There are (several) central limit theorems for dependent variables, but you often have to assume other things as well (e.g., stationarity, bounded third moment,

There are (several) central limit theorems for dependent variables, but you often have to assume other things as well (e.g., stationarity, bounded third moment, and/or limited-range correlations) for it to work. Example: https://link.springer.com/chapter/10.1007/978-1-4612-0865-5_9 https://link.springer.com/chapter/10.1007/978-1-4612-0865-5_...