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Structures such as bridges, offshore platforms, wind power facilities, and drilling rigs generate a corresponding periodic structural response under cyclic loads such as solar radiation, tides and sea-land breeze. Data recovery and forecasting are major parts of the work to ensure structural safety using periodic structural health monitoring data. In this context, a combined method of autoregressive (AR) model and matrix factorization (MF) method is presented to reaching the tasks of data imputation and prediction. The combined method with a graph-based temporal regularizer can well capture the cyclic characteristics and random character. The verification of the method is conducted using an in-situ temperature monitoring dataset of a high-speed railway steel bridge. The application of the method for both data recovery and forecasting with structured missing entries is carried out, which indicates the combined method owns outstanding performance in accurately recover missing entries and making predictions. In the last part, the analysis of rank order and length of time lag is made to show its influence on imputation accuracy. [ABSTRACT FROM AUTHOR]