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Mixed effect models for absolute log returns of ultra high frequency data
Author(s) -
Haug Stephan,
Czado Claudia
Publication year - 2006
Publication title -
applied stochastic models in business and industry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.413
H-Index - 40
eISSN - 1526-4025
pISSN - 1524-1904
DOI - 10.1002/asmb.614
Subject(s) - estimator , econometrics , statistics , volatility (finance) , mathematics , proxy (statistics) , realized variance
Considering absolute log returns as a proxy for stochastic volatility, the influence of explanatory variables on absolute log returns of ultra high frequency data is analysed. The irregular time structure and time dependency of the data is captured by utilizing a continuous time ARMA( p,q ) process. In particular, we propose a mixed effect model class for the absolute log returns. Explanatory variable information is used to model the fixed effects, whereas the error is decomposed in a non‐negative Lévy driven continuous time ARMA( p,q ) process and a market microstructure noise component. The parameters are estimated in a state space approach. In a small simulation study the performance of the estimators is investigated. We apply our model to IBM trade data and quantify the influence of bid‐ask spread and duration on a daily basis. To verify the correlation in irregularly spaced data we use the variogram, known from spatial statistics. Copyright © 2006 John Wiley & Sons, Ltd.