Local Adaptive Estimation For Nonstationary Time Series

We propose a method to analyze possibly nonstationary time series by adaptively dividing time series into finite number of intervals and estimating locally whether observable time series are stationary in that intervals. We suggest a test statistics based on maximum likelihood estimation (MLE) to test null hypothesis that observable time series are nearly stationary over the chosen interval against the alternative, that there is a change point in the interval. Different simulations were used to study the distribution of statistic.