Critical Overview of Privacy-Preserving Learning in Vector Autoregressive Models for Energy Forecasting

Cooperation between different data owners may lead to an improvement of forecasting skill by, for example, taking advantage of spatio-temporal dependencies in geographically distributed renewable energy time series. Due to business competitive factors and personal data protection, these 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. Mathematical proofs and numerical analysis are conducted to evaluate existing privacy-preserving methods divided into three categories: 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 iterative {fitting} processes in which intermediate results are shared can be exploited so that the original data can be inferred after some iterations.