带长记忆异方差误差项的时间序列模型的设定检验

发布时间：2018-05-31 20:31

  本文选题：长记忆 + 设定检验　； 参考：《南京大学》2017年硕士论文

【摘要】：近三十年来,基于半参数和非参数技术所提出的统计量被广泛地运用到独立的和短记忆时间序列模型的设定检验。然而,经济学,环境学和金融应用方面的研究表明,很多实际的时间序列数据都表现出了长记忆的性质。因此,本文主要研究带长记忆异方差误差项的时间序列模型的设定检验问题。在一定的假设条件下,我们推广了前人同方差误差项模型的结果。对于非线性时间序列模型Yt=m(Xt)+ σ(Xt)e 中未知函数m(.)的假设问题,当Xt～i.i.d.,{et}是长记忆严平稳线性过程时,我们提出了一般的检验统计量,并建立了该统计量的渐近分布理论。为了检验所提出的统计量在实际中的应用效果,我们首先通过参数自助法对统计量有限样本分布的1-γ水平临界值lγ进行了估计。为了检验该估计值的渐近性质,我们比较了不同参数设定下检验统计量的经验水平和功效值。最后,有限样本的数据模拟结果表明,本文提出的渐近理论和估计的临界值的实际效果都比较理想。
[Abstract]:In the last 30 years, the statistics based on semi-parametric and non-parametric techniques have been widely used to test the setting of independent and short-memory time series models. However, studies on economics, environmental science and financial applications show that many real time series data exhibit long memory properties. Therefore, this paper mainly studies the test of time series model with long memory heteroscedasticity error term. Under certain assumptions, we generalize the results of the previous error model of the same square difference. For the nonlinear time series model, Ytnmnu Xt) the unknown function mv.) In this paper, we propose a general test statistic and establish the asymptotic distribution theory of the statistic when Xttni.i.d., {et} is a strictly stationary linear process with long memory. In order to test the application effect of the proposed statistic in practice, we first estimate the critical value of 1- 纬 level of finite sample distribution by parameter self-help method. In order to test the asymptotic property of the estimator, we compare the empirical level and the efficacy value of the test statistic under different parameter settings. Finally, the simulation results of finite samples show that the asymptotic theory and the estimated critical value of the proposed method are satisfactory.
【学位授予单位】：南京大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O211.61
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本文编号：1961186