Delay times of sequential procedures for multiple time series regression models

Monitoring correlation change in a sequence of random variables

“…Note that, if a correlation change occurs soon after the historical dataset, then, choosing γ as large as possible, the stopping rule τ m will stop nearly instantaneously. Note that γ = 1/2 is excluded, since H 0 would else be rejected with probability one regardless whether it is true or not because of the law of the iterated logarithm for Brownian Motions at zero, see Aue et al (2009). Using the threshold function in Eq.…”

“…In particular, we analyze the case of changes in the correlation structure of a sequence of random variables. Other papers analyzing related problems under this framework are Chu et al (1996), Horváth et al (2004), Aue et al (2006), Aue et al (2009) and Aue et al (2011), among others.…”

Dependent functional linear models with applications to monitoring structural change

“…Examples of threshold functions can be found in Chu, Stinchcombe, and White (1996), Horváth et al (2004) and Aue, Horváth, and Reimherr (2009b), among others. We have the limit behavior of both the open-end and the closedend procedures under the null hypothesis.…”

“…Theorem 3 could be formulated so that k * is allowed to depend on m in a certain way. It would also be of interest to derive a theoretical result on the delay time of the detector as was done in Aue and Horváth (2004) for a simple change in location model, and in Aue, Horváth, and Reimherr (2009b) for more complex time series regressions. However, this is beyond the scope of the current account.…”

“…For more details on this see, for example, Aue, Horváth, and Reimherr (2009b). More precisely, critical values are provided for the values γ = −0.5, 0.1, 0.25, and 0.45 in the following.…”