  Cooperation between different data owners may lead to an improvement in
forecast quality - for instance by benefiting from spatial-temporal
dependencies in geographically distributed time series. Due to business
competitive factors and personal data protection questions, said data owners
might be unwilling to share their data, which increases the interest in
collaborative privacy-preserving forecasting. This paper analyses the
state-of-the-art and unveils several shortcomings of existing methods in
guaranteeing data privacy when employing Vector Autoregressive (VAR) models.
The paper also provides mathematical proofs and numerical analysis to evaluate
existing privacy-preserving methods, dividing them into three groups: data
transformation, secure multi-party computations, and decomposition methods. The
analysis shows that state-of-the-art techniques have limitations in preserving
data privacy, such as a trade-off between privacy and forecasting accuracy,
while the original data in iterative model fitting processes, in which
intermediate results are shared, can be inferred after some iterations.
