Change-point problem and bootstrap

Nonparametric estimation of structural change points in volatility models for time series

“…In testing hypothesis H 0 : T =0 versus H 1 : T = 0, where T = 2 2 − 2 1 , the advantage of using factor (k=T (1 − k=T )) 1=2− with 0 6 6 1=2 is that V k is sensitive with respect to the contiguous alternative T ∼ T −1=2 (see Corollary 2.2 below, or Cs orgő and Horvà ath, 1997; Antoch and Hu skovà a, 1995). We can use both statistics, V k andk( ), to deal with tests and estimates of change points.…”

Detecting the presence of insider trading via structural break tests

“…To gain further insight on the timing of these late rejections and see their statistical reliability we have also computed 95% confidence intervals using the bootstrap method described in Antoch et al (1995). The results suggest that from these 38 potential cases there are 4 cases in which the confidence interval indicates that the rejection is right before the announcement.…”

“…Theorems 1 and 2 of Antoch et al (1995) detail the consistency and the limiting distribution of the above estimator using the weight function q(t/T,m). The critical values of the CTSB test are obtained from the supremum of the weighted Brownian bridge process introduced above.…”

“…Further, following Gombay et al (1996) and Antoch et al (1995), a consistent estimator of t à ist à ; defined by:…”

“…The dataset covers 370 price sensitive announcements on FTSE 350 companies relating to the period 2000-2006. In order to maintain complete confidentiality, the series does not name any of the companies, the nature of the price sensitive announcement which could be due to a reporting of profits, a takeover bid, a profit warning or some other price sensitive announcement.4 Bootstrap confidence intervals cannot be computed for the CUSUM of Brown et alsince the method does not satisfy the assumptions inAntoch et al (1995). This represents another advantage of using statistical tests based on equation(15).…”