A multivariate time series model such as a Vector Auto Regression (VAR) model is built using fabric utilization, disk utilization, and CPU utilization time series data. The VAR model leverages interdependencies between multiple time-dependent variables to predict the start and length of an aperiodic backup time window, and to cause backup operations to occur during the aperiodic backup time window to thereby exploit the aperiodic backup time window for use in connection with backup operations. By automatically starting backup operations during predicted aperiodic backup time windows where the CPU, disk, and fabric utilization values are predicted to be low, it is possible to implement backup operations during time windows where the backup operations are less likely to interfere with primary application workloads, or system application workloads that need to be implemented to maintain optimal operation of the storage system.