  This paper focuses on the problem of semi-supervised domain adaptation for
time-series forecasting, which is underexplored in literatures, despite being
often encountered in practice. Existing methods on time-series domain
adaptation mainly follow the paradigm designed for the static data, which
cannot handle domain-specific complex conditional dependencies raised by data
offset, time lags, and variant data distributions. In order to address these
challenges, we analyze variational conditional dependencies in time-series data
and find that the causal structures are usually stable among domains, and
further raise the causal conditional shift assumption. Enlightened by this
assumption, we consider the causal generation process for time-series data and
propose an end-to-end model for the semi-supervised domain adaptation problem
on time-series forecasting. Our method can not only discover the Granger-Causal
structures among cross-domain data but also address the cross-domain
time-series forecasting problem with accurate and interpretable predicted
results. We further theoretically analyze the superiority of the proposed
method, where the generalization error on the target domain is bounded by the
empirical risks and by the discrepancy between the causal structures from
different domains. Experimental results on both synthetic and real data
demonstrate the effectiveness of our method for the semi-supervised domain
adaptation method on time-series forecasting.
