See for instance PARMA Models with Applications in R, Dudek et al (2015), which explains how Periodic autoregressive–moving-average models (periodic ARMA models, PARMA models) are used to model non-stationary time series with periodic structure. The book aims to provide appropriate tools for the complete analysis of periodic time series using PARMA modelling and to popularize this approach among non-specialists.
In addition, there is Periodic Autoregressive Time Series Models in R: The partsm Package by Lopez-Lacalle (2005) that introduces the package and references:
Franses, P. and Paap, R. (2004), Periodic Time Series Models, Advanced
Texts in Econometrics. Oxford University Press
See also Chapter 17 'Periodic VAR Processes and Intervention Models' in New Introduction to Multiple Time Series Analysis by Helmut Lutkepohl (2005), which discusses time-varying coefficients for multivariate time series, and co-integrated VAR models in particular.
From an applied perspective, see Forecasting with Prediction Intervals for periodic ARMA Models by Anderson et al (2013) on prediction with further references.