In the 72nd episode of the X and Y series (episode 872 of the entire Pokemon Anime) Ash and his friends stumble upon a man named Cole in an abandoned house. They find an old picture of him with the date July 14th, 1758 written on it. When Ash sees this, he comments, "What? This was more than 200 years ago!" This means that Ash's adventures take place sometime between 1958 and 2058. 

Oh, and in case you're wondering why Cole's picture is over 200 years old, it is because Cole is a ghost.