Delayed neutron noise measurements were carried out in an in-pile sodium loop, the Fission Product Loop 2 (FPL-2), installed on the Toshiba Training Reactor I. To clarify the characteristics and origin of delayed neutron count rate noise, a noise propagation mechanism was identified using a multivariate autoregressive model. The results show that a simulated fuel failure in the FPL-2, with recoil as the principal fission product release phenomena, produces a white spectrum of delayed neutron count rate noise. It was also found that the loop temperature fluctuation strongly affects the delayed neutron count rate noise at temperatures below 300°C, through the deposition of fission products on the surface of structures. These results provide useful information for the development of an early fuel failure detection method based on the delayed neutron signal.