Sparse and debiased Lasso estimation and statistical inference for long time series via divide-and-conquer

To tackle long time series with high-dimensional covariates and dependent non-Gaussian errors, we consider the divide-and-conquer strategy and develop a class of sparse and debiased Lasso estimators. To alleviate the serial correlation in long time series data, we sequentially split the long time series into several subseries and apply a generalized penalized least squares (GLS) method for linear regression models in each subseries allowing stationary covariates and AR(q) error processes. To make accurate statistical inference, we further propose a sparse and debiased estimator and investigate its asymptotic properties. By constructing a pseudo-response variable using a squared loss transformation, the proposed GLS method is extended to a unified M-estimation framework including Huber and quantile regression models to reduce computational burden. Extensive simulations validate theoretical properties and demonstrate that our proposed estimators have better performance than some existing methods. The proposed estimators are applied to Beijing Air Quality Data and NIFTY 50 Index Data to illustrate their validity and feasibility. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.