A goodness-of-fit test for GARCH innovation density

Koul, Hira L.; Mimoto, Nao

doi:10.1007/s00184-010-0318-4

Cited by 9 publications

(2 citation statements)

References 12 publications

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“…The objective here is to construct goodness-of-fit (GOF) statistics for distributional assumptions regarding these count time series models. In the classical (continuous type) framework of time-series models, this aspect of modelling has drawn considerable attention recently; see [1][2][3][4][5]. The standard approach in constructing GOF tests is to estimate the corresponding density or distribution function and thereby construct versions of the Kolmogorov-Smirnov, Cramér-von Mises and Bickel-Rosenblatt statistics.…”

Section: Introductionmentioning

confidence: 99%

Tests for time series of counts based on the probability-generating function

2014

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We propose testing procedures for the hypothesis that a given set of discrete observations may be formulated as a particular time series of counts with a specific conditional law. The new test statistics incorporate the empirical probability generating function computed from the observations. Special emphasis is given to the popular models of integer autoregression and Poisson autoregression. The asymptotic properties of the proposed test statistics are studied under the null hypothesis as well as under alternatives. A Monte Carlo power study on bootstrap versions of the new methods is included as well as real-data examples.

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Section: Introductionmentioning

confidence: 99%

Tests for time series of counts based on the probability-generating function

2014

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“…In other words, not knowing the nuisance location parameter has no effect on the asymptotic level of the test based on the analog of this statistic. Lee and Na (2002), Bachmann and Dette (2005) and Koul and Mimoto (2012) observed that this fact continues to hold for the analog of this test statistic when fitting an error density based on residuals in autoregressive and generalized autoregressive conditionally heteroscedastic time series models. This type of property makes these L 2 -distance type tests more desirable, compared to the tests based on residual empirical processes, because the asymptotic null distribution of the standardized residual empirical process depends on the estimators of the underlying nuisance parameters in these models in a complicated fashion, which renders it be unknown.…”

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confidence: 76%

Goodness-of-fit testing of error distribution in linear measurement error models

Koul¹,

Song²,

Zhu³

2018

Ann. Statist.

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This paper investigates a class of goodness-of-fit tests for fitting an error density in linear regression models with measurement error in covariates. Each test statistic is the integrated square difference between the deconvolution kernel density estimator of the regression model error density and a smoothed version of the null error density, an analog of the so-called Bickel and Rosenblatt test statistic. The asymptotic null distributions of the proposed test statistics are derived for both the ordinary smooth and super smooth cases. The asymptotic power behavior of the proposed tests against a fixed alternative and a class of local nonparametric alternatives for both cases is also described. The finite sample performance of the proposed test is evaluated by a simulation study. The simulation study shows some superiority of the proposed test over some other tests. Finally, a real data is used to illustrate the proposed test.

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