Topics in computational statistics with applications in finance

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2023-12

Authors

Rotiroti, Frank

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The dissertation comprises two parts, each commenced with an introduction to the principal ideas and methods therein: The first part concerns topics related to marginal and intractable likelihood estimation, focusing on the estimation of a density function at a particular point. In particular, we present a Monte Carlo estimator based on the Fourier integral theorem. The second part concerns Bayesian approaches to state-space models with applications in finance. First, we introduce a Bayesian vector autoregression to examine strategic asset allocation for long-run investors, given estimation risk and the choice of multiple risky assets. Then, we devise a variation on the Bayesian additive regression trees (BART) framework to incorporate time-dependent data, as well as stochastic volatility (SV), before applying this approach to the problem of predicting a firm’s stock return with observable firm characteristics. Joining the two parts is an interlude, which describes an approach to the particle filtering of hidden Markov models which reverses the standard sampling-resampling perspective and, along with several simulation studies, includes an example involving an SV model.

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