Tight risk bound for high dimensional time series completion

Initially designed for independent datas, low-rank matrix completion was successfully applied in many domains to the reconstruction of partially observed high-dimensional time series. However, there is a lack theory support application these methods dependent datas. In this paper, we propose general model multivariate, We show that least-square method with rank penalty leads error same order as Moreover, when series has some additional properties such periodicity or smoothness, rate can actually be faster than case.