Working Papers

The WNE Working Papers series has been published by the Faculty of Economic Sciences at the University of Warsaw since 2008.

The WNE Working Papers series provides a fast, open channel for disseminating research conducted at the Faculty of Economic Sciences, University of Warsaw. The papers hosted here are working versions (pre-prints) and may evolve as authors refine their analyses, incorporate feedback, or progress through formal peer-review. What you read is the current version released by the authors, timestamped and assigned DOI/ISSN identifiers to ensure precise citation and version tracking. Copyright remains with the authors, who may, at any time, upload a revised file or add a note directing readers to a later, peer-reviewed publication.

The Working Papers series accepts articles by research employees of the Faculty and publications from conferences organised at the Faculty of Economic Sciences at the University of Warsaw. Articles should be original research papers which have not been previously published, on the subject of economics.

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Number of Results 26

WP(30/2026)524. From Information to Communication: Generative Interaction in the Production of Knowledge

Authors: Kopczewski Tomasz, Lisicki Jan
Economic analysis of information explains how existing knowledge is distributed, revealed, and used, while the economics of innovation treats new ideas as outcomes of search and recombination. This paper examines a distinct role of communication in k…

WP524. From Information to Communication: Generative Interaction in the Production of Knowledge

Economic analysis of information explains how existing knowledge is distributed, revealed, and used, while the economics of innovation treats new ideas as outcomes of search and recombination. This paper examines a distinct role of communication in knowledge production: interaction can change the course of search itself. We define the mechanism as adaptive feedback, in which one participant responds to the current state of another participant's reasoning and thereby alters the directions subsequently explored. The resulting idea need not be contained in the feedback or previously possessed by either participant. In stronger cases, interaction can change the representation of the problem and make previously unavailable hypotheses accessible. The paper distinguishes this generative role of interaction from information transmission and access to others' knowledge. It argues that institutions shape knowledge production through both information structure and interaction structure, including the timing of interaction and the balance between independent search and mutual influence.


DOI: https://doi.org/10.33138/2957-0506.2026.30.524
Kopczewski Tomasz, Lisicki Jan
communication knowledge production generative interaction search innovation problem representation

WP(10/2026)504. Clashing narratives about economic inequality in the economic and sociological textbooks

Authors: Weychert Ewa, Kopczewski Tomasz
Students of introductory economics courses pointed out that economic inequality the most significant challenge in the 21st century (Bowles & Carlin, 2020). However, there is limited research on how this issue is portrayed in introductory textbook…

WP504. Clashing narratives about economic inequality in the economic and sociological textbooks

Students of introductory economics courses pointed out that economic inequality the most significant challenge in the 21st century (Bowles & Carlin, 2020). However, there is limited research on how this issue is portrayed in introductory textbooks. Our study aims to investigate the presentation of economic inequality in economics textbooks compared to sociological ones. We conduct a mixed-method study to examine differences in how introductory economics and sociology textbooks portray economic inequality. By focusing on the comparison between economic and sociological textbooks, we aim to highlight the importance of an interdisciplinary approach to studying economic inequalities, as advocated by economist Thomas Piketty (Korom, 2019). Comparing textbooks across disciplines is essential for informing curriculum development, encouraging interdisciplinary learning, and enhancing the relevance of education to real-world issues. This comparison provides insights that help integrate diverse perspectives on economic inequality into educational practices in both disciplines. Our analysis includes twelve introductory economics textbooks and three introductory sociological textbooks. We find significant differences: top-selling economics textbooks focus on statistical measurements of inequality and the trade-off between equality and efficiency, while sociological textbooks consider economic inequality from historical, cultural, and philosophical perspectives.


DOI: https://doi.org/10.33138/2957-0506.2026.10.504
Weychert Ewa, Kopczewski Tomasz
income inequality wealth inequality textbook analysis narrative economics qualitative research

WP(13/2024)449. The Hybrid Forecast of S&P 500 Volatility ensembled from VIX, GARCH and LSTM models

Authors: Natalia Roszyk, Ślepaczuk Robert
Predicting the S&P 500 index's volatility is crucial for investors and financial analysts as it helps in assessing market risk and making informed investment decisions. Volatility represents the level of uncertainty or risk related to the siz…

WP449. The Hybrid Forecast of S&P 500 Volatility ensembled from VIX, GARCH and LSTM models

Predicting the S&P 500 index's volatility is crucial for investors and financial analysts as it helps in assessing market risk and making informed investment decisions. Volatility represents the level of uncertainty or risk related to the size of changes in a security's value, making it an essential indicator for financial planning. This study explores four methods to improve the accuracy of volatility forecasts for the S&P 500: the established GARCH model, known for capturing historical volatility patterns; an LSTM network that utilizes past volatility and log returns; a hybrid LSTM-GARCH model that combines the strengths of both approaches; and an advanced version of the hybrid model that also factors in the VIX index to gauge market sentiment. This analysis is based on a daily dataset that includes data for S&P 500 and VIX index, covering the period from January 3, 2000, to December 21, 2023. Through rigorous testing and comparison, we found that machine learning approaches, particularly the hybrid LSTM models, significantly outperform the traditional GARCH model. The inclusion of the VIX index in the hybrid model further enhances its forecasting ability by incorporating real-time market sentiment. The results of this study offer valuable insights for achieving more accurate volatility predictions, enabling better risk management and strategic investment decisions in the volatile environment of the S&P 500.


DOI: https://doi.org/10.33138/2957-0506.2024.13.449
Natalia Roszyk, Ślepaczuk Robert
volatility forecasting LSTM-GARCH S&P 500 index hybrid forecasting models VIX index machine learning financial time series analysis walk-forward process hyperparameters tuning deep learning recurrent neural networks

WP(25/2023)432. Hedging Properties of Algorithmic Investment Strategies using Long Short-Term Memory and Time Series models for Equity Indices

Authors: Michańków Jakub, Sakowski Paweł, Ślepaczuk Robert
This paper proposes a novel approach to hedging portfolios of risky assets when financial markets are affected by financial turmoils. We introduce a completely novel approach to diversification activity not on the level of single assets but on the le…

WP432. Hedging Properties of Algorithmic Investment Strategies using Long Short-Term Memory and Time Series models for Equity Indices

This paper proposes a novel approach to hedging portfolios of risky assets when financial markets are affected by financial turmoils. We introduce a completely novel approach to diversification activity not on the level of single assets but on the level of ensemble algorithmic investment strategies (AIS) built based on the prices of these assets. We employ four types of diverse theoretical models (LSTM - Long Short-Term Memory, ARIMA-GARCH - Autoregressive Integrated Moving Average - Generalized Autoregressive Conditional Heteroskedasticity, momentum, and contrarian) to generate price forecasts, which are then used to produce investment signals in single and complex AIS. In such a way, we are able to verify the diversification potential of different types of investment strategies consisting of various assets (energy commodities, precious metals, cryptocurrencies, or soft commodities) in hedging ensemble AIS built for equity indices (S&P 500 index). Empirical data used in this study cover the period between 2004 and 2022. Our main conclusion is that LSTM-based strategies outperform the other models and that the best diversifier for the AIS built for the S&P 500 index is the AIS built for Bitcoin. Finally, we test the LSTM model for a higher frequency of data (1 hour). We conclude that it outperforms the results obtained using daily data.


Michańków Jakub, Sakowski Paweł, Ślepaczuk Robert
machine learning recurrent neural networks long short-term memory algorithmic investment strategies testing architecture loss function walk-forward optimization over-optimization

WP(23/2023)430. Mean Absolute Directional Loss as a New Loss Function for Machine Learning Problems in Algorithmic Investment Strategies

Authors: Michańków Jakub, Sakowski Paweł, Ślepaczuk Robert
This paper investigates the issue of an adequate loss function in the optimization of machine learning models used in the forecasting of financial time series for the purpose of algorithmic investment strategies (AIS) construction. We propose the Mea…

WP430. Mean Absolute Directional Loss as a New Loss Function for Machine Learning Problems in Algorithmic Investment Strategies

This paper investigates the issue of an adequate loss function in the optimization of machine learning models used in the forecasting of financial time series for the purpose of algorithmic investment strategies (AIS) construction. We propose the Mean Absolute Directional Loss (MADL) function, solving important problems of classical forecast error functions in extracting information from forecasts to create efficient buy/sell signals in algorithmic investment strategies. Finally, based on the data from two different asset classes (cryptocurrencies: Bitcoin and commodities: Crude Oil), we show that the new loss function enables us to select better hyperparameters for the LSTM model and obtain more efficient investment strategies, regarding risk-adjusted return metrics on the out-of-sample data.


Michańków Jakub, Sakowski Paweł, Ślepaczuk Robert
machine learning recurrent neural networks long short-term memory algorithmic investment strategies testing architecture loss function walk-forward optimization over-optimization

WP(20/2023)427. Ensembling ARIMAX Model in Algorithmic Investment Strategies on Commodities Market

Authors: Jakubowski Paweł, Ślepaczuk Robert, Windorbski Franciszek
This paper presents the results of investment strategies based on predictions from an ARIMA with exogenous variables (ARIMAX/ARIMAX-Garch) model, using the prices of selected commodities and companies from the DJIA index as explanatory variables. The…

WP427. Ensembling ARIMAX Model in Algorithmic Investment Strategies on Commodities Market

This paper presents the results of investment strategies based on predictions from an ARIMA with exogenous variables (ARIMAX/ARIMAX-Garch) model, using the prices of selected commodities and companies from the DJIA index as explanatory variables. The explained variables are four Invesco ETF funds (DBE, DBA, DBP, DBB) corresponding to baskets of energy, agricultural, precious, and industrial metals. The models are optimized using the Walk-Forward technique, and the selection of exogenous variables is based on Granger causality tests. By analyzing the results, we conclude that ARIMAX/ARIMAX-Garch models are not useful tools for making buy or sell decisions for the selected commodity baskets. Out of the 80 estimated models, 44 outperform the Buy & Hold strategy, however, none achieved statistically significant results. Combining individual models into an investment portfolio reduced the risk without significantly reducing the profit, enabling us to consistently beat the benchmark. We also observe that using returns of commodities listed on stock exchanges is more effective than using stock returns. Sensitivity analysis shows instability in results with changes in the length of the training and testing windows. The highest annual return rate of 15.37% from 02.01.2008 to 01.12.2022 was characterized by an ARIMAX model with one commodity exogenous variable.


Jakubowski Paweł, Ślepaczuk Robert, Windorbski Franciszek
ARIMA(X) GARCH ARIMA(X)/GARCH Algorithmic Investment Strategies Granger Causality Investment Performance Evaluation Trading Systems Forecasting Models

WP(17/2023)424. Optimal Markowitz Portfolio Using Returns Forecasted with Time Series and Machine Learning Models

Authors: Ślusarczyk Damian, Ślepaczuk Robert
We aim to answer the question of whether using forecasted stock returns based on machine learning and time series models in a mean-variance portfolio framework yields better results than relying on historical returns. Nevertheless, the problem of the…

WP424. Optimal Markowitz Portfolio Using Returns Forecasted with Time Series and Machine Learning Models

We aim to answer the question of whether using forecasted stock returns based on machine learning and time series models in a mean-variance portfolio framework yields better results than relying on historical returns. Nevertheless, the problem of the efficient stock selection has been tested for more than 50 years, the issue of adequate construction of mean-variance portfolio framework and incorporating forecasts of returns in it has not been solved yet. Stock returns portfolios were created using ’raw’ historical returns and forecasted return based on ARIMA-GARCH and the XGBoost models. Two optimization problems were concerned: global maximum information ratio and global mini-mum variance. Then strategies were compared with two benchmarks – an equally weighted portfolio and buy and hold on the DJIA index. Strategies were tested on Dow Jones Industrial Average stocks in the period from 2007-01-01 to 2022-12-31 and daily data was used. The main portfolio performance metrics were information ratio* and information ratio**. The results showed that using forecasted returns we can enhance our portfolio selection based on Markowitz framework, but it is not a universal solution, and we have to control all the parameters and hyperparameters of selected models.


Ślusarczyk Damian, Ślepaczuk Robert
Algorithmic Investment Strategies Markowitz framework portfolio optimization forecasting ARIMA GARCH XGBoost minimum variance

WP(29/2022)405. The efficiency of various types of input layers of LSTM model in investment strategies on S&P500 index

Authors: Nguyen Thi Thu Giang, Ślepaczuk Robert
The study compares the use of various Long Short-Term Memory (LSTM) variants to conventional technical indicators for trading the S&P 500 index between 2011 and 2022. Two methods were used to test each strategy: a fixed training data set from 200…

WP405. The efficiency of various types of input layers of LSTM model in investment strategies on S&P500 index

The study compares the use of various Long Short-Term Memory (LSTM) variants to conventional technical indicators for trading the S&P 500 index between 2011 and 2022. Two methods were used to test each strategy: a fixed training data set from 2001–2010 and a rolling train–test window. Due to the input sensitivity of LSTM models, we concentrated on data processing and hyperparameter tuning to find the best model. Instead of using the traditional MSE function, we used the Mean Absolute Directional Loss (MADL) function based on recent research to enhance model performance. The models were assessed using the Information Ratio and the Modified Information Ratio, which considers the maximum drawdown and the sign of the annualized return compounded (ARC). LSTM models' performance was compared to benchmark strategies using the SMA, MACD, RSI, and Buy&Hold strategies. We rejected the hypothesis that algorithmic investment strategy using signals from LSTM model consisting only from daily returns in its input layer is more efficient. However, we could not reject the hypothesis that signals generated by LSTM model combining daily returns and technical indicators in its input layer are more efficient. The LSTM Extended model that combined daily returns with MACD and RSI in the input layer generated a better result than Buy&Hold and other strategies using a single technical indicator. The results of the sensitivity analysis show how sensitive this model is to inputs like sequence length, batch size, technical indicators, and the length of the rolling train - test window.


Nguyen Thi Thu Giang, Ślepaczuk Robert
algorithmic investment strategies machine learning testing architecture deep learning recurrent neural networks LSTM technical indicators forecasting financial-time series technical indicators hyperparameter tuning S&P 500 Index

WP(28/2021)376. The effectiveness of Value-at-Risk models in various volatility regimes

Authors: Schiffers Aleksander, Chlebus Marcin
There is an ongoing discussion, what is the most efficient approach to Value-at-Risk estimation. Subsequent studies and meta-analyzes show that there is no scientific consensus in this field and the necessity of further research is frequently underli…

WP376. The effectiveness of Value-at-Risk models in various volatility regimes

There is an ongoing discussion, what is the most efficient approach to Value-at-Risk estimation. Subsequent studies and meta-analyzes show that there is no scientific consensus in this field and the necessity of further research is frequently underlined. In this study, authors try to assess the comparative performance of models used for Value-at-Risk estimations in changing market volatility regimes. The models considered are: the Historical Simulation, the Risk Metrics®, the GARCH(1,1)-n, the GARCH(1,1)-t, the GARCH(1,1)-st, the GARCH(1,1)-QML. GARCH models are additionally enriched with additional, exogenous regressors in the form of lagged commodity futures contracts returns. The analysis is conducted on a set of utility sector stock indices from six developed countries across the globe: WIG Energia (Poland), Dow Jones Utilities Average (USA), CAC Utilities (France), Tokyo SE Topix-17 Power & Gas (Japan), S&P ASX 200 Utilities (Australia), and DAX All Utilities (Germany). Three samples of different characteristics are distinguished from the last 10 years of data and one of them covers the upsurge in market volatility caused by the Covid-19 pandemic. In order to evaluate the VaR forecasts performance of each model, conditional/unconditional coverage tests of Kupiec and Christoffersen, Dynamic Quantile test, and Diebold-Marino test were used. Empirical results of the study indicate that in the volatile market periods, overall quality of forecasts deteriorates for all models to a varying degree. However, the GARCH(1,1)-st with external regressors is considered the most efficient and robust model due to its ability to capture stylized facts of data distribution. Exogenous variables are worth considering but their contribution to performance improvement may be model and market dependent.


Schiffers Aleksander, Chlebus Marcin
risk management market risk Value-at-risk GARCH Historical Simulation Risk Metrics® risk modelling benchmark model quality assessment

WP(25/2021)373. Applying Hybrid ARIMA-SGARCH in Algorithmic Investment Strategies on S&P500 Index

Authors: Nguyen Vo, Ślepaczuk Robert
This research aims to compare the performance of ARIMA as linear model with that of the combination of ARIMA and GARCH family models to forecast S&P500 log returns in order to construct algorithmic investment strategies on this index. We use the …

WP373. Applying Hybrid ARIMA-SGARCH in Algorithmic Investment Strategies on S&P500 Index

This research aims to compare the performance of ARIMA as linear model with that of the combination of ARIMA and GARCH family models to forecast S&P500 log returns in order to construct algorithmic investment strategies on this index. We use the data collected from Yahoo Finance. The dataset has daily frequency and covers the period from 01/01/2000 to 31/12/2019. By using rolling window approach, we compare ARIMA with the hybrid models to examine whether hybrid ARIMA-SGARCH and ARIMA-EGARCH can really reflect the specific time-series characteristics and have better predictive power than simple ARIMA model. In order to assess the precision and quality of these models in forecasting, we decide to compare their equity lines, their forecasting error metrics (MAE, MAPE, RMSE, MAPE) as well as their performance metrics (annualized return compounded, annualized standard deviation, maximum drawdown, information ratio and adjusted information ratio). The results show that the hybrid models outperform ARIMA and the benchmark (Buy&Hold strategy on S&P500 index). These results are not sensitive to varying window sizes, the type of distribution and the type of the GARCH model.


Nguyen Vo, Ślepaczuk Robert
algorithmic investment strategies ARIMA ARIMA-SGARCH ARIMA-EGARCH hybrid model forecast stock returns model robustness
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