Goodness of Fit Problem and Scanning Innovation Martingales

Khmaladze, Estáte V.

doi:10.1214/aos/1176349152

Cited by 102 publications

(90 citation statements)

References 22 publications

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“…Their focus is the specification of the conditional mean, rather than the conditional distribution. Incidentally, extension of the transformation to AR(2) or multiple-regressor marked-empirical processes is non-trivial because, among other technical difficulties, Khmaladze's transformation is not unique for multivariate empirical processes, see Khmaladze (1988Khmaladze ( , 1993. A marked empirical process for high dimensional models is a multivariate process (in-dexed by a vector).…”

Section: Related Literature and Contributions Of This Papermentioning

confidence: 99%

Testing Parametric Conditional Distributions of Dynamic Models

Bai

2003

Review of Economics and Statistics

209

262

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This paper proposes a nonparametric test for parametric conditional distributions of dynamic models. The test is of the Kolmogorov type coupled with Khmaladze's martingale transformation. The proposed test is asymptotically distribution free and has non-trivial power against root-n local alternatives. The method is applicable for various dynamic models, including autoregressive and moving average models (ARMA), generalized autoregressive conditional heteroskedasticity (GARCH), integrated GARCH (IGARCH), and general nonlinear time series regressions. The method is also applicable for cross sectional models. Finally, we apply the procedure to testing conditional normality and conditional t-distribution in a GARCH model for the NYSE equal-weighted returns.

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Section: Related Literature and Contributions Of This Papermentioning

confidence: 99%

Testing Parametric Conditional Distributions of Dynamic Models

Bai

2003

Review of Economics and Statistics

209

262

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“…This proposition is one of the key statements of [9] and is more or less known to statistical communities because of the consequences it has for goodness of fit theory (see, e.g., [12]). It is less known to specialists in stochastic analysis, in particular to those interested in martingales in multi-dimensional time.…”

Section: Proposition 23 For Any Scanning Family the Operator Umentioning

confidence: 99%

Some new connections between Brownian bridges and Brownian motions

Khmaladze¹

2015

COSA

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“…Khmaladze (1981Khmaladze ( , 1988Khmaladze ( , 1993 introduced the operator T in a series of papers exploring limiting distributions of empirical processes with possibly parametric means.…”

Section: Khmaladze Transformmentioning

confidence: 99%

“…These extensions are important in our application because even under the null hypothesis of no causal relationship, the observed time series are not Markovian and do not have a martingale di¤erence structure. Most importantly, direct application of the Khmaladze (1988Khmaladze ( ,1993 method in a multivariate context appears to work poorly in practice. We therefore use a Rosenblatt (1952) transformation of the data in addition to the Khmaladze transformation 3 .…”

Section: Introductionmentioning

confidence: 99%

“…: Section 4 discusses a martingale transform proposed by Khmaladze (1988Khmaladze ( , 1993 to remove the e¤ect of variability inV n (v) stemming from estimation of : The corrected test statistic then has the same limiting distribution as V n (v); and thus, in a second step, critical values that are valid for V n (v) can be used to carry out tests based on the transformed version ofV n (v):…”

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confidence: 99%

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Causal Effects of Monetary Shocks: Semiparametric Conditional Independence Tests with a Multinomial Propensity Score

Angrist

Kuersteiner

2011

Review of Economics and Statistics

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We develop semiparametric tests for conditional independence in time series models of causal e¤ects. Our approach is motivated by empirical studies of monetary policy e¤ects. Our approach is semiparametric in the sense that we model the process determining the distribution of treatment -the policy propensity score -but leave the model for outcomes unspeci…ed. A conceptual innovation is that we adapt the cross-sectional potential outcomes framework to a time series setting. We also develop root-T consistent distribution-free inference methods for full conditional independence testing, appropriate for dependent data and allowing for …rst-step estimation of the (multinomial) propensity score.

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Goodness of Fit Problem and Scanning Innovation Martingales

Cited by 102 publications

References 22 publications

Testing Parametric Conditional Distributions of Dynamic Models

Testing Parametric Conditional Distributions of Dynamic Models

Some new connections between Brownian bridges and Brownian motions

Causal Effects of Monetary Shocks: Semiparametric Conditional Independence Tests with a Multinomial Propensity Score

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