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Exact confidence sets and goodness-of-fit methods for stable distributions

JOURNAL OF econometrics 2014年第1期181卷 3-14页

作者： Beaulieu, Marie-Claude Dufour, Jean-Marie Khalaf, Lynda CIRPEE Montreal PQ Canada Univ Laval Dept Finance Assurance & Immobilier Quebec City PQ G1K 7P4 Canada McGill Univ Dept Econ Montreal PQ H3A 2T5 Canada CIREQ Montreal PQ Canada Ctr Interuniv Rech Anal Org CIRANO Montreal PQ Canada Univ Laval Grp Rech Econ Energie Environm & Ressources Nat G Quebec City PQ G1K 7P4 Canada Carleton Univ Dept Econ Ottawa ON K1S 5B6 Canada

Usual inference methods for stable distributions are typically based on limit distributions. But asymptotic approximations can easily be unreliable in such cases, for standard regularity conditions may not apply or may hold only weakly. This paper proposes finite-sample tests and confidence sets for tail thickness and asymmetry parameters (alpha and beta) of stable distributions. The confidence sets are built by inverting exact goodness-of-fit tests for hypotheses which assign specific values to these parameters. We propose extensions of the Kolmogorov-Smirnov, Shapiro-Wilk and Filliben criteria, as well as the quantile-based statistics proposed by McCulloch (1986) in order to better capture tail behavior. The suggested criteria compare empirical goodness-of-fit or quantile-based measures with their hypothesized values. Since the distributions involved are quite complex and non-standard, the relevant hypothetical measures are approximated by simulation, and p-values are obtained using Monte Carlo (MC) test techniques. The properties of the proposed procedures are investigated by simulation. In contrast with conventional wisdom, we find reliable results with sample sizes as small as 25. The proposed methodology is applied to daily electricity price data in the US over the period 2001-2006. The results show clearly that heavy kurtosis and asymmetry are prevalent in these series. (C) 2014 Published by Elsevier B.V.

关键词： Stable distribution Skewness Asymmetry Exact test Monte Carlo test Specification test Goodness-of-fit Tail parameter Electricity price

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Tests for m-dependence based on sample splitting methods

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JOURNAL OF econometrics 2013年第2期173卷 143-159页

作者： Moon, Seongman Velasco, Carlos Univ Carlos III Madrid Dept Econ Getafe Madrid 28903 Spain

This paper develops new test methods for m-dependent data. Our approach is based on sample splitting by regular sampling of the original data at lower frequencies, so that standard techniques for testing independence can be used for each individual subsample. We then propose several alternative statistics that aggregate information across subsamples and investigate their asymptotic and finite sample properties. We apply our methods to test the predictability of excess returns in foreign exchange markets. We also illustrate how our serial dependence tests can provide useful information for identifying particular economic alternatives when testing the expectations hypothesis in foreign exchange markets. (C) 2012 Elsevier B.V. All rights reserved.

关键词： m-dependence sample splitting Pooled method Wald method Minimum/maximum/median method Expectations hypothesis

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Model averaging by jackknife criterion in models with dependent data

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JOURNAL OF econometrics 2013年第2期174卷 82-94页

作者： Zhang, Xinyu Wan, Alan T. K. Zou, Guohua Chinese Acad Sci Acad Math & Syst Sci Beijing 100190 Peoples R China City Univ Hong Kong Dept Management Sci Kowloon Hong Kong Peoples R China

The past decade witnessed a literature on model averaging by frequentist methods. For the most part, the asymptotic optimality of various existing frequentist model averaging estimators has been established under i.i.d. errors. Recently, Hansen and Racine [Hansen, B.E., Racine, J., 2012. jackknife model averaging. Journal of econometrics 167, 38-46] developed a jackknife model averaging (JMA) estimator, which has an important advantage over its competitors in that it achieves the lowest possible asymptotic squared error under heteroscedastic errors. In this paper, we broaden Hansen and Racine's scope of analysis to encompass models with (i) a non-diagonal error covariance structure, and (ii) lagged dependent variables, thus allowing for dependent data. We show that under these set-ups, the JMA estimator is asymptotically optimal by a criterion equivalent to that used by Hansen and Racine. A Monte Carlo study demonstrates the finite sample performance of the JMA estimator in a variety of model settings. (C) 2013 Elsevier B.V. All rights reserved.

关键词： asymptotic optimality Autocorrelation Cross-validation Lagged dependent variables Model averaging Squared error

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Unit root testing under a local break in trend

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JOURNAL OF econometrics 2012年第1期167卷 140-167页

作者： Harvey, David I. Leybourne, Stephen J. Taylor, A. M. Robert Univ Nottingham Sch Econ Nottingham NG7 2RD England

Recent approaches to testing for a unit root when uncertainty exists over the presence and timing of a trend break employ break detection methods, so that a with-break unit root test is used only if a break is detected by some auxiliary statistic. While these methods achieve near asymptotic efficiency in both fixed trend break and no trend break environments, in finite samples pronounced "valleys" in the power functions of the tests (when mapped as functions of the break magnitude) are observed, with power initially high for very small breaks, then decreasing as the break magnitude increases, before increasing again. In response to this problem, we propose two practical solutions, based either on the use of a with-break unit root test but with adaptive critical values, or on a union of rejections principle taken across with-break and without-break unit root tests. These new procedures are shown to offer improved reliability in terms of finite sample power. We also develop local limiting distribution theory for both the extant and the newly proposed unit root statistics, treating the trend break magnitude as local-to-zero. We show that this framework allows the asymptotic analysis to closely approximate the finite sample power valley phenomenon, thereby providing useful analytical insights. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Unit root test Local trend break Union of rejections Adaptive critical values asymptotic local power

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Semiparametric robust estimation of truncated and censored regression models

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JOURNAL OF econometrics 2012年第2期168卷 347-366页

作者： Cizek, Pavel Tilburg Univ Dept Econometr & Operat Res CentER NL-5000 LE Tilburg Netherlands

Many estimation methods of truncated and censored regression models such as the maximum likelihood and symmetrically censored least squares (SCLS) are sensitive to outliers and data contamination as we document. Therefore, we propose a semiparametric general trimmed estimator (GTE) of truncated and censored regression, which is highly robust but relatively imprecise. To improve its performance, we also propose data-adaptive and one-step trimmed estimators. We derive the robust and asymptotic properties of all proposed estimators and show that the one-step estimators (e.g., one-step SCLS) are as robust as GTE and are asymptotically equivalent to the original estimator (e.g., SCLS). The finite-sample properties of existing and proposed estimators are studied by means of Monte Carlo simulations. (C) 2012 Elsevier B.V. All rights reserved.

关键词： asymptotic normality Censored regression One-step estimation Robust estimation Trimming Truncated regression

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Uniform confidence bands for functions estimated nonparametrically with instrumental variables

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JOURNAL OF econometrics 2012年第2期168卷 175-188页

作者： Horowitz, Joel L. Lee, Sokbae Northwestern Univ Dept Econ Evanston IL 60208 USA Seoul Natl Univ Dept Econ Seoul 151742 South Korea Inst Fiscal Studies Ctr Microdata Methods & Practice London WC1E 7AE England

This paper is concerned with developing uniform confidence bands for functions estimated nonparametrically with instrumental variables. We show that a sieve nonparametric instrumental variables estimator is pointwise asymptotically normally distributed. The asymptotic normality result holds in both mildly and severely ill-posed cases. We present methods to obtain a uniform confidence band and show that the bootstrap can be used to obtain the required critical values. Monte Carlo experiments illustrate the finite-sample performance of the uniform confidence band. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Bootstrap Instrumental variables Sieve estimator Uniform confidence band

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Non-parametric detection and estimation of structural change

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econometrics JOURNAL 2012年第3期15卷 420-461页

作者： Kristensen, Dennis UCL Dept Econ London WC1E 6BT England Inst Fiscal Studies Ctr Microdata Methods & Practice London WC1E 7AE England Aarhus Univ Ctr Res Econometr Anal Time Series DK-8000 Aarhus C Denmark

We propose a semi-non-parametric approach to the estimation and testing of structural change in time series regression models. Under the null of a given set of the coefficients being constant, we develop estimators of both the time-varying (non-parametric) and constant (parametric) components. Given the estimators under null and alternative, generalized F and Wald tests are developed. The asymptotic distributions of the estimators and test statistics are derived. A simulation study examines the finite-sample performance of the estimators and tests. The techniques are employed in the analysis of structural change in the US productivity and the Eurodollar term structure.

关键词： Estimation Generalized likelihood ratio Locally stationary Non-parametric Structural change Testing Time series regression Time varying

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Market microstructure noise, integrated variance estimators, and the accuracy of asymptotic approximations

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JOURNAL OF econometrics 2011年第1期160卷 145-159页

作者： Bandi, Federico M. Russell, Jeffrey R. Johns Hopkins Univ Carey Business Sch Baltimore MD 21201 USA Univ Chicago Booth Sch Business Chicago IL 60637 USA Edhec Risk Inst F-06202 Nice 3 France

A growing literature has been advocating consistent kernel estimation of integrated variance in the presence of financial market microstructure noise. We find that, for realistic sample sizes encountered in practice, the asymptotic results derived for the proposed estimators may provide unsatisfactory representations of their finite sample properties. In addition, the existing asymptotic results might not offer sufficient guidance for practical implementations. We show how to optimize the finite sample properties of kernel-based integrated variance estimators. Empirically, we find that their suboptimal implementation can, in some cases, lead to little or no finite sample gains when compared to the classical realized variance estimator. Significant statistical and economic gains can, however, be recovered by using our proposed finite sample methods. (C) 2010 Published by Elsevier B.V.

关键词： Integrated variance Realized variance Microstructure noise Kernel-based estimators

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A family of empirical likelihood functions and estimators for the binary response model

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JOURNAL OF econometrics 2011年第2期164卷 207-217页

作者： Mittelhammer, Ron C. Judge, George Washington State Univ Sch Econ Sci Pullman WA 99164 USA Univ Calif Berkeley Grad Sch Berkeley CA 94720 USA

The minimum discrimination information principle is used to identify an appropriate parametric family of probability distributions and the corresponding maximum likelihood estimators for binary response models. Estimators in the family subsume the conventional logit model and form the basis for a set of parametric estimation alternatives with the usual asymptotic properties. Sampling experiments are used to assess finite sample performance. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Binary response models and estimators Conditional moment equations Cressie-Read family of likelihood functions Information theoretic methods Minimum power divergence Minimum discrimination information

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SADDLEPOINT AND ESTIMATED SADDLEPOINT APPROXIMATIONS FOR OPTIMAL UNIT ROOT TESTS

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ECONOMETRIC THEORY 2011年第5期27卷 1026-1047页

作者： Marsh, Patrick Univ York Dept Econ York YO10 5DD N Yorkshire England

This paper provides a (saddlepoint) tail probability approximation for the distribution of an optimal unit root test. Under restrictive assumptions, Gaussianity, and known covariance structure, the order of error of the approximation is given. More generally, when innovations are a linear process in martingale differences, the estimated saddlepoint is proved to yield valid asymptotic inference. Numerical evidence, considered over a range of models, demonstrates some finite-sample superiority over approximations for a directly comparable test based on simulation of its limiting stochastic representation.

关键词： TIME series analysis econometrics ANALYSIS of covariance SIMULATION methods & models STOCHASTIC processes METHOD of steepest descent (Numerical analysis) GAUSSIAN processes

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