Time varying estimation of regression model using ols estimates

We know that in general linear model the YN × 1 = X(N×K) β(k×1) + eN × 1 OLS estimator of parametric vector β is and it gives constant estimates for the entire study period. In this context we will make an attempt to propose a method of computing time varying estimates using OLS estimates of different subsets (s) with equal size (n) of the given data. Validity of the proposed method is ascertained by comparing with usual OLS method through numerical examples using the concept of minimum residual sum of squares.