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Semiparametric time series models with log-concave innovations: maximum likelihood estimation and its consistency. (English) Zbl 1378.62061

Summary: 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 FTSE100 index.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G32 Statistics of extreme values; tail inference
62G20 Asymptotic properties of nonparametric inference
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