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theses

In this dissertation, we proposed a new test for the serial correlation under high dimensionality, based on the maximum self-normalized autocovariances. We show that the asymptotic distribution of the test statistics is the extreme value distribution of type I. To calibrate the size of test, we use a multiplier bootstrap procedure, and prove the consistency under mixing conditions. Our new test has a more accurate empirical rejection rate under the null hypothesis, compared to the white noise test using the maximum cross correlation proposed by Chang et al. (2017). We also consider a second test statistic, which is the sum of squared maximum and minimum self-normalized autocovariances. It aims at killing two birds with one stone: to have an empirical size that is closer to the nominal one, and to gain more power for detecting non-zero autocorrelations. We demonstrate the sizes and powers of the proposed tests through extensive numerical studies and a real example on economic indicators, which confirm their superiority over existing methods. Since the convergence rate of the normal extreme is of critical importance for hypothesis tests based on extreme type test statistics, we consider a transform of the normal extreme, with improved convergence rates. In this second project, we show that after a monotone transformation, the convergence rate of the squared normal extreme is of the order $(log n)^{-3}$, which is faster than the existing results, of the order $(log n)^{-2}$ at their best. More strikingly, we demonstrate that the empirical convergence speed is uniformly improved, especially at the tails, even when the sample is of a moderate size.

ETD_10739

Ph.D.

Includes bibliographical references

doi:10.7282/t3-9edy-2594

ETD doctoral

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