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  本文選題：長記憶 + 設定檢驗��； 參考：《南京大學》2017年碩士論文

【摘要】：近三十年來,基于半?yún)?shù)和非參數(shù)技術所提出的統(tǒng)計量被廣泛地運用到獨立的和短記憶時間序列模型的設定檢驗。然而,經濟學,環(huán)境學和金融應用方面的研究表明,很多實際的時間序列數(shù)據(jù)都表現(xiàn)出了長記憶的性質。因此,本文主要研究帶長記憶異方差誤差項的時間序列模型的設定檢驗問題。在一定的假設條件下,我們推廣了前人同方差誤差項模型的結果。對于非線性時間序列模型Yt=m(Xt)+ σ(Xt)e 中未知函數(shù)m(.)的假設問題,當Xt～i.i.d.,{et}是長記憶嚴平穩(wěn)線性過程時,我們提出了一般的檢驗統(tǒng)計量,并建立了該統(tǒng)計量的漸近分布理論。為了檢驗所提出的統(tǒng)計量在實際中的應用效果,我們首先通過參數(shù)自助法對統(tǒng)計量有限樣本分布的1-γ水平臨界值lγ進行了估計。為了檢驗該估計值的漸近性質,我們比較了不同參數(shù)設定下檢驗統(tǒng)計量的經驗水平和功效值。最后,有限樣本的數(shù)據(jù)模擬結果表明,本文提出的漸近理論和估計的臨界值的實際效果都比較理想。
[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- 緯 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.
【學位授予單位】：南京大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O211.61
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本文編號：1961186