HSV have been struggling to find their best form in the opening weeks of the 2012-13 campaign, and are one of four teams that are still pointless after two games.
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"I have signed a contract for the next three years, regardless of the competition we play in," Van der Vaart was quoted as saying by Bild.
"I do not think we will be relegated. We have a good team and I am confident that we will soon hit our stride. We will have to do it all together, though. I cannot do it all by myself.
"The team has a lot of potential. I would not have joined the club if I didn't think that."
Van der Vaart joined HSV from Tottenham Hotspur on deadline day of the summer transfer window. The Netherlands international previously played at the Bundesliga club from 2005 until 2008.