Abstract: The statistical change-point problem is considered in a variety of settings. In particular, a number of statistical models are developed that may be applied to the problem of detecting the existence of a statistical change-point and then estimating its location in one and several dimensions. Of primary interest in the univariate case are statistical change-points in mean, variance, and multiple change-points. For the multivariate case these cases are also investigated, but also considered is the question in which dimensions the change-point occurred. New methods proposed in this dissertation answer these questions by applying a Bayesian statistical analysis on the wavelet detail coefficients after a Discrete Wavelet Transform is taken of the original time series. This new approach is shown to offer several advantages from previously known classical methods. Furthermore, through the use of random matrix dimension reduction techniques, applications to high dimensional time series are also presented. Finally, the method of Reversible Jump Markov Chain Monte Carlo is applied to the multivariate change-point problem to detect dimensional statistical change-points. Along with detailed derivations of theoretical results, numerical experiments involving both simulated and real world data will be presented.