Uniform and L p convergences for nonparametric continuous time regressions with semiparametric applications
Uniform and L p convergences for nonparametric continuous time regressions with semiparametric applications
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半参数应用非参数连续时间回归的均匀收敛和 L p 收敛
DOI：
10.1016/j.jeconom.2023.02.006
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发表时间：
2023
影响因子：
6.3
通讯作者：
Bu R
中科院分区：
文献类型：
--
作者：
Bu R
在一般回归扩散模型下，得到了连续时间回归的瞬时条件均值和方差函数的核型非参数估计的一致收敛速度和Lp收敛速度.我们的渐近性是在一般的设置下开发的，具有缩小的采样间隔和增加的时间跨度，并且没有平稳性假设。基于我们的收敛性结果，我们发展了连续时间预测回归的半参数推断过程。特别地，提出了一种稳健的线性可预报性半参数似然比检验方法，并建立了其极限分布。我们还应用我们的收敛结果，以获得半参数最大似然估计的漂移经常扩散的渐近性。在我们的模拟研究中，我们研究了有限样本的性能，我们的强大的测试对现有的几个测试文献。本文以股利价格比和收益价格比为预测因子，对两大股指的超额收益率进行了实证检验。
We obtain uniform and L p convergence rates of kernel type nonparametric estimators for the instantaneous conditional mean and variance functions of continuous time regressions, where the regressor is assumed to be a general recurrent diffusion. Our asymptotics are developed under a general set-up, with a shrinking sampling interval and an increasing time span, and without the stationarity assumption. Based on our convergence results, we develop a semiparametric inferential procedure for continuous time predictive regressions. In particular, a robust semiparametric likelihood ratio test for linear predictability is proposed, with its limit distribution established. We also apply our convergence results to obtain the asymptotics of a semiparametric maximum likelihood estimator of the drift of recurrent diffusions. In our simulation study, we examine the finite sample performance of our robust test against several existing tests in the literature. An empirical illustration is presented to test the predictability of the excess returns of two major stock indices using the commonly used dividend–price ratio and earnings–price ratio as the predictor.