Nonlinear dynamic factor models

Giudice, Gianluca (2022) Nonlinear dynamic factor models. PhD thesis, London School of Economics and Political Science.

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Abstract

This thesis discusses latent variable models with the aim of uncovering hidden structure in multi-dimensional data. In rich data settings, dimension reduction has made latent variable methods, such as Dynamic Factor Models, extremely popular. Nonetheless, the dynamics of the factors have in most cases been modelled as independent and identically distributed (i.i.d.) white noise even though many financial and economic variables exhibit conditional heteroskedasticity, i.e., their variances conditional on the past evolve with time. This feature, modelled in the literature by GARCH models, has been applied to factor analysis either in the finite n case or by use of two-step estimators, producing inefficient results. In the first chapter, we show that when n ! 1, estimators for the latent factors and their conditional variance are, indeed, consistent. First, we convert the model in state-space form explicitly taking into account heteroskedasticity. Subsequently, we apply the Kalman filter to jointly estimate the parameter via the Expectation Conditional Maximization Either algorithm (ECME). This version of the EM replaces some of the steps which conditionally maximize the expected complete-data log-likelihood, with steps that maximize the real prediction-error likelihood, thus dealing with the lack of closed-form solution for the GARCH parameters. We then propose further modifications to the original model, introducing potential Dynamic Conditional Correlation (DCC) dynamics in the factors and a time-varying volatility for the observation equation disturbances. These extensions are subsequently assessed empirically, in the context of portfolio allocation and the economically relevant Growth at Risk (GaR). Finally, when the data dimension is limited, a Multi-Output Gaussian Process with Semiparametric Latent Factor structure can provide an extremely valuable opportunity to explore unobserved states in a multivariate setting. These non-linear models offer a novel and efficient approach to estimate the causal effect of interventions in time. As such, we analyse whether the early and intense vaccination campaign introduced in the UK affected the number of deaths and level of contagiousness of Covid-19 in the first semester of 2021.

Item Type:	Thesis (PhD)
Additional Information:	© 2022 Gianluca Giudice
Library of Congress subject classification:	Q Science > QA Mathematics
Sets:	Departments > Statistics
Supervisor:	Barigozzi, Matteo and Kalogeropoulos, Kostas
URI:	http://etheses.lse.ac.uk/id/eprint/4495

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