arXiv subjects

Joanna Janczura

Publications and source records attributed to Joanna Janczura.

11 recordsLinked to original sources

arXiv2026

Improved mean squared displacement analysis for anomalous single particle trajectories

The mean squared displacement (MSD) is a cornerstone in the analysis of diffusion processes in complex media. When the system is heterogeneous and, in particular, when single-particle trajectories are short, it is essential to extract maximal information from each measured trajectory. This is typically done by time-averaging squared increments and examining the scaling of the time-averaged MSD in log-log space. However, classical regression methods perform poorly in this setting because time-averaging introduces correlations aggravated by those inherent to anomalous diffusion. We tackle these limitations by applying a generalized least squares framework, which substantially reduces variance and bias in diffusion parameter estimates, especially for short (around 100 points) and ultra-short (around 10 points) trajectories. The method is fully automated and requires no supervision. Furthermore, it enables prediction of estimation error probability density, which is asymptotically Gaussian, for both classical and enhanced approaches. Leveraging this prediction, we introduce a specialized deconvolution algorithm that reconstructs the underlying particle ensemble structure from experimental data.

cond-mat.stat-mech↗

arXiv2026

Scenario generation of intraday electricity price paths for optimal trading in continuous markets

Continuous intraday electricity markets play an increasingly important role in short-term trading and balancing, yet decision-making under rapidly evolving price dynamics remains challenging. This paper proposes a comprehensive framework for ensemble forecasting of intraday electricity price trajectories and their translation into adaptive trading decisions. Building on a corrected Support Vector Regression model, the approach extends point predictions to probabilistic trajectory forecasts by introducing scenario generation based on forecast errors of fundamental variables and proposing a novel Support Vector Sorting procedure for the efficient selection of representative scenarios. The framework is evaluated using transaction level data from the German intraday continuous market. Empirical results show improvements over benchmark methods in both statistical and economic terms. Fundamental scenarios enhance median trajectory accuracy but produce more concentrated predictive distributions, while historical simulation with scenario selection better captures tail risk. From an economic perspective, ensemble-based forecasts outperform naive benchmarks across most of the trading strategies. Dynamic updating through scenario reweighting further improves profitability with limited impact on downside risk. Overall, the results demonstrate that combining kernel-based learning with scenario driven uncertainty and adaptive updating provides a flexible and effective approach for forecasting and trading in continuous electricity markets.

stat.AP↗

arXiv2024

Corrected Support Vector Regression for intraday point forecasting of prices in the continuous power market

In this paper, we develop a new approach to the very short-term point forecasting of electricity prices in the continuous market. It is based on the Support Vector Regression with a kernel correction built on additional forecast of dependent variable. We test the proposed approach on a dataset from the German intraday continuous market and compare its forecast accuracy with several benchmarks: classic SVR, the LASSO model, Random Forest and the naïve forecast. The analysis is performed for different forecasting horizons, deliveries, and lead times. We train the models on three expert sets of explanatory variables and apply the forecast averaging schemes. Overall, the proposed cSVR approach with the averaging scheme yields the highest forecast accuracy, being at the same time the fastest from the considered benchmarks. The highest improvement in forecast accuracy is obtained for deliveries in the morning and evening peaks.

stat.AP↗

arXiv2024

Expectile regression averaging method for probabilistic forecasting of electricity prices

In this paper we propose a new method for probabilistic forecasting of electricity prices. It is based on averaging point forecasts from different models combined with expectile regression. We show that deriving the predicted distribution in terms of expectiles, might be in some cases advantageous to the commonly used quantiles. We apply the proposed method to the day-ahead electricity prices from the German market and compare its accuracy with the Quantile Regression Averaging method and quantile -- as well as expectile-based historical simulation. The obtained results indicate that using the expectile regression improves the accuracy of the probabilistic forecasts of electricity prices, but a variance stabilizing transformation should be applied prior to modelling.

stat.AP↗

arXiv2022

Dependence structure for the product of bi-dimensional finite-variance VAR(1) model components. An application to the cost of electricity load prediction errors

In this paper we analyze the product of bi-dimensional VAR(1) model components. For the introduced time series we derive general formulas for the autocovariance function and study its properties for different cases of cross-dependence between the VAR(1) model components. The theoretical results are then illustrated in the simulation study for two types of bivariate distributions of the residual series, namely the Gaussian and Student's t. We also show a possible practical application of the obtained results based on the data from the electricity market.

stat.ME↗

arXiv2021

On the distribution of the product of two continuous random variables with an application to electricity market transactions. Finite and infinite-variance case

In this paper we study the distribution of a product of two continuous random variables. We derive formulas for the probability density functions and moments of the products of the Gaussian, log-normal, Student's t and Pareto random variables. In all cases we analyze separately independent as well as correlated random variables. Based on the theoretical results we use the general maximum likelihood approach for the estimation of the parameters of the product random variables and apply the methodology for a real data case study. We analyze a distribution of the transaction values, being a product of prices and volumes, from a continuous trade on the German intraday electricity market.

math.PR↗

arXiv2021

Market risk factors analysis for an international mining company. Multi-dimensional, heavy-tailed-based modelling

Mining companies to properly manage their operations and be ready to make business decisions, are required to analyze potential scenarios for main market risk factors. The most important risk factors for KGHM, one of the biggest companies active in the metals and mining industry, are the price of copper (Cu), traded in US dollars, and the Polish zloty (PLN) exchange rate (USDPLN). The main scope of the paper is to understand the mid- and long-term dynamics of these two risk factors. For a mining company it might help to properly evaluate potential downside market risk and optimise hedging instruments. From the market risk management perspective, it is also important to analyze the dynamics of these two factors combined with the price of copper in Polish zloty (Cu in PLN), which jointly drive the revenues, cash flows, and financial results of the company. Based on the relation between analyzed risk factors and distribution analysis, we propose to use two-dimensional vector autoregressive (VAR) model with the $α-$stable distribution. The non-homogeneity of the data is reflected in two identified regimes: first - corresponding to the 2008 crisis and second - to the stable market situation. As a natural implication of the model fitted to market assets, we derive the dynamics of the copper price in PLN, which is not a traded asset but is crucial for the KGHM company risk exposure. A comparative study is performed to demonstrate the effect of including dependencies of the assets and the implications of the regime change. Since for various international companies, risk factors are given rather in the national than the market currency, the approach is universal and can be used in different market contexts, like mining or oil companies, but also other commodities involved in the global trading system.

q-fin.ST↗

arXiv2020

Classification of particle trajectories in living cells: machine learning versus statistical testing hypothesis for fractional anomalous diffusion

Single-particle tracking (SPT) has become a popular tool to study the intracellular transport of molecules in living cells. Inferring the character of their dynamics is important, because it determines the organization and functions of the cells. For this reason, one of the first steps in the analysis of SPT data is the identification of the diffusion type of the observed particles. The most popular method to identify the class of a trajectory is based on the mean square displacement (MSD). However, due to its known limitations, several other approaches have been already proposed. With the recent advances in algorithms and the developments of modern hardware, the classification attempts rooted in machine learning (ML) are of particular interest. In this work, we adopt two ML ensemble algorithms, i.e. random forest and gradient boosting, to the problem of trajectory classification. We present a new set of features used to transform the raw trajectories data into input vectors required by the classifiers. The resulting models are then applied to real data for G protein-coupled receptors and G proteins. The classification results are compared to recent statistical methods going beyond MSD.

q-bio.QM↗

arXiv2012

Pricing electricity derivatives within a Markov regime-switching model

In this paper analytic formulas for electricity derivatives are calculated. To this end, we assume that electricity spot prices follow a 3-regime Markov regime-switching model with independent spikes and drops and periodic transition matrix. Since the classical derivatives pricing methodology cannot be used in case of non-storable commodities, we employ the concept of the risk premium. The obtained theoretical results are then used for the European Energy Exchange (EEX) market data. The 3-regime model is calibrated to the spot electricity prices. Next, the risk premium is derived and used to calculate prices of European options written on spot, as well as, forward prices.

q-fin.PR↗

arXiv2011

Anomalous diffusion models: different types of subordinator distribution

Subordinated processes play an important role in modeling anomalous diffusion-type behavior. In such models the observed constant time periods are described by the subordinator distribution. Therefore, on the basis of the observed time series, it is possible to conclude on the main properties of the subordinator. In this paper we analyze the anomalous diffusion models with three types of subordinator distribution: α-stable, tempered stable and gamma. We present similarities and differences between the analyzed processes and point at their main properties (like the behavior of moments or the mean squared displacement).

math-ph↗

arXiv2011

Black swans or dragon kings? A simple test for deviations from the power law

We develop a simple test for deviations from power law tails, which is based on the asymptotic properties of the empirical distribution function. We use this test to answer the question whether great natural disasters, financial crashes or electricity price spikes should be classified as dragon kings or 'only' as black swans.

q-fin.ST↗