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Length and location of the test sample: $p, q$

The default parameter pair is$(p,q)=(K,m+1)$; in this case we use $2M\!-\!1$ observations$x_{n+m-M+2},$$\ldots,$$x_{n+m+M}$ including $M$ new points to construct $M$ test vectors $X_j^{(n)} (j=m-M+2, \ldots,m+1)$. To get a smooth behaviour of the test statistics ${\calD}_{n,I,p,q}$ we need to select $q$ slightly larger than $p$. If the difference $q-p$ is too large, then the behaviour of ${\calD}_{n,I,p,q}$ becomes too smooth. This is happening in case (A1): in this case $q-p=K$, which is typically quite large. There are no particular reasons why $q-p$ should equal $M$.