  Time series prediction with missing values is an important problem of time
series analysis since complete data is usually hard to obtain in many
real-world applications. To model the generation of time series, autoregressive
(AR) model is a basic and widely used one, which assumes that each observation
in the time series is a noisy linear combination of some previous observations
along with a constant shift. To tackle the problem of prediction with missing
values, a number of methods were proposed based on various data models. For
real application scenarios, how do these methods perform over different types
of time series with different levels of data missing remains to be
investigated. In this paper, we focus on online methods for AR-model-based time
series prediction with missing values. We adapted five mainstream methods to
fit in such a scenario. We make detailed discussion on each of them by
introducing their core ideas about how to estimate the AR coefficients and
their different strategies to deal with missing values. We also present
algorithmic implementations for better understanding. In order to
comprehensively evaluate these methods and do the comparison, we conduct
experiments with various configurations of relative parameters over both
synthetic and real data. From the experimental results, we derived several
noteworthy conclusions and shows that imputation is a simple but reliable
strategy to handle missing values in online prediction tasks.
