On the ARCH model with stationary liquidity

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Journal Title
Journal ISSN
Volume Title
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
Date
2021-02
Major/Subject
Mcode
Degree programme
Language
en
Pages
Series
METRIKA
Abstract
The classical ARCH model together with its extensions have been widely applied in the modeling of financial time series. We study a variant of the ARCH model that takes account of liquidity given by a positive stationary process. We provide minimal assumptions that ensure the existence and uniqueness of the stationary solution for this model. Moreover, we give necessary and sufficient conditions for the existence of the autocovariance function. After that, we derive an AR(1) characterization for the stationary solution yielding Yule–Walker type quadratic equations for the model parameters. In order to define a proper estimation method for the model, we first show that the autocovariance estimators of the stationary solution are consistent under relatively mild assumptions. Consequently, we prove that the natural estimators arising out of the quadratic equations inherit consistency from the autocovariance estimators. Finally, we illustrate our results with several examples and a simulation study.
Description
Keywords
ARCH model, Consistency, Estimation, Stationarity
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Citation
Voutilainen , M , Ilmonen , P , Torres , S , Tudor , C & Viitasaari , L 2021 , ' On the ARCH model with stationary liquidity ' , METRIKA , vol. 84 , no. 2 , pp. 195-224 . https://doi.org/10.1007/s00184-020-00779-x