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理解长时间跨度下的高频观测回归AI 解读

In this paper, we analyze regressions with observations collected at small time intervals over a long period of time. For the formal asymptotic analysis, we assume that samples are obtained from continuous time stochastic processes, and let the sampling interval δ shrink down to zero and the sample span T increase up to infinity. In this setup, we show that the standard Wald statistic diverges to infinity and the regression becomes spurious as long as δ → 0 sufficiently fast…

Hawkes 及一般点过程的自助法推断AI 解读

Inference and testing in general point process models such as the Hawkes model is predominantly based on asymptotic approximations for likelihood-based estimators and tests. As an alternative, and to improve finite sample performance, this paper considers bootstrap-based inference for interval estimation and testing. Specifically, for a wide class of point process models we consider a novel bootstrap scheme labeled ‘fixed intensity bootstrap’ (FIB), where the conditional…

高频采样下的平稳性检验AI 解读

The high frequency behavior of the KPSS test, which is most commonly used to test for stationarity, is analyzed in a continuous time framework. Our asymptotics show that the test has no discriminatory power at high frequency: It either always rejects stationarity or has no nontrivial power at high frequency. The test becomes valid at high frequency only when the bandwidth of its long-run variance estimate is chosen suitably in our framework. We also analyze the…

利用离散样本估计连续时间随机过程的长期方差AI 解读

This paper develops the methodology and asymptotic theory for the estimation of longrun variance of continuous time process. We analyze the asymptotic bias and variance of the longrun variance estimator in continuous time, and provide the optimal bandwidth balancing them off and minimizing the asymptotic mean squared error. In the paper, we present not only how to consistently estimate the longrun variance of continuous time process, but also how to choose bandwidth…