Time series from different regions of interest (ROI) of default mode network (DMN) from Functional Magnetic Resonance Imaging (fMRI) can reveal significant differences between healthy and unhealthy people. Here, we propose the utility of an existing metric quantifying the lack/presence of structure in a signal called, "deviation from stochasticity" (DS) measure to characterize resting-state fMRI time series. The hypothesis is that differences in the level of structure in the time series can lead to discrimination between the subject groups. In this work, an autoencoder-based model is utilized to learn efficient representations of data by training the network to reconstruct its input data. The proposed methodology is applied on fMRI time series of 50 healthy individuals and 50 subjects with Alzheimer's Disease (AD), obtained from publicly available ADNI database. DS measure for healthy fMRI as expected turns out to be different compared to that of AD. Peak classification accuracy of 95% was obtained using Gradient Boosting classifier, using the DS measure applied on 100 subjects.