[eng] We propose the multivariate representation of univariate and bivariate (possibly nonstationary) periodic models as a benchmark for the imposition of common periodic correlation (CPC) feature restrictions to obtain parameter parsimony. CPCs are short-run common dynamic features that co-vary across the different days of the week and possibly also across weeks and that can be common across different time series. We also show how periodic models can be used to describe interesting dynamic links in the interaction between stock and flow variables. We apply the proposed modeling framework to a dataset of daily arrivals and departures in airport transit data