Rate-distortion formulation is the information-theoretic approach to the study of signal encoding systems. Since a more general approach to model the nonstationarity exhibited by real-world signals is to use appropriately fitted time varying autoregressive (TVAR) models, we have investigated the rate-distortion function for the class of time varying nonstationary signals. In this study, we present formulations of the rate-distortion function for the Gaussian TVAR processes. The rate-distortion function can serve as an information-theoretic bound on the performance achievable by source encoding techniques when the processing signal is represented exclusively by a Gaussian TVAR model.