Age-period-cohort analysis of vital data has received much attention recently, and it is already well known that the exact linear relation of the three time factors creates a non-identifiability problem. Previous studies have shown that the curvature terms of these factors are estimable but the linear trends are not. However, little attention has been paid to the possibility that the effects due to cohort and/or period might change through time stochastically rather than deterministically and hence display a stochastic trend. In this paper, we model the cohort effects as an AR(1) process and use lung cancer mortality data from 1966 to 1990 for males in Taiwan as an example. The parameters are identifiable in the proposed model and the estimates are found to be stable. However, the assumption made in the model should be carefully considered before using our methodology.