Estimation of the Distribution of Noise in an Autoregression Scheme

Boldin, M. V.

doi:10.1137/1127098

Cited by 71 publications

(26 citation statements)

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“…Note that this is a modeling assumption, not an assumption about the distribution. Asymptotic theory for empirical process for |α| < 1, α = 1 and |α| > 1, have been found by Boldin (1981), Lee and Wei (1999) and Koul and Leventhal (1989), respectively. The result for α = −1 has not been studied in the context of empirical processes.…”

Section: T )mentioning

confidence: 89%

The empirical process of autoregressive residuals

Engler

Nielsen²

2009

Econometrics Journal

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The empirical process of the residuals from general autoregressions is investigated. If an intercept is included in the regression, the empirical process is asymptotically Gaussian and free of nuissance parameters. This contrasts the known result that in the unit root case without intercept the empirical process is asymptotically non-Gaussian. The result is used to establish asymptotic theory for the Kolmogorov-Smirnov test, Probability-Probability plots, and QuantileQuantile plots. The link between sample moments and the empirical process of the residuals is established and used to establish the properties of the cumulant based tests for normality referred to as the Jarque-Bera test.

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Section: T )mentioning

confidence: 89%

The empirical process of autoregressive residuals

Engler

Nielsen²

2009

Econometrics Journal

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“…Define Boldin (1982), divide the real line into N(n) parts by points -oo = z < z\ < < ZN( n ) = oo with F(z,) = iiV(n) Proof of (iii). Follows from the same type of arguments as in the proof of (ii).…”

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confidence: 99%

Testing for Parameter Constancy in Linear Regressions: An Empirical Distribution Function Approach

Bai¹

1996

Econometrica

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“…Next, using an argument similar to that in Bickel(l975) or Boldin (1983) . We will show that For a suitable choice of 6, this implies that for each a,, a2 >O, P(sup{ r(n); jjn1'2n (1 <K} > 6,) < 6, for all n large enough and this shows (A.12).…”

Section: Supn1'2~[f~(~)-f(~)]-[f~(~i)-f(~i)]imentioning

confidence: 99%

Aligned rank tests for the linear model with heteroscedastic errors

Akritas¹,

Albers²

1993

Journal of Statistical Planning and Inference

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Abstract:We consider the problem of testing subhypotheses in a heteroscedastic linear regression model. The proposed test statistics are based on the ranks of scaled residuals obtained under the null hypothesis. Any estimator that is n"2-consistent under the null hypothesis can be used to form the residuals. The error variances are estimated through a parametric model. This extends the theory of aligned rank tests to the heteroscedastic linear model. A real data set is used to illustrate the procedure.

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Estimation of the Distribution of Noise in an Autoregression Scheme

Cited by 71 publications

References 1 publication

The empirical process of autoregressive residuals

The empirical process of autoregressive residuals

Testing for Parameter Constancy in Linear Regressions: An Empirical Distribution Function Approach

Aligned rank tests for the linear model with heteroscedastic errors

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