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Title: Functional GARCH models Authors:  Clement Cerovecki - Univ libre de Bruxelles (Belgium) [presenting]
Siegfried Hormann - Universite Libre de Bruxelles (Belgium)
Christian Francq - CREST and University Lille III (France)
Jean-Michel Zakoian - CREST (France)
Abstract: Increasing availability of high frequency data has triggered many new research areas in statistics. Functional data analysis (FDA) is one of these disciplines. In FDA densely observed data are transformed into curves and then each (random) curve is considered as one data object. A natural, but still relatively unexplored context for FDA methods is related to financial data, where high-frequency trading nowadays takes a significant proportion of trading volumes. Recently, articles on functional versions of the famous ARCH and GARCH models have been brought fourth. Due to their technical complexity, existing estimators of the underlying functional parameters are moment based, an approach which is known to be relatively inefficient in this context. We promote quasi likelihood approaches. We focus on a finite dimensional and hence feasible framework which allows a realistic practical implementation. Moreover, we can go beyond consistency results and are able to obtain asymptotic normality of the estimators. We support the superiority of our approach by simulations and illustrate its use by forecasting realized volatility of the S\&P100 market index.