  Periodicity detection is an important task in time series analysis, but still
a challenging problem due to the diverse characteristics of time series data
like abrupt trend change, outlier, noise, and especially block missing data. In
this paper, we propose a robust and effective periodicity detection algorithm
for time series with block missing data. We first design a robust trend filter
to remove the interference of complicated trend patterns under missing data.
Then, we propose a robust autocorrelation function (ACF) that can handle
missing values and outliers effectively. We rigorously prove that the proposed
robust ACF can still work well when the length of the missing block is less
than $1/3$ of the period length. Last, by combining the time-frequency
information, our algorithm can generate the period length accurately. The
experimental results demonstrate that our algorithm outperforms existing
periodicity detection algorithms on real-world time series datasets.
