High-performance frequency standards are affected by power-law noises and characterized by structure functions (i.e., variances). These variances with specified averaging time quantify the frequency stability of the oscillator. To improve the stability estimated from the measured data and extend its maximum averaging time, a method called "StONA" (oscillator noise analysis under stochastic restrictions) is proposed based on convex optimization techniques. StONA also measures the intensity coefficients of noise processes as a by-product of extending averaging time. To test the method against real data, we recompute the distribution regions of total and Hadamard variances estimated from 14 days of satellite clock data and predict the stability of extended averaging time. The recomputed and predicted variances are inconsistent with the ones estimated from 168 days of data and have smaller uncertainty than those estimated from 84 days of time deviations.