The research group in Mathematical Statistics and Data Science studies advanced methods and models for analysing and representing data. We employ probability theory and stochastic processes to rigorously model uncertainty and randomness, and abstract and linear algebra to understand the structure of statistical models and the relationships between their parameters.
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Pauliina Ilmonen Professor Multivariate extreme values, functional data analysis, cancer epidemiology |
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Lasse Leskelä Professor Mathematical statistics, probability theory, network analysis |
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Kaie Kubjas Associate Professor Algebraic statistics |
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Vanni Noferini Associate Professor Network analysis, random matrix theory |
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Jukka Kohonen University Lecturer Statistics, combinatorics |
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Pekka Pere University Lecturer Statistics |
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Jonas Tölle Senior University Lecturer Stochastic processes, probability theory |
Recovering the latent efficient price from limit order book data is a fundamental challenge in econometrics, since the price that price discovery aims to reveal is never directly observed. This thesis studies whether statistical methods can reliably recover the latent price, and under what conditions one approach outperforms another. The analysis is carried out in a Monte Carlo simulation framework in which the true efficient price is known by construction, allowing a direct comparison of estimation accuracy. The data generating process incorporates the empirically relevant features of market microstructure. A driftless Brownian motion drives the latent price, order flow follows a persistent AR(1) process with linear price impact, and microstructure noise is state-dependent and heteroskedastic. Two estimators are compared across three microstructure regimes: a misspecified linear Kalman filter and a nonlinear XGBoost model. The Kalman filter performs better when distortions are mild, reacting to directional price changes roughly 0.3 seconds faster, whereas XGBoost achieves up to 48% lower mean squared error in the high-noise regime by capturing nonlinear order flow patterns the filter cannot represent. The framework is then extended to a multi-ETF setting in which three funds with different liquidity profiles track the same underlying index. Cross-asset information improves XGBoost uniformly across all ETFs, while the Kalman filter responds asymmetrically, improving for the less liquid ETFs but deteriorating for the most liquid one. The two estimators converge to near-identical accuracy once cross-asset information is available. Taken together, the results suggest that efficient price recoverability is regime- and specification-dependent, with implications for estimator selection and the design of cross-ETF statistical arbitrage strategies.
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