Emery took over from long-serving Arsenal manager Arsene Wenger in May and, after a rocky start to his debut Premier League campaign which saw the north Londoners lose their first two games, the 46-year-old has since overseen wins over West Ham and Cardiff.
Rosicky, who retired last year, has been watching his former club with keen interest this term and believes Emery - whose list of managerial silverware includes three Europa League titles and a treble in France - is experienced enough to successfully lead Arsenal into a new era.
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Speaking to Standard Sport, Rosicky said: "There are some positives, some negatives. We have to get used to it and we would all like to see the team grow.
"The team is scoring goals, even in difficult games like Chelsea away, which is important. There are a lot of positives obviously, a lot of negatives as well because the team is conceding.
"But Unai Emery is very experienced and was successful everywhere he has been. I trust him and I hope he will do well and we will see the team grow and develop."