Research accomplishments and vision

Background 

My research is focused on cutting-edge methods for Bayesian Learning and the analysis of high-frequency time series in a multidisciplinary domain spanning Machine Learning (ML), statistics, and econometrics. The increased availability of data, its growing size, the amount of detail, and the frequency at which it is collected, are perceptible and ubiquitous trends for the future. It is not surprising to expect that ML and statistical models are attracting more and more attention as fundamental technical tools for modeling, forecasting, and decision-making. Such a trend is a broad tendency, not specific to a particular domain or area, that demands adequate and reliable big and complex data analysis pipelines and methods applicable at a large scale (McAfee et al., 2012). In this framework and general view, my research spans different interconnected aspects, in particular (i) Bayesian Learning and (ii) time-series analysis with both traditional econometric tools and Machine Learning methods.

Ph.D. research

During my Ph.D., I worked in the area of high-frequency econometrics. In modern financial markets, electronically-driven trading occurs through the limit-order book system. Despite the spread of such a system, its analytics and modeling are quite complex1. In (Ntakaris, Magris, et al., 2018), we provided the first statistical analysis on the properties of inter- and cross- trade/order durations, finding an unanticipated amount of very slowly-decaying high-frequency autocorrelation in the series. Along with their remarkable non-linear dynamics, we devised the using ML methods as practical tools for predicting price dynamics. In (Magris, Kim, et al., 2017), we were the first to perform such analyses, discussing the extent to which several ML algorithms serve this scope. Importantly, we developed and published a limit-order book dataset with precomputed features for future research and experiments. The dataset received large attention, and nowadays, our results and data constitute a solid benchmark that, for more than five years, researchers all around the globe have extensively adopted. Along with the considerable potential of ML methods proved (Ntakaris, Magris, et al., 2018), in (D. T. Tran, Magris, et al., 2017), we established a new estimation and training approach based on tensor representations of the high-frequency limit-order book data, showing that such representations outperform vector-based approaches and other competing ones.

Modern market data’s high-frequency, intraday nature, opens the way to improved estimation of daily volatility and new modeling approaches. In (Magris, 2019a), I constructed on the linear form of the econo- metric Heterogeneous Autoregressive Model a non-linear extension for forecasting realized volatility measures based on the state-of-the-art Vine copula models, showing significant predictive gains over the benchmark. In (Kanniainen and Magris, 2018) high-frequency data was used to analyze the efficiency of options markets based on intraday option prices, and volatility surface dynamics around price jumps in (Magris, Barholm, and Kanniainen, 2017). All these results about the limit-order book dynamics and how new econometric and ML approaches can be applied in modeling and forecasting limit-order book data are significant and relevant. They unfolded the understanding of the complexity of modern financial markets and advanced effective approaches that practitioners can rely upon in the future. For these contributions, my doctoral thesis (Magris, 2019b) was evaluated among the best 10% in the field.

Postdoctoral research

Bayesian statistics and, in particular, Bayesian modeling have gained considerable attention due to their ability to well-generalize, avoid overfitting, and deal with uncertainties. The principal research line of my postdoctoral research was motivated by using Bayesian learning as a tool for bridging the gap between econometrics and ML. Through my doctoral research and other research in the field, it has been extensively shown that machine learning methods outperform traditional econometrics and statistical ones on a variety of tasks related to financial data forecasting. Yet, they lack the probabilistic dimension typical of econometrics methods. Econometrics models are parsimonious, well-thought, interpretable, and of desirable properties, especially from a probabilistic perspective.

In my research, I showed that Bayesian learning techniques can bridge this gap and engage ML models with the probabilistic dimension that they typically lack of, that, conversely, characterizes the econometric practice. In (Magris, Shabani, and Iosifidis, 2023), we provided a first analysis in this regard, showing that a Bayesian framework is of high potential with respect to standard gradient-descent optimization. Besides providing gains in terms of out-of-sample performance, our Bayesian network is interpretable, and the trained posterior distribution allows for a new set of statistical tools to be applied, in support of risk- aware financial decision-making. The modern estimation of Bayesian neural networks is generally performed through the use of Variational inference. Variational Inference (VI) is an approximate statistical method that turns the Bayesian integration problem into a simpler optimization problem, significantly easing the inference process. The adoption of VI principles at a large scale on high-dimensional ML models is a cutting- edge area of research. Limitations in current VI-based optimizers, and their dependency on architectures requiring automatic differentiation, pointed my research toward alternative gradient-free approaches. Based on the recent literature in statistics, in (Magris, Shabani, and Iosifidis, 2022c) I exploited the natural and mean parametrization of exponential family distribution to develop a new gradient-free optimizer, boosted by efficient natural-gradient computations that do not require the online inversion and computation of large Fisher matrices. Yet to guarantee positive-definite constraints on the estimated covariance matrix, I developed a second gradient-free optimizer, based on the theory of manifold optimization (Magris, Shabani, and Iosifidis, 2022b). On a variety of financial datasets, with traditional econometric models and embedding modern machine learning architectures, I proved the validity of the above approaches, confirming that engaging machine learning with Bayesian inference principles can bridge the gap with econometric modeling practice. These significant contributions were included in my field review (Magris and Iosifidis, 2023), presented at three non-technical conferences, and as a dedicated lecture at a summer school (details in the CV). My most recent contribution (Lillelund, Magris, and Pedersen, 2023) involves the application of Bayesian learning in the context of survival data analysis, with a positive attitude towards collaborative research in new areas.

Besides the above results in VI, I continued my earlier research on high-frequency datasets. With multi- variate analyses involving limit-order book data of multiple stocks, we showed that the dynamic of the prices is tied and, in a certain sense, synchronized (Shabani, Magris, et al., 2023). For the first time, we show that epochs of synchronization are predictable and can accordingly support the risk management of financial portfolios. Moreover, in (Shabani, D. T. Tran, et al., 2022), we established that for the task of modeling and predicting price changes, the temporal dimension of the regressors, besides their qualitative interpretation, plays a major role, so the inclusion of temporal attention masks has a remarkable impact on forecasts. In a purely econometric context, in (Kanniainen and Magris, 2021) developed a non-parametric approach for jump detection from intraday options’ quotes, and in (Magris and Iosifidis, 2021) discussed a Bayesian unit root testing approach based on Bayes factors.

Final remarks

Overall, I extensively contributed to the understanding of the functioning of high-frequency financial markets, providing feasible modeling approaches and reliable tools for their forecasting. At the same time, I developed two Bayesian optimizers for performing VI in high-dimensional models. I showed how ML research can go hand-in-hand with econometrics, through the use of the Bayesian framework. Both of them, represent significant, non-trivial, and relevant advances in the literature.