TY - JOUR
T1 - Functional GARCH models
T2 - The quasi-likelihood approach and its applications
AU - Cerovecki, Clément
AU - Francq, Christian
AU - Hörmann, Siegfried
AU - Zakoïan, Jean Michel
PY - 2019/4/1
Y1 - 2019/4/1
N2 - The increasing availability of high frequency data has initiated many new research areas in statistics. Functional data analysis (FDA) is one such innovative approach towards modelling time series data. 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 currently takes a significant proportion of trading volumes. Recently, articles on functional versions of the famous ARCH and GARCH models have appeared. 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. In this paper, we promote an alternative quasi-likelihood approach, for which we derive consistency and asymptotic normality results. We support the relevance of our approach by simulations and illustrate its use by forecasting realised volatility of the S&P100 Index.
AB - The increasing availability of high frequency data has initiated many new research areas in statistics. Functional data analysis (FDA) is one such innovative approach towards modelling time series data. 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 currently takes a significant proportion of trading volumes. Recently, articles on functional versions of the famous ARCH and GARCH models have appeared. 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. In this paper, we promote an alternative quasi-likelihood approach, for which we derive consistency and asymptotic normality results. We support the relevance of our approach by simulations and illustrate its use by forecasting realised volatility of the S&P100 Index.
KW - Functional QMLE
KW - Functional time series
KW - High-frequency volatility models
KW - Intraday returns
KW - Stationarity of functional GARCH
UR - http://www.scopus.com/inward/record.url?scp=85061362787&partnerID=8YFLogxK
U2 - 10.1016/j.jeconom.2019.01.006
DO - 10.1016/j.jeconom.2019.01.006
M3 - Article
AN - SCOPUS:85061362787
SN - 0304-4076
VL - 209
SP - 353
EP - 375
JO - Journal of Econometrics
JF - Journal of Econometrics
IS - 2
ER -