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.