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

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

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Article ID: iaor201523752
Volume: 42
Issue: 1
Start Page Number: 1
End Page Number: 31
Publication Date: Mar 2015
Journal: Scandinavian Journal of Statistics
Authors:
Keywords: statistics: distributions, time series: forecasting methods
Abstract:

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.

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