Semiparametric Time Series Models with Log-concave Innovations: Maximum Likelihood Estimation and its Consistency

Yining Chen

Scandinavian Journal of Statistics, 2015, vol. 42, issue 1, 1-31

Abstract: type="main" xml:id="sjos12092-abs-0001"> We study semiparametric time series models with innovations following a log-concave distribution. We propose a general maximum likelihood framework that allows us to estimate simultaneously the parameters of the model and the density of the innovations. This framework can be easily adapted to many well-known models, including autoregressive moving average (ARMA), generalized autoregressive conditionally heteroscedastic (GARCH), and ARMA-GARCH models. Furthermore, we show that the estimator under our new framework is consistent in both ARMA and ARMA-GARCH settings. We demonstrate its finite sample performance via a thorough simulation study and apply it to model the daily log-return of the FTSE 100 index.

Date: 2015
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