  In this paper, we investigate the impact of correlated noise on fast radio
burst (FRB) searching. We found that 1) the correlated noise significantly
increases the false alarm probability; 2) the signal-to-noise ratios (S/N) of
the false positives become higher; 3) the correlated noise also affects the
pulse width distribution of false positives, and there will be more false
positives with wider pulse width. We use 55-hour observation for M82 galaxy
carried out at Nanshan 26m radio telescope to demonstrate the application of
the correlated noise modelling. The number of candidates and parameter
distribution of the false positives can be reproduced with the modelling of
correlated noise. We will also discuss a low S/N candidate detected in the
observation, for which we demonstrate the method to evaluate the false alarm
probability in the presence of correlated noise.Possible origins of the
candidate are discussed, where two possible pictures, an M82-harbored giant
pulse and a cosmological FRB, are both compatible with the observation.
