Can autocorrelation be observed in a non-ordered data? Autocorrelation means that the error terms are serially correlated. However, if we have an un-ordered dataset, we can always shuffle the data to change the serial ordering then we can change the covariance matrix of errors.
This question has startled me to some extent. If we have a dataset that is not ordered by time (purely non-time series data), we should never theoretically observe a serial correlation.


Autocorrelation means that the error terms are serially correlated.

Not exactly, autocorrelation of order $k$ can be defined as $C(y_t,y_{t-k})$, error terms are not involved.

Can autocorrelation be observed in a non-ordered data?

No, ordering is needed.
Terms like autocorrelation and serial correlation make sense in time series or in some stochastic process sense. Therefore some ordering is needed, usually time ordering. Indeed you have to manage the dataset carefully, ordering matters a lot.
As opposite, for general correlation no specific ordering is needed.
