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 18

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(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(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

WP(11/2021)359. Comparison of the accuracy in VaR forecasting for commodities using different methods of combining forecasts

Authors: Lis Szymon, Chlebus Marcin
No model dominates existing VaR forecasting comparisons. This problem may be solved by combine forecasts. This study investigates the daily volatility forecasting for commodities (gold, silver, oil, gas, copper) from 2000-2020 and identifies the sour…

WP359. Comparison of the accuracy in VaR forecasting for commodities using different methods of combining forecasts

No model dominates existing VaR forecasting comparisons. This problem may be solved by combine forecasts. This study investigates the daily volatility forecasting for commodities (gold, silver, oil, gas, copper) from 2000-2020 and identifies the source of performance improvements between individual GARCH models and combining forecasts methods (mean, the lowest, the highest, CQOM, quantile regression with the elastic net or LASSO regularization, random forests, gradient boosting, neural network) through the MCS. Results indicate that individual models achieve more accurate VaR forecasts for the confidence level of 0.975, but combined forecasts are more precise for 0.99. In most cases simple combining methods (mean or the lowest VaR) are the best. Such evidence demonstrates that combining forecasts is important to get better results from the existing models. The study shows that combining the forecasts allows for more accurate VaR forecasting, although it's difficult to find accurate, complex methods.


Lis Szymon, Chlebus Marcin
Combining forecasts Econometric models Finance Financial markets GARCH models Neural networks Regression Time series Risk Value-at-Risk Machine learning Model Confidence Set

WP(10/2021)358. HCR & HCR-GARCH – novel statistical learning models for Value at Risk estimation

Authors: Woźniak Michał, Chlebus Marcin
Market risk researchers agree that an ideal model for Value at Risk (VaR) estimation does not exist, different models performance strongly depends on current economic circumstances. Under the conditions of sudden volatility increase, such as during t…

WP358. HCR & HCR-GARCH – novel statistical learning models for Value at Risk estimation

Market risk researchers agree that an ideal model for Value at Risk (VaR) estimation does not exist, different models performance strongly depends on current economic circumstances. Under the conditions of sudden volatility increase, such as during the global economic crisis caused by the Covid-19 pandemic, no classical VaR model worked properly even for the group of the largest market indices. Therefore, the aim of the article is to present and formally test three novel statistical learning models for VaR estimation: HCR, HCR-GARCH and HCR-QML-GARCH, which, by considering additional volatility term (due to time context and statistical moments), should be able to perform well in times of market turbulence. In the benchmark procedure we compare the 1% and 2.5% one-day-ahead VaR forecasts obtained with the above models against the estimates of classical methods like: Historical Simulation, KDE, Modified Cornish-Fisher Expansion, GARCH(1,1) with varied distributions, RiskMetrics™, EVT and QML-GARCH. Four periods that vary in terms of market volatility: 2006-9, 2008-11, 2014-17 and mid-2016 to mid-2020 for six different stock market indexes: DAX, WIG 20, MOEX, S&P 500, Nikkei and SHC are selected. Models quality is tested from two perspectives: fulfilling regulatory requirements and forecasting adequateness. Obtained results show that HCR-GARCH outperforms other models during periods of sudden increased volatility in the markets. At the same time, HCR-QML-GARCH liberalizes the conservative estimates of HCR-GARCH and allows its use under moderate volatility, without any major loss of quality in times of crisis.


Woźniak Michał, Chlebus Marcin
Value at Risk Hierarchical Correlation Reconstruction GARCH Standardized Residuals

WP(8/2021)356. GARCHNet - Value-at-Risk forecasting with novel approach to GARCH models based on neural networks

Authors: Buczyński Mateusz, Chlebus Marcin
This study proposes a new GARCH specification, adapting a long short-term memory (LSTM) neural network's architecture. Classical GARCH models have been proven to give substantially good results in the case of financial modeling, where high volati…

WP356. GARCHNet - Value-at-Risk forecasting with novel approach to GARCH models based on neural networks

This study proposes a new GARCH specification, adapting a long short-term memory (LSTM) neural network's architecture. Classical GARCH models have been proven to give substantially good results in the case of financial modeling, where high volatility can be observed. In particular, their high value is often praised in the case of Value-at-Risk. However, the lack of nonlinear structure in most of the approaches entails that the conditional variance is not represented in the model well enough. On the contrary, recent rapid advancement of deep learning methods is said to be capable of describing any nonlinear relationships prominently. We suggest GARCHNet - a nonlinear approach to conditional variance that combines LSTM neural networks with maximum likelihood estimators of probability in GARCH. The distributions of the innovations considered in the paper are: normal, t and skewed t, however the approach does enable extensions to other distributions as well. To evaluate our model, we have executed an empirical study on the log returns of WIG 20 (Warsaw Stock Exchange Index) in four different time periods throughout 2005 and 2021 with varying levels of observed volatility. Our findings confirm the validity of the solution, however we present several directions to develop it further.


Buczyński Mateusz, Chlebus Marcin
Value-at-Risk GARCH neural networks LSTM

WP(28/2020)334. Value-at-risk — the comparison of state-of-the-art models on various assets

Authors: Kielak Karol, Ślepaczuk Robert
This paper compares different approaches to Value-at-Risk measurement based on parametric and non-parametric approaches. Three portfolios are taken into consideration — the first one containing only stocks from the London Stock Exchange, the se…

WP334. Value-at-risk — the comparison of state-of-the-art models on various assets

This paper compares different approaches to Value-at-Risk measurement based on parametric and non-parametric approaches. Three portfolios are taken into consideration — the first one containing only stocks from the London Stock Exchange, the second one based on different assets of various origins and the third one consisting of cryptocurrencies. Data used cover the period of more than 20y. In the empirical part of the study, parametric methods based on mean-variance framework are compared with GARCH(1,1) and EGARCH(1,1) models. Different assumptions concerning returns' distribution are taken into consideration. Adjustment for the fat tails effect is made by using Student t distribution in the analysis. One-day-ahead 95%VaR estimation is then calculated. Thereafter, models are validated using Kupiec and Christoffersen tests and Monte Carlo Simulation for reliable verification of the hypotheses. The overall goal of this paper is to establish if analyzed models accurately estimate Value-at-Risk measure, especially if we take into account assets with various returns distribution characteristics.


Kielak Karol, Ślepaczuk Robert
risk management Value-at-Risk GARCH models returns distribution Monte Carlo Simulation asset class cryptocurrencies

WP(17/2020)323. Political connections and the super-rich in Poland

Authors: Brzeziński Michał, Sałach Katarzyna
We use newly collected original panel data on the super-wealthy individuals in Poland (observed over 2002-2018) to study the impact of the rich’s political connections on their wealth level, mobility among the rich and the risk of dropping off …

WP323. Political connections and the super-rich in Poland

We use newly collected original panel data on the super-wealthy individuals in Poland (observed over 2002-2018) to study the impact of the rich’s political connections on their wealth level, mobility among the rich and the risk of dropping off the rich list. The multimillionaires are classified as politically connected if we find reliable news stories linking their wealth to political contacts or questionable licenses, or if a person was formerly an informant of communist Security Service or member of the communist party, or when the origins of wealth are connected to the privatization process. We find that political connections are not associated with the wealth level of Polish multimillionaires, but that they are linked to the 20-30% lower probability of upward mobility in the ranking of the rich. Moreover, being a former member of the communist party or secret police informant increases the risk of dropping off the Polish rich list by 79%. Taken together, our results show that, contrary to some other post-socialist countries such as Russia or Ukraine, there is little evidence that the Polish economy suffers from crony capitalism.


Brzeziński Michał, Sałach Katarzyna
the super-rich billionaires oligarchs wealth inequality top wealth political connections crony capitalism Poland
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