Recently there has been considerable focus on methods that enable time varying estimation of parameters in econometric models in the presence of, possibly stochastic, structural change. An interesting strand of this literature dispenses with the, computationally expensive and theoretically unclear, standard Bayesian estimation methods in favour of kernel estimation. Giraitis, Kapetanios and Yates (2014) provide theoretical, Monte Carlo and empirical results in favour of this approach. In this paper we extend that strand of the literature to the case of large dimensional datasets and perhaps the most commonly explored problem of covariance estimation. We combine kernel estimation with fixed coefficient estimation methods for large dimensional covariance matrices. We provide theoretical results that allow both stochastic structural change and hold under weaker conditions than usually assumed. Both extensions are novel in the literature. We carry out extensive Monte Carlo analysis that illustrates clearly the utility of our methods and provide a brief but illustrative empirical application in the context of forecasting macroeconomic data. Joint with Yiannis Dendramis (Athens University of Economics and Business) and Liudas Giraitis (Queen Mary University of  London).