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部分观测随机游走中的一致估计AI 解读

If a discrete-time random walk, consisting of the sum of independent increments from an unknown underlying distribution, is observed at every time instant then it is clear that the underlying distribution can be consistently estimated. If, however, we are restricted to observing only a subset of the times, and if this subset is too sparse, then a central limit effect takes over and only two moments can be consistently estimated. We show that divergence of the sum of the…

时间序列周期性的检验AI 解读

A one-parameter family of tests for periodicity in a time series is proposed that contains Fisher's test as a special case. Some tests in this family have substantially larger power than Fisher's test against many alternatives, yet retain comparable power against those alternatives for which Fisher's test is optimal. A Monte Carlo power study establishes this and also provides a basis for the selection of a test from this family. Critical values are obtained by using a…