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Asymptotic Properties Of Error Distribution Function Estimation For Nonlinear Time Series

Posted on:2020-05-05Degree:MasterType:Thesis
Country:ChinaCandidate:P H GuFull Text:PDF
GTID:2370330575452472Subject:Probability theory and mathematical statistics
Abstract/Summary:PDF Full Text Request
For a general linear autoregressive model,the prediction error comes from the model itself on the one hand and the random term in the model on the other hand.The confidence interval we predict depends on the cumulative distribution function of the random term.The predecessor proposed a method for estimating the cumulative distribution function of random terms(errors)under linear conditions.That is,using the kernel estimation method to estimate the distribution function of the error.Based on this,the error estimation method of nonlinear autoregressive models is proposed in this paper.We prove that the kernel estimation for the nonlinear model also have the similar asymptotic behavior,that is,the cumulative distribution function can be replaced by the kernel distribution estimator.In terms of data analysis,we use simulation data to verify the efficiency and the asymptotic behavior of the error estimation method.At the same time,we also use the actual SP500 index to apply nonlinear autoregressive models for estimation and prediction analysis.Finally,we try to extend this method to estimate and predict long memory time series models.We investigate the simulation results to show the influence of long memory parameter d on the error distribution estimation.
Keywords/Search Tags:kernel distribution estimation, nonlinear, error, long memory, autoregressive models
PDF Full Text Request
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