The Curonian Lagoon, the largest in Europe, suffers from nuisance cyanobacterial blooms during summer, probably triggered by unbalanced nutrient availability. However, nutrient delivery to this system was never analysed in detail. During 2012–2016, we analysed the monthly discharge, nutrient loads, and ecological stoichiometry at the closing section of the Nemunas River, the main nutrient source to the lagoon. The aim of this study was to investigate seasonal and annual variations of nitrogen (N), silica (Si), and phosphorous (P) with respect to discharge, climatic features, and historical trends. The nutrient loads varied yearly by up to 50% and their concentrations underwent strong seasonality, with summer N and Si limitation. The river discharge (16 ± 4 km³·yr⁻¹) was lower than the historical average (21.8 km³·yr⁻¹). Changes in agricultural practices resulted in similar N export from the river watershed compared to historical data (1986–2002), while sewage treatment plant improvements led to a ~60% decrease of P loads. This work contributes new data to the scattered available information on the most important nutrient source to the Curonian Lagoon. Further P reduction is needed to avoid unbalanced dissolved inorganic nitrogen and phosphorus (DIN:DIP~10) ecological stoichiometry in summer, which may stimulate undesired cyanobacterial blooms.

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This article is concerned with an original approach to generative classification of spatiotemporal areal (or lattice) data based on implementation of spatial weighting to Hidden Markov Models (HMMs). In the framework of this approach data model at each areal unit is specified by conditionally independent Gaussian observations and first-order Markov chain for labels and call it local HMM. The proposed classification is based on modification of conventional HMM by the implementation of spatially weighted estimators of local HMMs parameters. We focus on classification rules based on Bayes discriminant function (BDF) with plugged in the spatially weighted parameter estimators obtained from the labeled training sample. For each local HMM, the estimators of regression coefficients and variances and two types of transition probabilities are used in two levels (higher and lower) of spatial weighting. The average accuracy rate (ACC) and balanced accuracy rate (BAC), computed from confusion matrices evaluated from a test sample, are used as performance measures of classifiers. The proposed methodology is illustrated for simulated data and for real dataset, i.e., annual death rate data collected by the Institute of Hygiene of the Republic of Lithuania from the 60 municipalities in the period from 2001 to 2019. Critical comparison of proposed classifiers is done. The experimental results showed that classifiers based on HMM with higher level of spatial weighting in majority cases have advantage in spatial–temporal consistency and classification accuracy over one with lower level of spatial weighting.

The object of the study is the behavior of stock market volatility in response to sudden shocks and crisis-driven fluctuations, with a specific focus on capturing its complex temporal structure and memory effects. One of the biggest challenges in this domain lies in the inherent stochastic nature of volatility: it evolves irregularly over time, cannot be directly observed, and must be estimated from indirect indicators. Conventional models, particularly those grounded in classical Brownian motion, often fall short in accurately representing such dynamics, as they neglect the long-range dependence – or “market memory” – commonly observed in real financial time series. This oversight can lead to significant errors in volatility estimation, especially during phases of market turbulence such as financial crises or global events. A fractional diffusion framework was used during the study to model asset price dynamics, incorporating a time-dependent and initially unknown volatility function. This approach relies on fractional Brownian motion, whose non-Markovian properties enable the model to effectively account for long-term correlations in market behavior. To estimate the volatility, it is possible to employ statistical tools based on p-variations, which allowed to compute the Hurst index and reconstruct the underlying path of realized volatility with high sensitivity to structural market changes. It is possible to obtain that this method significantly improves the accuracy of volatility tracking, particularly under stress conditions, such as those observed during the 2020 COVID-19 crisis. It is connected to the fact that the suggested method has a number of features, in particular its ability to incorporate memory effects and to respond adaptively to high-frequency data variations. Thanks to that, let’s manage to capture abrupt volatility spikes and sustained market uncertainty more precisely. Compared to the standard models, it is possible to achieve the following advantages: enhanced responsiveness to market dynamics, improved reliability of volatility forecasts during crisis periods, and a more realistic reflection of financial market complexity.