Regularized Estimation of High-Dimensional Vector AutoRegressions with Weakly Dependent Innovations
This work addresses a gap in time series analysis for high-dimensional data, extending sparse regularization methods beyond Gaussian or mixing sequences to more general weakly dependent processes.
The paper tackles the problem of estimating high-dimensional vector autoregressions with weakly dependent and heavy-tailed innovations, establishing oracle properties for LASSO estimation under minimal assumptions on conditional heteroskedasticity.
There has been considerable advance in understanding the properties of sparse regularization procedures in high-dimensional models. In time series context, it is mostly restricted to Gaussian autoregressions or mixing sequences. We study oracle properties of LASSO estimation of weakly sparse vector-autoregressive models with heavy tailed, weakly dependent innovations with virtually no assumption on the conditional heteroskedasticity. In contrast to current literature, our innovation process satisfy an $L^1$ mixingale type condition on the centered conditional covariance matrices. This condition covers $L^1$-NED sequences and strong ($α$-) mixing sequences as particular examples.