Bayesian mixed-frequency vector autoregressions (MF-VARs) are commonly used to produce timely and high-frequency estimates of low-frequency variables. A typical application uses quarterly data on output, for a given country, and monthly indicator data to produce monthly estimates of national output. But, when working at subnational levels, data limitations preclude the use of standard MF-VARs. The frequency mismatch is more complicated, key variables can have missing data, and release delays can be substantial. In this chapter, we develop a novel MF-VAR that addresses all these issues and use it to produce historical estimates of subregional output growth in the UK. The model combines information in the annual subregional data (when available) with data from the UK regions and the UK as a whole. The model is estimated using variational Bayesian methods with shrinkage priors, reflecting the “big data” setup. We use our model to produce a new database of quarterly estimates of subregional GVA growth back to the 1960s, that importantly, because the MF-VAR imposes temporal and cross-sectional restrictions, is consistent with those official data that do exist. We illustrate the use of these new estimates by showing how they can be used to characterize the considerable heterogeneity in subregional business cycle dynamics in the UK and contribute to our understanding of regional economic resilience.