  Prediction based on Irregularly Sampled Time Series (ISTS) is of wide concern
in the real-world applications. For more accurate prediction, the methods had
better grasp more data characteristics. Different from ordinary time series,
ISTS is characterised with irregular time intervals of intra-series and
different sampling rates of inter-series. However, existing methods have
suboptimal predictions due to artificially introducing new dependencies in a
time series and biasedly learning relations among time series when modeling
these two characteristics. In this work, we propose a novel Time Encoding (TE)
mechanism. TE can embed the time information as time vectors in the complex
domain. It has the the properties of absolute distance and relative distance
under different sampling rates, which helps to represent both two
irregularities of ISTS. Meanwhile, we create a new model structure named Time
Encoding Echo State Network (TE-ESN). It is the first ESNs-based model that can
process ISTS data. Besides, TE-ESN can incorporate long short-term memories and
series fusion to grasp horizontal and vertical relations. Experiments on one
chaos system and three real-world datasets show that TE-ESN performs better
than all baselines and has better reservoir property.
