1 Erratum to: Metrika (2015) 78:665–689 DOI 10.1007/s00184-014-0522-8

In the original publication, the form of the change point estimate presented in Section 4 is not suitable. The correct form of the estimate with correct assertion of Theorem 3 is given below. The corrected version of the original paper can be found on arXiv http://arxiv.org/abs/1509.01291.

Having a sequence of weights \(\{w(t)\}_{t=2}^T\), let us define the estimate of \(\tau \) as

$$\begin{aligned} \widehat{\tau }_N:=\arg \min _{t=2,\ldots ,T}\frac{1}{w(t)}\sum _{i=1}^N\sum _{s=1}^t(Y_{i,s}-\bar{Y}_{i,t})^2. \end{aligned}$$
(3)

Assumption E1

The sequence \(\left\{ \frac{t}{w(t)}\left( 1-\frac{r(t)}{t^2}\right) \right\} _{t=2}^T\) is decreasing.

Assumption E2

There exist constants \(L>0\) and \(N_0\in \mathbb {N}\) such that

$$\begin{aligned} L<\sigma ^2\left[ \frac{t}{w(t)}\left( 1-\frac{r(t)}{t^2}\right) -\frac{\tau }{w(\tau )}\left( 1-\frac{r(\tau )}{\tau ^2}\right) \right] +\frac{\tau (t-\tau )}{tw(t)}\frac{1}{N}\sum _{i=1}^N\delta _i^2, \end{aligned}$$

for each \(t=\tau +1,\ldots ,T\) and \(N\ge N_0\).

Assumption E3

\(\lim _{N\rightarrow \infty }\frac{1}{N^2}\sum _{i=1}^N\delta _i^2=0\).

Assumption E4

\(\mathsf {E}\,\varepsilon _{1,t}^4<\infty ,\,t\in \{1,\ldots ,T\}\).

Theorem 3

(Change point estimate consistency) Suppose that \(\tau \ne 1\). Then, under Assumptions A1, E1, E2, E3, and E4

$$\begin{aligned} \lim _{N\rightarrow \infty }\mathsf {P}\,[\widehat{\tau }_N=\tau ]=1. \end{aligned}$$