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.

Please send your paper by e-mail: %a`'*x^y9?JY|I$uZKv_7ndA0&r]#[yQSnngFju++Lp`xd@TlWDTI39t_ 

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(1) the main text without the title of the article and the authors (DOC/DOCX file) and

(2) the title page including: the title of the paper, the authors and their affiliation (DOC/DOCX file).

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Number of Results 17

WP(16/2024)452. Enhancing literature review with NLP methods Algorithmic investment strategies case

Authors: Łaniewski Stanisław, Ślepaczuk Robert
This study utilizes machine learning algorithms to analyze and organize knowledge in the field of algorithmic trading, based on filtering 136 million research papers to 14,342 articles ranging from 1956 to Q1 2020. We compare previously used practice…

WP452. Enhancing literature review with NLP methods Algorithmic investment strategies case

This study utilizes machine learning algorithms to analyze and organize knowledge in the field of algorithmic trading, based on filtering 136 million research papers to 14,342 articles ranging from 1956 to Q1 2020. We compare previously used practices such as keyword-based algorithms and embedding techniques with state-of-the-art dimension reduction and clustering for topic modeling method (BERTopic) to compare the popularity and evolution of different approaches and themes. We show new possibilities created by the last iteration of Large Language Models (LLM) like ChatGPT. The analysis reveals that the number of research articles on algorithmic trading is increasing faster than the overall number of papers. The stocks and main indices comprise more than half of all assets considered, but the growing trend in some classes is much stronger (e.g. cryptocurrencies). Machine learning models have become the most popular methods nowadays, but they are often flawed compared to seemingly simpler techniques. The study demonstrates the usefulness of Natural Language Processing in asking intricate questions about analyzed articles, like comparing the efficiency of different models. We demonstrate the efficiency of LLMs in refining datasets. Our research shows that by breaking tasks into smaller ones and adding reasoning steps, we can effectively address complex questions supported by case analyses.


Łaniewski Stanisław, Ślepaczuk Robert
trading quantitative finance neural networks literature review knowledge representation natural language processing (NLP) topic modeling model comparison artificial intelligence

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(7/2024)443. LSTM-ARIMA as a Hybrid Approach in Algorithmic Investment Strategies

Authors: Kashif Kamil, Ślepaczuk Robert
This study focuses on building an algorithmic investment strategy employing a hybrid approach that combines LSTM and ARIMA models referred to as LSTM-ARIMA. This unique algorithm uses LSTM to produce final predictions but boost results of this RNN by…

WP443. LSTM-ARIMA as a Hybrid Approach in Algorithmic Investment Strategies

This study focuses on building an algorithmic investment strategy employing a hybrid approach that combines LSTM and ARIMA models referred to as LSTM-ARIMA. This unique algorithm uses LSTM to produce final predictions but boost results of this RNN by adding the residuals obtained from ARIMA predictions among other inputs. The algorithm is tested across three equity indices (S&P 500, FTSE 100, and CAC 40) using daily frequency data spanning from January, 2000 to August, 2023. The architecture of testing is based on the walk-forward procedure which is applied for hyperparameter tunning phase that uses using Random Search and backtesting the algorithms. The selection of the optimal model is determined based on adequately selected performance metrics combining focused on risk-adjusted return measures. We considered two strategies for each algorithm: Long-Only and Long-Short in order to present situation of two various groups of investors with different investment policy restrictions. For each strategy and equity index, we compute the performance metrics and visualize the equity curve to identify the best strategy with the highest modified information ratio. The findings conclude that the LSTM-ARIMA algorithm outperforms all the other algorithms across all the equity indices what confirms strong potential behind hybrid ML-TS (machine learning - time series) models in searching for the optimal algorithmic investment strategies.


DOI: https://doi.org/10.33138/2957-0506.2024.7.443
Kashif Kamil, Ślepaczuk Robert
Deep Learning Recurrent Neural Networks Algorithmic Investment Strategy LSTM ARIMA Hybrid/Ensemble Models Walk-Forward Process

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(15/2023)422. Ensembled LSTM with Walk Forward Optimization in Algorithmic Trading

Authors: Chojnacki Karol, Ślepaczuk Robert
This study compares well-known tools of technical analysis (Moving Average Crossover MAC) with Machine Learning based strategies (LSTM and XGBoost) and Ensembled Machine Learning Strategies (LSTM ensembled with XGBoost and MAC). All models were …

WP422. Ensembled LSTM with Walk Forward Optimization in Algorithmic Trading

This study compares well-known tools of technical analysis (Moving Average Crossover MAC) with Machine Learning based strategies (LSTM and XGBoost) and Ensembled Machine Learning Strategies (LSTM ensembled with XGBoost and MAC). All models were compared to Buy and Hold benchmark and evaluated using Performance Metrics, that is Annualized Return Compounded, Maximum Drawdown, Maximum Loss Duration, and three types of Information Ratio. This research uses daily S&P 500 index data ranging from 2000 to 2023. Every strategy was optimized with novel walk forward approach consisting of numerous in sample and out of sample periods. MAC and best performing ML methods were subjected to sensitivity analysis. The results show that LSTM ensembled with XGBoost and MAC yields the most promising results in terms of risk-adjusted returns which suggest further research focused on ensembling of individual ML strategies. Finally, we show that classical methods of technical analysis (that is, MAC) are much less robust and indifferent to change in hyperparameters than machine learning based algorithms, especially LSTM.


Chojnacki Karol, Ślepaczuk Robert
Algorithmic Investment Strategies Machine Learning Recurrent Neural Networks Long Short-Term Memory XGBoost Walk Forward Optimization Trading algorithms Technical Analysis Indicators

WP(5/2023)412. The performance of time series forecasting based on classical and machine learning methods for S&P 500 index

Authors: Uzzal Maudud Hassan, Ślepaczuk Robert
Based on one step ahead forecasts, this study compares the forecasting abilities of the traditional technique (ARIMA) with recurrent neural network (LSTM). In order to check the possible use of these forecasts in different asset management methods, t…

WP412. The performance of time series forecasting based on classical and machine learning methods for S&P 500 index

Based on one step ahead forecasts, this study compares the forecasting abilities of the traditional technique (ARIMA) with recurrent neural network (LSTM). In order to check the possible use of these forecasts in different asset management methods, these forecasts are afterwards included into trading signals of investment strategies. As a benchmark method, the Random Walk model producing naive forecasts has been utilized. This research examines daily data from the S&P 500 index for 20 years, from 2000 to 2020, and it includes information on some significant market turbulence. The methods were tested in terms of robustness to changes in parameters and hyperparameters and evaluated based on various error metrics (MAE, MAPE, RMSE MSE). The results show that ARIMA outperforms LSTM in terms of one step ahead forecasts. Finally, LSTM model with a variety of hyperparameters - including a number of epochs, a loss function, an optimizer, activation functions, a number of units, a batch size, and a learning rate - was tested in order to check its robustness.


Uzzal Maudud Hassan, Ślepaczuk Robert
deep learning recurrent neural networks ARIMA algorithmic investment strategies trading systems LSTM walk-forward process optimization

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(25/2022)401. Daily and intraday application of various architectures of the LSTM model in algorithmic investment strategies on Bitcoin and the S&P 500 Index

Authors: Kryńska Katarzyna, Ślepaczuk Robert
This thesis investigates the use of various architectures of the LSTM model in algorithmic investment strategies. LSTM models are used to generate buy/sell signals, with previous levels of Bitcoin price and the S&P 500 Index value as inputs. Four…

WP401. Daily and intraday application of various architectures of the LSTM model in algorithmic investment strategies on Bitcoin and the S&P 500 Index

This thesis investigates the use of various architectures of the LSTM model in algorithmic investment strategies. LSTM models are used to generate buy/sell signals, with previous levels of Bitcoin price and the S&P 500 Index value as inputs. Four approaches are tested: two are regression problems (price level prediction) and the other two are classification problems (prediction of price direction). All approaches are applied to daily, hourly, and 15-minute data and are using a walk-forward optimization procedure. The out-of-sample period for the S&P 500 Index is from February 6, 2014 to November 27, 2020, and for Bitcoin it is from January 15, 2014 to December 1, 2020. We discover that classification techniques beat regression methods on average, but we cannot determine if intra-day models outperform inter-day models. We come to the conclusion that the ensembling of models does not always have a positive impact on performance. Finally, a sensitivity analysis is performed to determine how changes in the main hyperparameters of the LSTM model affect strategy performance. 


Kryńska Katarzyna, Ślepaczuk Robert
machine learning deep learning recurrent neural networks LSTM algorithmic trading ensemble investment strategy intra-day trading S&P 500 Index Bitcoin

WP(21/2022)397. A comparison of LSTM and GRU architectures with novel walk-forward approach to algorithmic investment strategy

Authors: Baranochnikov Illia, Ślepaczuk Robert
The aim of this work is to build a profitable algorithmic investment strategy on various types of assets. The algorithm is built using recurrent neural networks (LSTM and GRU) as the primary source of  signals to buy/sell financial instruments. …

WP397. A comparison of LSTM and GRU architectures with novel walk-forward approach to algorithmic investment strategy

The aim of this work is to build a profitable algorithmic investment strategy on various types of assets. The algorithm is built using recurrent neural networks (LSTM and GRU) as the primary source of  signals to buy/sell financial instruments. LSTM and GRU architectures are compared in terms of obtaining the best results and beating the market. The algorithm is tested for four financial instruments (Bitcoin, Tesla, Brent Oil and Gold) on daily and hourly data frequencies. The out-of-sample period is from 1 January 2021 to 1 April 2022. A walk-forward process is responsible for training models and selecting the best model to forecast asset prices in the future. Ten model architectures with various hyperparameters are trained during each step of the walk-forward process. The model architecture with the highest Information Ratio (IR*) in the validation period is used for forecasting in the out-of-sample period. For each strategy, the performance metrics are calculated based on which the profitability of the algorithm is evaluated. At the end, a detailed sensitivity analysis with regards to the main hyperparameters is conducted. The results reveal that LSTM outperforms GRU in most of the cases and that investment strategy built based on LSTM/GRU architecture is able to beat the market only on 50% of tested cases. 


Baranochnikov Illia, Ślepaczuk Robert
deep learning recurrent neural networks algorithm trading strategy LSTM GRU walk-forward process
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