The time series modeling approach is introduced to estimate the prompt-neutron decay constant. Neutron flux noise data of three fuel cycles of a high flux isotope reactor are analyzed. The noise data detected from an ionization chamber outside the reactor core surrounded by a beryllium reflector were recorded at full-power operation. The decay constant corresponding to a rounded-off corner break frequency can be estimated from the characteristic roots of adequate autoregressive moving average models. This implicit characteristic identification is one of the advantages of off-line modeling analysis. The estimated neutron lifetime in the beginning of fuel cycle is 38 µs (expected value = 35 µs). The estimated lifetime near the end of cycle is 66 µs (expected value = 70 µs).