An econophysics approach to analyse uncertainty in financial markets: an application to the Portuguese stock market

In recent years there has been a closer interrelationship between several scientific areas trying to obtain a more realistic and rich explanation of the natural and social phenomena. Among these it should be emphasized the increasing interrelationship between physics and financial theory. In this field the analysis of uncertainty, which is crucial in financial analysis, can be made using measures of physics statistics and information theory, namely the Shannon entropy. One advantage of this approach is that the entropy is a more general measure than the variance, since it accounts for higher order moments of a probability distribution function. An empirical application was made using data collected from the Portuguese Stock Market.Comment: 8 pages, 2 figures, presented in the conference Next Sigma-Phi 200

Long Memory and Volatility Clustering: is the empirical evidence consistent across stock markets?

Long memory and volatility clustering are two stylized facts frequently related to financial markets. Traditionally, these phenomena have been studied based on conditionally heteroscedastic models like ARCH, GARCH, IGARCH and FIGARCH, inter alia. One advantage of these models is their ability to capture nonlinear dynamics. Another interesting manner to study the volatility phenomena is by using measures based on the concept of entropy. In this paper we investigate the long memory and volatility clustering for the SP 500, NASDAQ 100 and Stoxx 50 indexes in order to compare the US and European Markets. Additionally, we compare the results from conditionally heteroscedastic models with those from the entropy measures. In the latter, we examine Shannon entropy, Renyi entropy and Tsallis entropy. The results corroborate the previous evidence of nonlinear dynamics in the time series considered.Comment: 8 pages; 2 figures; paper presented in APFA 6 conferenc

Mutual information: a dependence measure for nonlinear time series

This paper investigates the possibility to analyse the structure of unconditional or conditional (and possibly nonlinear) dependence in financial returns without requiring the specification of mean-variance models or a theoretical probability distribution. The main goal of the paper is to show how mutual information can be used as a measure of dependence in financial time series. One major advantage of this approach resides precisely in its ability to account for nonlinear dependencies with no need to specify a theoretical probability distribution or use of a mean-variance model.Mutual information, nonlinear dependence, market efficiency

Data frequency and forecast performance for stock markets: A deep learning approach for DAX index

[EN] Due to non-stationary, high volatility, and complex nonlinear patterns of stock market fluctuation, it is demanding to predict the stock price accurately. Nowadays, hybrid and ensemble models based on machine learning and economics replicate several patterns learned from the time series. This paper analyses the SARIMAX models in a classical approach and using AutoML algorithms from the Darts library. Second, a deep learning procedure predicts the DAX index stock prices. In particular, LSTM (Long Short-Term Memory) and BiLSTM recurrent neural networks (with and without stacking), with optimised hyperparameters architecture by KerasTuner, in the context of different time-frequency data (with and without mixed frequencies) are implemented. Nowadays great interest in multi-step-ahead stock price index forecasting by using different time frequencies (daily, one-minute, five-minute, and ten-minute granularity), focusing on raising intraday stock market prices. The results show that the BiLSTM model forecast outperforms the benchmark models –the random walk and SARIMAX - and slightly improves LSTM. More specifically, the average reduction error rate by BiLSTM is 14-17% compared to SARIMAX. According to the scientific literature, we also obtained that high-frequency data improve the forecast accuracy by 3-4% compared with daily data since we have some insights about volatility driving forces.Mendes, DA.; Ferreira, N.; Mendes, V. (2023). Data frequency and forecast performance for stock markets: A deep learning approach for DAX index. Editorial Universitat Politècnica de València. 39-40. http://hdl.handle.net/10251/201760394

Linear and nonlinear models for the analysis of the relationship between stock market prices and macroeconomic and financial factors

The main objective of this paper is to assess how mutual information as a measure of global dependence between stock markets and macroeconomic factors can overcome some of the weaknesses of the traditional linear approaches commonly used in this context. One of the advantages of mutual information is that it does not require any prior assumption regarding the specification of a theoretical probability distribution or the specification of the dependence model. This study focuses on the Portuguese stock market where we evaluate the relevance of the macroeconomic and financial variables as determinants of the stock prices behaviour.nonlinear dependence, stock market, financial and macroeconomic factors

Measuring and Controlling the Chaotic Motion of Profits

The study of economic systems has generated deep interest in exploring the complexity of chaotic motions in economy. Due to important developments in nonlinear dynamics, the last two decades have witnessed strong revival of interest in nonlinear endogenous business chaotic models. The inability to predict the behavior of dynamical systems in the presence of chaos suggests the application of chaos control methods, when we are more interested in obtaining regular behavior. In the present article, we study a specific economic model from the literature. More precisely, a system of three ordinary differential equations gather the variables of profits, reinvestments and financial flow of borrowings in the structure of a firm. Firstly, using results of symbolic dynamics, we characterize the topological entropy and the parameter space ordering of kneading sequences, associated with one-dimensional maps that reproduce significant aspects of the model dynamics. The analysis of the variation of this numerical invariant, in some realistic system parameter region, allows us to quantify and to distinguish different chaotic regimes. Finally, we show that complicated behavior arising from the chaotic firm model can be controlled without changing its original properties and the dynamics can be turned into the desired attracting time periodic motion (a stable steady state or into a regular cycle). The orbit stabilization is illustrated by the application of a feedback control technique initially developed by Romeiras et al. [1992]. This work provides another illustration of how our understanding of economic models can be enhanced by the theoretical and numerical investigation of nonlinear dynamical systems modeled by ordinary differential equations