Filtered derivative with p-value method for multiple change-points detection

In different applications (health, finance,...), abrupt changes on the spectral density of long memory processes provide relevant information. In this work, we concern ourself with off-line detection. However, our method is close to the sliding window which is typically a sequential analysis method. We model data by Gaussian processes with locally stationary and long memory increments. By using a wavelet analysis, one obtains a series with short memory. We compare numerically the efficiency of different methods for off-line detection of these changes, namely penalized least square estimators introduced by Bai and Perron (1998) versus a modification of the filtered derivative introduced by Basseville and Nikiforov (1993). The enhancement consists in computing the p-value of every change point and then apply an adaptive strategy. Since estimation of abrupt changes on spectral density is a specific problem, we first study a more standard model. In Section 1, we concern ourself to off-line detection of abrupt changes in the mean of independent Gaussian variables with known variance and we numerically compare the efficiency of the different estimators in this case. In Section 2, we recall the definition of Gaussian processes with locally stationary increments and the properties of their wavelet coefficients. Then, we compare the different off-line detection methods on simulated locally fBm and present some results on real data.