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High-dimensional time series data exist in numerous areas such as finance,genomics, healthcare, and neuroscience. An unavoidable aspect of all suchdatasets is missing data, and dealing with this issue has been an importantfocus in statistics, control, and machine learning. In this work, we consider ahigh-dimensional estimation problem where a dynamical system, governed by astable vector autoregressive model, is randomly and only partially observed ateach time point. Our task amounts to estimating the transition matrix, which isassumed to be sparse. In such a scenario, where covariates are highlyinterdependent and partially missing, new theoretical challenges arise. Whiletransition matrix estimation in vector autoregressive models has been studiedpreviously, the missing data scenario requires separate efforts. Moreover,while transition matrix estimation can be studied from a high-dimensionalsparse linear regression perspective, the covariates are highly dependent andexisting results on regularized estimation with missing data fromi.i.d.~covariates are not applicable. At the heart of our analysis lies 1) anovel concentration result when the innovation noise satisfies the convexconcentration property, as well as 2) a new quantity for characterizing theinteractions of the time-varying observation process with the underlyingdynamical system.

Missing Data in Sparse Transition Matrix Estimation for Sub-Gaussian Vector Autoregressive Processes