Iteratively reweighted adaptive lasso for conditional heteroscedastic time series with applications to AR-ARCH type processes

Due to the increasing impact of big data, shrinkage algorithms are of great importance in almost every area of statistics, as well as in time series analysis. In current literature the focus is on lasso type algorithms for autoregressive time series models with homoscedastic residuals. In this paper we present an iteratively reweighted adaptive lasso algorithm for the estimation of time series models under conditional heteroscedasticity in a high-dimensional setting. We analyse the asymptotic behaviour of the resulting estimator that turns out to be significantly better than its homoscedastic counterpart. Moreover, we discuss a special case of this algorithm that is suitable to estimate multivariate AR-ARCH type models in a very fast fashion. Several model extensions like periodic AR-ARCH or ARMA-GARCH are discussed. Finally, we show different simulation results and an application to electricity price and load data.