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Quantile Regression for Location‐Scale Time Series Models with Conditional Heteroscedasticity
Author(s) -
Noh Jungsik,
Lee Sangyeol
Publication year - 2016
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12199
Subject(s) - heteroscedasticity , mathematics , autoregressive model , quantile regression , asymptotic distribution , quantile , autoregressive conditional heteroskedasticity , estimator , statistics , star model , conditional variance , econometrics , autoregressive–moving average model , series (stratigraphy) , time series , autoregressive integrated moving average , volatility (finance) , paleontology , biology
This paper considers quantile regression for a wide class of time series models including autoregressive and moving average (ARMA) models with asymmetric generalized autoregressive conditional heteroscedasticity errors. The classical mean‐variance models are reinterpreted as conditional location‐scale models so that the quantile regression method can be naturally geared into the considered models. The consistency and asymptotic normality of the quantile regression estimator is established in location‐scale time series models under mild conditions. In the application of this result to ARMA‐generalized autoregressive conditional heteroscedasticity models, more primitive conditions are deduced to obtain the asymptotic properties. For illustration, a simulation study and a real data analysis are provided.