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HIGH AND INFINITE DIMENSIONAL MODELS IN TIME SERIES
Resumo Geral da Sessão Temática
High and infinite dimensional time series have been very popular topics in time series analysis recently. In this session, we will mainly discuss about three modelling approaches related to these topics: factor models, curve time series models and machine learning. In terms of factor models, if on one hand the joint analysis of a large number of time series enriches information about the phenomenon under study, on the other hand difficulties with the curse of dimensionality arise and variable dimension reduction techniques are in order. In this sense, factor models have proven to be a rich and important class of models, and state-of-the-art methods will be considered. Machine learning methods have more recently been adopted in the time series literature to face the challenges brought into play by high dimensional and big data related problems. Another subject that will be explored in this session is curve time series, or infinite dimensional time series, or yet functional time series. This encompasses problems where the data is curves observed over time, opposite to scalars or vectors. This approach leads to new ways of performing statistical analyses and forecasting, which will be here explored.
Nome do Palestrante 1 e Moderador / Instituição / Currículo / Título da Fala / Resumo da fala
Nome: Flavio A. Ziegelmann
Instituição: Universidade Federal do Rio Grande do Sul (UFRGS)
CV Lattes: http://lattes.cnpq.br/2060620128806238
Título: Dynamics of Financial Returns Densities: A Functional Approach for Forecasting
Resumo: We model the stochastic evolution of probability density functions (pdf's) of intraday returns over business days, in a functional time series framework. Our theoretical background relies on a paper by Bathia, Yao and Ziegelmann (Annals of Statistics, 2010). In our empirical analysis of BOVESPA index, we find evidence that the pdf's dynamic structure reduces to a vector process lying on a two-dimensional space. Our main contributions are as follows. First we provide further insight on the finite-dimensional decomposition of the curve process: it is shown that its evolution can be interpreted as a dynamic dispersion-symmetry shift. Second, we provide an application to realized volatility forecasting, with a forecasting ability comparable to HAR Realized Volatility models in the Model Confidence Set framework.
Nome do Palestrante 2 / Instituição / Currículo / Título da Fala / Resumo da fala
Nome: Marcelo C. Medeiros
CV Lattes: http://lattes.cnpq.br/1545155828572491
Título: Forecasting Inflation in Data Rich environments: the benefits of machine learning methods
Nome do Palestrante 3 / Instituição / Currículo / Título da Fala / Resumo da fala
Nome: Marc Hallin
Instituição: European Center for Advanced Research in Economics and Statistics (ECARES)
Título: Optimal dimension reduction for time series and dynamic factor models
Resumo: Dimension reduction techniques are at the core of the statistical analysis of high-dimensional observations. Whether the data are vector- or function-valued, principal component techniques, in this context, play a central role. The success of principal components in the dimension reduction problem is explained by the fact that, for any K≤p, the K first coefficients in the expansion of a p-dimensional random vector X in terms of its principal components is providing the best linear K-dimensional summary of X in the mean square sense. This optimality feature, however, no longer holds true in a time series context: principal components, when the observations are serially dependent, are losing their optimal dimension reduction property to the so-called dynamic principal components introduced by Brillinger in 1981 in the vector case and, in the functional case, their functional extension proposed by Hormann, Kidzinski and Hallin (JRSS Ser.B, 2015). Principal components similarly are central tools in the estimation of factor models: traditional principal components in the approach proposed by Stock and Watson (JASA, 2002) or Bai and Ng (Econometrica, 2002); dynamic ones for the Forni et al. (Review of Economics and Statistics, 2000). The optimal dimension reduction properties of the latter explain why, the latter, in general, are more parcimonious and perform better, under less restrictive assumptions.
Researchers and students interested in modern time series methods.
The proposed session relates to modern state of-the-art methods in time series analysis. The topics involve high-dimensional and complex functional data. As so, it becomes extremely relevant for the Brazilian statistical community.
Marc Hallin é um dos palestrantes convidados do SINAPE, e portanto sua participação nessa sessão não traria despesas adicionais. Quanto aos demais palestrantes, se houver fonte de financiamento da conferência, gostariam de usá-la. Entretanto, caso não exista tal fonte, eles financiarão suas viagens.
Flavio Augusto Ziegelmann, Marcelo Cunha Medeiros, Marc Hallin