A new state–space methodology to disaggregate multivariate time series

. This article addresses the problem of disaggregating multivariate time series sampled at different frequencies using state–space models. In particular, we consider the relation between the high‐frequency and low‐frequency models, the possible loss of observability and identifiability in the latter with respect to the former, the estimation of the parameters of the low‐frequency model by maximum likelihood, and the prediction and interpolation of high‐frequency figures when only low‐frequency data are available. Since vector autoregressive moving average models are a special case of state–space models, our results are also valid for those models, but they include other models as well, like structural models. We provide a rigorous theoretical development of the aforementioned issues, including a comparison with the classical model‐based approaches, and we propose a practical methodology to disaggregate multivariate time series that is both efficient and easy to implement.