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Multivariate Markov Chains: When Categorizing Costs You Accuracy: Trade-offs in Applying Multivariate Markov Chains
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Resumo(s)
Multivariate Markov Chains (MMCs) are increasingly explored as tools for modeling
and forecasting categorical time series. However, their application to real-world data
typically requires an initial discretization step, as most available data is continuous in
nature. This transformation raises an essential trade-off: while discretization allows
the use of MMCs and offers potential advantages in terms of model interpretability and
robustness, it can also degrade performance by discarding relevant information from
the original signal. This thesis investigates the consequences of discretizing continuous
variables for the purpose of applying MMCs to forecasting tasks. Through a comprehensive Monte Carlo simulation framework, we assess how different discretization
strategies — including Equal Width, Equal Frequency, and K-means — affect both information retention and forecast accuracy. Comparisons are made between discretized
traditional linear models (AR and VAR) and their Markov-based counterparts (MC and
MTD-Probit MMC), across varying levels of autocorrelation, bin number, and forecast
horizons. Forecast performance is evaluated using RMSE, while information loss is
quantified through entropy-based metrics including Mutual Information, Information
Loss Ratio (ILR), and Information Change Ratio (ICR). The results highlight that while
more refined discretizations can reduce information loss, they do not necessarily translate into improved forecasting accuracy. The findings reveal a fundamental limitation:
even under optimized discretization conditions, MMCs rarely outperform continuous
models in terms of predictive accuracy. Nonetheless, the framework developed here
provides a valuable basis for future research on discretization-aware model design
and multivariate time series analysis. These insights are particularly relevant for researchers considering MMCs in real-world forecasting applications, as they underscore
the importance of carefully balancing model interpretability with the potential loss of
predictive performance due to discretization.
Descrição
Dissertation presented as the partial requirement for obtaining a Master's degree in Data Science and Advanced Analytics, specialization in Data Science
Palavras-chave
Multivariate Markov Chains Time Series Forecasting Discretization Information Loss SDG 4 - Quality education SDG 8 - Decent work and economic growth SDG 9 - Industry, innovation and infrastructure SDG 17 - Partnerships for the goals