Arsenal have won only five of their last 32 meetings against Manchester City, Manchester United, Chelsea, Liverpool and Tottenham Hotspur, dating back to the 2015-16 season.
Arsenal started the season with defeats by City and Chelsea, and the weekend's clash against Liverpool will be a litmus test for Emery's resurgent squad, who are unbeaten in their last 13 games in all competitions.
When asked about Arsenal's record against their 'Big Six' opponents, Emery said: "We want to write a new history.
"With our players, our quality and our capacity, I believe in my players and this project. We are starting this project in a very positive way with what we are doing.
"It is a very big test because it is against Liverpool. They are a very good team, an intense team and they require a lot of work for us to battle them. But I believe in our team and our players."
Emery last faced Liverpool manager Juergen Klopp in the 2016 Europa League final, when his Sevilla side won 3-1.
Liverpool have since reached the Champions League final last season and are currently level on points with Premier League leaders Manchester City.
Emery believes Klopp's continued progress at Anfield is an example for Arsenal to follow in the near-future.
"This team three seasons ago, they were playing in the final of the Europa League," Emery said.
"Their development was to last season play the final in the Champions League. Now, for us, it's a good, big example of how you can improve also in your way." (Reporting by Hardik Vyas in Bengaluru Editing by Toby Davis)
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