A Scale-space Approach For Detecting Non-stationarities In Time Series And Its Application

The change-point detection is an active research field recently, and has been applied extensively in many field of study which includes economics, finance, biological, atmosphere, signal processing and so on. The presented method called Significant Non-stationarities, represents an exploratory tool for identifying significant changes in the mean, the variance, and the first-lag autocorrelation coefficient of a time series. The changes are detected on different time scale. In this thesis two aspects are studied. 1) Test statistics expressed as ratios of quadratic forms. Firstly, the mean, the variance, and the fist-lag autocovariance test statistics be translated to a ratio of quadratic forms. And then, the saddlepoint method gives the cumulative distribution function and the probability density function of the test statistics. 2) The number and location of changes in different time scale. In the significance map, significance increases or decreases in a parameter are depicted as black or white pixels respectively. A real change is usually detected for more than one scale and/or test statistic. If a change is detected only at one time point for one time scale, it means some spurious detections occur.The performance of the given method is thoroughly studied by simulations in terms of observed significance level and power. Including a real data set, are studied. The examples illustrate that it is important to carry out the analysis on several time horizons.