volume in mBank, Millennium, BOŚ, and UNICREDIT, suggesting that warmer-than-average temperatures encourage active investment and alter the systemic risk landscape of financial institutions [40]. Nominal snowfall duration (sn_time) also had a significant negative influence on trading volume across four banks, including ALIOR, MILLENNIUM, UNICREDIT, and BOŚ. Extended snow precipitation physically and cognitively suppresses market participation, restricting overall turnover and trading velocity. This aligns with the findings of Loughran and Schultz [27], who documented a dramatic decline in local trading volume of over 17% during major snowstorms and nearly 15% on the subsequent day due to physical disruptions.

Crucially, the overwhelming dominance of fundamental variables (such as the STOXX600 and the EUR/PLN rate) during the 2020-2025 period must be interpreted within the context of compounding global crises, including the COVID-19 pandemic, the war in Ukraine, and the European energy crisis [53,95]. The crisis-dominated sample provides a plausible context in which weather effects may have been relatively less salient. This phenomenon is highly consistent with the "investor distraction hypothesis" originally proposed by Hirshleifer et al. [96]. In the context of climate finance, Mao et al. [57] demonstrated that when global financial market risk is exceptionally high, the system's sensitivity and responsiveness to a monthly climate change news index (CCND) significantly declines. This occurs because highly salient, immediate shocks in fundamental variables flood the market, exhausting the limited attention of investors and temporarily masking the transmission of environmental factors. By extension, under such extreme systemic distress, investors naturally prioritize fundamental variables, which temporarily obscures the high-frequency transmission of daily local physical weather anomalies. Furthermore, pandemic-induced lockdowns physically isolated retail investors from outdoor weather anomalies, temporarily neutralizing traditional psychological transmission channels, save for pervasive indoor variables such as atmospheric pressure. This is because while indoor climate control and air conditioning systematically insulate investors from external temperature fluctuations, variations in barometric pressure easily penetrate physical indoor environments, continuing to have a subconscious psychological influence on trading decisions [58].

6. Conclusions

This study investigated the relative explanatory power of daily weather variables evaluated through both nominal values and seasonal anomalies versus fundamental variables in driving the daily logarithmic returns and changes of trading volume of the individual stocks of companies included in the WIG-BANKING sectoral index listed on the WSE between 2020 and 2025. Utilizing advanced GARCH-family econometric configurations (GARCH, EGARCH, and GJR-GARCH) across thirteen systemically important banking entities, the research evaluated the behavioural transmission of environmental risks in one of the main CEE financial markets.

Based on the empirical results, both hypotheses of the study (MH1 and MH2) cannot be fully supported, as the empirical evidence demonstrates that weather variables are not associated with stronger effects on daily bank stock logarithmic returns and daily changes of trading volumes than fundamental variables. Instead, fundamental variables maintain an overwhelmingly superior and dominant relationship with both evaluated dependent variables [67]. The empirical models in this study reveal that the STOXX Europe 600 index and the EUR/PLN exchange rate demonstrate vastly frequency of statistically significant association compared to daily weather variables and bank-specific fundamentals, confirming the general dominance of macro-financial shocks observed in the Polish banking sector by Dziwok and Szczepaniak [21]. This dominant relationship confirms that Polish banking companies behave primarily as high-beta, cyclical assets deeply integrated into the broader European financial ecosystem, leaving limited room for atmospheric influences to act as primary valuation drivers [9,36].

Despite the overall dominance of fundamental variables, the empirical models yield highly nuanced, secondary behavioural insights that align closely with established cognitive frameworks. Crucially, the models reveal that nominal weather readings have a weak, unstable, and mainly statistically insignificant influence on daily logarithmic stock returns and changes of trading volume [9]. In contrast, incorporating weather anomalies—operationalized as deviations from long-term monthly averages—significantly improves model diagnostics and the frequency of statistical significance across GARCH-type estimations. This discrepancy provides robust empirical support for the salience theory of choice under risk, indicating that investors do not react to absolute weather levels but are instead triggered by unexpected deviations from seasonal norms [94]. Behavioural mood-transmission channels on the stock market are thus activated by cognitive surprise rather than absolute atmospheric conditions, highlighting the critical role of cognitive perception in environmental finance [69].

In the specific context of MH1, although weather variables are subordinated to macroeconomic fundamentals in explaining stock returns, localized anomalies still inject transient psychological noise. Specifically, unusually high barometric pressure, as well as positive temperature and relative humidity anomalies, exhibit statistically significant positive relationships with daily logarithmic returns for several WSE-listed banks. These meteorological deviations act as subtle emotional boosters that temporarily elevate short-term market sentiment [48,49]. However, the presence of negative coefficients in isolated cases (e.g., UniCredit) reveals a degree of institutional heterogeneity, suggesting that the transmission of atmospheric mood effects is modulated by bank-specific structural characteristics and investor bases. Similarly, regarding MH2, while weather variables do not drive trading activity to a comparable extent as financial fundamentals, adverse weather anomalies systematically function as high-frequency physical and cognitive inhibitors. Specifically, abnormal heavy rainfall and extended snowfall duration have statistically significant negative effects on daily changes of trading volume [87]. These physical impediments and associated cognitive dampening restrict overall market participation, thereby reducing short-term market liquidity [17].

Finally, the supplementary and state-dependent nature of weather-induced distortions in this study is heavily contextualized by the unique 2020-2025 timeframe. Characterized by compounding global crises—including the COVID-19 pandemic, geopolitical conflicts in Eastern Europe, and severe energy crises—this period flooded the financial markets with highly salient macroeconomic and geopolitical shocks [24]. The dominance of market-wide variables may be consistent with the investor distraction hypothesis. Under this framework, the sheer volume of high-salience fundamental news overwhelmed the limited cognitive attention of market participants, temporarily masking or suppressing the high-frequency transmission of daily physical weather anomalies [57]. Consequently, the behavioural impact of weather variables remains highly state-dependent, surfacing primarily as high-frequency noise during periods when dominant macroeconomic shocks subside.

The findings of this study carry important theoretical and practical implications for financial theory, market participants, and regulatory authorities. Theoretically, this research advances behavioural finance by refining the boundaries of the salience theory of choice under risk. It demonstrates that behavioural mood-transmission channels on stock markets are activated by localized weather anomalies (cognitive surprise) rather than nominal weather readings. Furthermore, by showing that extreme macro-financial volatility during compounding global crises temporarily masks high-frequency weather perturbations, this study provides robust empirical support for the investor distraction hypothesis, establishing a critical temporal boundary for environmental behavioural anomalies [16]. Practically, the results offer vital insights for portfolio managers and algorithmic traders in Central and Eastern Europe, who can leverage these high-frequency weather-induced liquidity and return distortions to optimize short-term trading strategies and liquidity risk management during non-crisis periods. Most importantly, for bank executives, central banks, and financial supervisors (such as the Polish Financial Supervision Authority and the European Central Bank), these insights underscore that physical climate risks cannot be assessed in isolation. Instead of treating localized weather shocks as independent anomalies, they must be integrated as supplementary, state-dependent risk-amplifiers within broader, fundamentals-driven stress-testing and macroprudential surveillance frameworks [21].

Despite its contributions, this study is subject to certain limitations. First, the analysis relies heavily on the Polish WSE as a proxy for the broader CEE region. Although while Poland represents the largest market, regional heterogeneities in climate exposure [44] and banking structures across other CEE nations were not directly tested. Second, the reliance on meteorological data from individual weather stations closest to bank headquarters assumes a spatial alignment with trading behaviour. In an increasingly digitized financial market, retail investors and algorithmic trading systems operate in decentralized locations, potentially diluting the observable impact of localized weather data. Finally, the selected 2020-2025 timeframe was characterized by unprecedented systemic disruptions (e.g., pandemic lockdowns), which may have temporarily suppressed traditional behavioural transmission channels associated with outdoor meteorological phenomena.

To address these limitations and expand upon the current findings, future research should pursue several distinct avenues. Subsequent studies should broaden the geographical scope to include a comparative panel analysis of multiple CEE exchanges (e.g., Romania, Hungary, Czech Republic) to evaluate regional resilience and cross-market contagion dynamics. Furthermore, analysing intraday, high-frequency trading data could provide deeper insights into the immediate, hour-by-hour psychological reactions of investors to sudden weather shifts. Finally, future methodological frameworks would benefit from integrating granular, geospatial physical risk (as the short-term manifestations by weather variables) mapping at the individual bank branch level, allowing for a more precise assessment of how severe local meteorological shocks directly impair collateral values and operational stability.