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Recovering missing values in time series is critical when performing time series analysis. And the blackouts issue studied in this paper, described as losing all the data during a certain period, is among the most urgent issues due to its devastating impact on service quality, and is challenging because of the absence of coevolving data sequences for reference. As a result, many existing approaches that rely on data from other coevolving sequences for missing value recovery are infeasible in handling blackouts. To address the issue, this work proposes a novel Hankel matrix factorization approach, HKMF-T, to recover missing values during blackouts for tagged time series, where a tagged time series consists of a data sequence and a corresponding tag sequence. Motivated by real-world observations, HKMF-T decomposes the data sequence into two components: 1) an internal, slowly-varying smooth trend, and 2) external impacts indicated by the tag sequence. By transforming a partially observed data sequence into a corresponding Hankel matrix, we learn the above two components and estimate the missing values under a unified framework of Hankel matrix factorization. Extensive experiments are conducted to evaluate the practical performance of HKMF-T on real-world data sets. And the results suggest HKMF-T outperforms the baseline approaches for blackouts with long durations. [ABSTRACT FROM AUTHOR]