||In our research, we focus on locally stationary models exploiting wavelet analysis to fitting time varying autoregressive models. We develop a wavelet time-varying vector error correction model to unravel short and long-term dynamics of economic systems. Firstly, we critically revise the current literature of time-varying models, as these methods are often ailed by the problem of non-stationary time series. The proposed model overcomes the non-stationarity issue by assuming only locally stationary time-series. Since the framework of vector autoregressive models is well known, we go a step further and enhance this methodology with a framework working in time and frequency. Moreover, we provide the economic applications such as a setup for an economy that may be compared with Bayesian and other time-varying models. The wavelet approach provides a novel way of fitting the time-varying autoregressive model without prior-beliefs, thus potentially making current findings in the literature more robust or potentially challenging them. Furthermore, the model, as member of the family of VAR (VECM), may serve for forecasts and shock responses analyses.