Analysis of nonuniform DAR(1) processes with mismatched explanatory variables

While most existing methods assume uniformly sampled time series, real-world applications-particularly in medical and financial domains-frequently encounter irregular observation intervals and mismatched covariates. Typical examples include asynchronous vital sign recordings in the PhysioNet 2019 sepsis dataset and temporal mismatches caused by non-synchronized trading schedules in financial markets. To address these challenges, we propose a novel nonuniform double first-order autoregressive (DAR(1)) model that explicitly incorporates mismatched explanatory variables. Unlike conventional approaches such as last value carried forward (LVCF) or interpolation methods, our framework employs a kernel-weighted quasi-maximum exponential likelihood (QMEL) estimator that systematically accounts for temporal discrepancies through time-distance-based observation weighting. We establish the theoretical validity of our approach by deriving the asymptotic properties of the proposed estimator. Extensive simulation studies demonstrate the superior performance of our method compared to existing alternatives. Empirical validation using both Shanghai Stock Exchange and S&P 500 datasets further confirms the practical utility of our framework. To the best of our knowledge, this work represents the first comprehensive solution for handling mismatched covariates within a DAR(1) framework, thereby addressing a significant gap in time series analysis methodology.