Evaluation Of The Returns And Nonlinear Features

We propose and develop mean-variance-ratio (MVR) statistics for comparing theperformance of prospects (e.g., investment portfolios, assets, etc.) after the efect of thebackground risk has been mitigated. We investigate the performance of the statisticsin large and small samples, and show that in the non-asymptotic framework, the MVRstatistic produces a uniformly most powerful unbiased (UMPU) test. We discuss theapplicability of the MVR test in the case of large samples and illustrate its superiorityin the case of small samples by analyzing Korea and Singapore stock returns afterthe impact of the American stock returns (which we view as the background risk) hasbeen deducted. We find, in particular, that when samples are small, the MVR statisticcan detect diferences in asset performances while the Sharpe ratio test, which is themean-standard-deviation-ratio statistic, may not be able to do so.On the other aspect, study on the structure especially nonlinear feature of a returnis more and more important, since we need to choice a good investment to increaseour profit. In this article we propose a quick, efcient, and easy method to detectwhether a time series possesses any nonlinear feature. The advantage of our proposednonlinearity test is that it is not required to know the exact nonlinear features and thedetailed nonlinear forms. Our simulation results show that our proposed test is stableand powerful while our illustrations on Wolf’s sunspots numbers and random walkhypothesis testing are consistent with the findings from existing literature.