Arbeitspapier

A note on the Bickel-Rosenblatt test in autoregressive time series

to connected objects

In a recent paper Lee and Na (2001) introduced a test for a parametric form of the distribution of the innovations in autoregressive models, which is based on the integrated squared error of the nonparametric density estimate from the residuals and a smoothed version of the parametric fit of the density. They derived the asymptotic distribution under the null-hypothesis, which is the same as for the classical Bickel-Rosenblatt (1973) test for the distribution of i.i.d. observations. In this note we first extend the results of Bickel and Rosenblatt to the case of fixed alternatives, for which asymptotic normality is still true but with a different rate of convergence. As a by-product we also provide an alternative proof of the Bickel and Rosenblatt result under substantially weaker assumptions on the kernel density estimate. As a further application we derive the asymptotic behaviour of Lee and Na's statistic in autoregressive models under fixed alternatives. The results can be used for the calculation of the probability of the type II error of the Bickel-Rosenblatt test for the parametric form of the error distribution and for testing interval hypotheses in this context.

Language: Englisch

Bibliographic citation: Series: Technical Report ; No. 2004,17

Subject: Autoregressive process
goodness-of-fit test
nonparametric density estimation
asymptotic distribution under fixed alternatives
Nichtparametrisches Verfahren
Theorie
Autokorrelation

Event: Geistige Schöpfung

(who): Bachmann, Dirk
Dette, Holger

Event: Veröffentlichung

(who): Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen

(where): Dortmund

(when): 2004

Handle: http://hdl.handle.net/10419/49336

Last update: 10.03.2025, 11:44 AM CET

Data provider

This object is provided by:
ZBW - Deutsche Zentralbibliothek für Wirtschaftswissenschaften - Leibniz-Informationszentrum Wirtschaft. If you have any questions about the object, please contact the data provider.

Show original at data provider

Object type

Arbeitspapier

Associated

Bachmann, Dirk
Dette, Holger
Universität Dortmund, Sonderforschungsbereich 475 - Komplexitätsreduktion in Multivariaten Datenstrukturen

Time of origin

2004

Other Objects (12)

Robust designs for series estimation

Arbeitspapier

Robust designs for series estimation

A Note on the Bickel-Rosenblatt Test in Autoregressive Time Series

A Note on the Bickel-Rosenblatt Test in Autoregressive Time Series

On robust and efficient designs for risk estimation in epidemiologic studies

Arbeitspapier

On robust and efficient designs for risk estimation in epidemiologic studies

Canonical moments, orthogonal polynomials with application to statistics

Arbeitspapier

Canonical moments, orthogonal polynomials with application to statistics

Strong approximation of eigenvalues of large dimensional Wishart matrices by roots of generalized Laguerre polynomials

Arbeitspapier

Strong approximation of eigenvalues of large dimensional Wishart matrices by roots of generalized Laguerre polynomials

A note on a specification test for time series models based on spectral density estimation

Arbeitspapier

A note on a specification test for time series models based on spectral density estimation

Bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities

Arbeitspapier

Bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities

A Bootstrap Test for the Comparison of Nonlinear Time Series - with Application to Interest Rate Modelling

Arbeitspapier

A Bootstrap Test for the Comparison of Nonlinear Time Series - with Application to Interest Rate Modelling

Analyzing dynamic dependencies in time series

Hochschulschrift

Analyzing dynamic dependencies in time series

Matrix Measures, Moment Spaces and Favard's Theorem for the interval [0,1] and [0, infinity)

Matrix Measures, Moment Spaces and Favard's Theorem for the interval [0,1] and [0, infinity)

Uniform approximation of eigenvalues in Laguerre and Hermite â-ensembles by roots of orthogonal polynomials

Uniform approximation of eigenvalues in Laguerre and Hermite â-ensembles by roots of orthogonal polynomials

Optimal designs for estimating individual coefficients in Fourier regression models and figures figure 1, figure 2, figure 3 and figure 4

Optimal designs for estimating individual coefficients in Fourier regression models and figures figure 1, figure 2, figure 3 and figure 4

Robust designs for series estimation

Arbeitspapier

Robust designs for series estimation

A Note on the Bickel-Rosenblatt Test in Autoregressive Time Series

A Note on the Bickel-Rosenblatt Test in Autoregressive Time Series

On robust and efficient designs for risk estimation in epidemiologic studies

Arbeitspapier

On robust and efficient designs for risk estimation in epidemiologic studies

Canonical moments, orthogonal polynomials with application to statistics

Arbeitspapier

Canonical moments, orthogonal polynomials with application to statistics

Strong approximation of eigenvalues of large dimensional Wishart matrices by roots of generalized Laguerre polynomials

Arbeitspapier

Strong approximation of eigenvalues of large dimensional Wishart matrices by roots of generalized Laguerre polynomials

A note on a specification test for time series models based on spectral density estimation

Arbeitspapier

A note on a specification test for time series models based on spectral density estimation

Bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities

Arbeitspapier

Bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities

A Bootstrap Test for the Comparison of Nonlinear Time Series - with Application to Interest Rate Modelling

Arbeitspapier

A Bootstrap Test for the Comparison of Nonlinear Time Series - with Application to Interest Rate Modelling

Analyzing dynamic dependencies in time series

Hochschulschrift

Analyzing dynamic dependencies in time series

Matrix Measures, Moment Spaces and Favard's Theorem for the interval [0,1] and [0, infinity)

Matrix Measures, Moment Spaces and Favard's Theorem for the interval [0,1] and [0, infinity)

Uniform approximation of eigenvalues in Laguerre and Hermite â-ensembles by roots of orthogonal polynomials

Uniform approximation of eigenvalues in Laguerre and Hermite â-ensembles by roots of orthogonal polynomials

Optimal designs for estimating individual coefficients in Fourier regression models and figures figure 1, figure 2, figure 3 and figure 4

Optimal designs for estimating individual coefficients in Fourier regression models and figures figure 1, figure 2, figure 3 and figure 4

Robust designs for series estimation

Arbeitspapier

Robust designs for series estimation

A Note on the Bickel-Rosenblatt Test in Autoregressive Time Series

A Note on the Bickel-Rosenblatt Test in Autoregressive Time Series

On robust and efficient designs for risk estimation in epidemiologic studies

Arbeitspapier

On robust and efficient designs for risk estimation in epidemiologic studies

Canonical moments, orthogonal polynomials with application to statistics

Arbeitspapier

Canonical moments, orthogonal polynomials with application to statistics

Strong approximation of eigenvalues of large dimensional Wishart matrices by roots of generalized Laguerre polynomials

Arbeitspapier

Strong approximation of eigenvalues of large dimensional Wishart matrices by roots of generalized Laguerre polynomials

A note on a specification test for time series models based on spectral density estimation

Arbeitspapier

A note on a specification test for time series models based on spectral density estimation

Bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities

Arbeitspapier

Bootstrapping frequency domain tests in multivariate time series with an application to comparing spectral densities

A Bootstrap Test for the Comparison of Nonlinear Time Series - with Application to Interest Rate Modelling

Arbeitspapier

A Bootstrap Test for the Comparison of Nonlinear Time Series - with Application to Interest Rate Modelling

Analyzing dynamic dependencies in time series

Hochschulschrift

Analyzing dynamic dependencies in time series

Matrix Measures, Moment Spaces and Favard's Theorem for the interval [0,1] and [0, infinity)

Matrix Measures, Moment Spaces and Favard's Theorem for the interval [0,1] and [0, infinity)

Uniform approximation of eigenvalues in Laguerre and Hermite â-ensembles by roots of orthogonal polynomials

Uniform approximation of eigenvalues in Laguerre and Hermite â-ensembles by roots of orthogonal polynomials

Optimal designs for estimating individual coefficients in Fourier regression models and figures figure 1, figure 2, figure 3 and figure 4

Optimal designs for estimating individual coefficients in Fourier regression models and figures figure 1, figure 2, figure 3 and figure 4

Cultural heritage institutions wishing to register will find more information here.

Fields marked * need to be filled in.

Username*

Please enter your username

Email*

Please enter your email address

Please do not fill this field

First name

Last name

Password*

Please enter your password

Confirm password*

Please enter the same password

I have read the terms of use and the privacy policy for the collection of personal data and accept them. *

This field is required.

I would like to subscribe to the newsletter of the Deutsche Digitale Bibliothek. See newsletter subscription info.

Account created

Your "My DDB" account has been successfully created. Before you can log in to your account, you must click the confirmation link in the message we just sent to the email address you provided.