Penalized multiply robust estimation in high-order autoregressive processes with missing explanatory variables

Multiply robust estimation with missing data is considered as an important field in statistics, which incorporates information by weighting multiply candidate models and loosens the requirement of the model specification. Nevertheless, in high-dimensional cases one more flexible hypothesis is the "true structure"beyond the correct model. In this paper, we study the parametric estimation for high-order autoregressive processes with a lagged-dependent binary explanatory variable that is missing at random (MAR). Based on the "true structure"specification, we propose a penalized multiply robust estimation equation in the presence of multiply candidate model sets. The selecting criterion for optimal tuning parameters is modified for the model identification with incomplete data. We validate that our tuning criterion can correctly distinguish the true autoregressive coefficients from zero asymptotically, the estimators of population parameters enjoy the oracle properties as well. Some simulations are carried out and we apply the method to fit the model for the U.S. Industrial Production Index data and produce out-of-sample forecasts to confirm the rationality of results. (C) 2021 Elsevier Inc. All rights reserved.