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Large Sample Sieve Estimation of SemiNonparametric Models
 Handbook of Econometrics
, 2007
"... Often researchers find parametric models restrictive and sensitive to deviations from the parametric specifications; seminonparametric models are more flexible and robust, but lead to other complications such as introducing infinite dimensional parameter spaces that may not be compact. The method o ..."
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Cited by 92 (17 self)
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Often researchers find parametric models restrictive and sensitive to deviations from the parametric specifications; seminonparametric models are more flexible and robust, but lead to other complications such as introducing infinite dimensional parameter spaces that may not be compact. The method of sieves provides one way to tackle such complexities by optimizing an empirical criterion function over a sequence of approximating parameter spaces, called sieves, which are significantly less complex than the original parameter space. With different choices of criteria and sieves, the method of sieves is very flexible in estimating complicated econometric models. For example, it can simultaneously estimate the parametric and nonparametric components in seminonparametric models with or without constraints. It can easily incorporate prior information, often derived from economic theory, such as monotonicity, convexity, additivity, multiplicity, exclusion and nonnegativity. This chapter describes estimation of seminonparametric econometric models via the method of sieves. We present some general results on the large sample properties of the sieve estimates, including consistency of the sieve extremum estimates, convergence rates of the sieve Mestimates, pointwise normality of series estimates of regression functions, rootn asymptotic normality and efficiency of sieve estimates of smooth functionals of infinite dimensional parameters. Examples are used to illustrate the general results.
Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative
, 1995
"... . The nonparametric and the nuisance parameter approaches to consistently testing statistical models are both attempts to estimate topological measures of distance between a parametric and a nonparametric fit, and neither dominates in experiments. This topological unification allows us to greatly ex ..."
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Cited by 55 (10 self)
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. The nonparametric and the nuisance parameter approaches to consistently testing statistical models are both attempts to estimate topological measures of distance between a parametric and a nonparametric fit, and neither dominates in experiments. This topological unification allows us to greatly extend the nuisance parameter approach. How and why the nuisance parameter approach works and how it can be extended bears closely on recent developments in artificial neural networks. Statistical content is provided by viewing specification tests with nuisance parameters as tests of hypotheses about Banachvalued random elements and applying the Banach Central Limit Theorem and Law of Iterated Logarithm, leading to simple procedures that can be used as a guide to when computationally more elaborate procedures may be warranted. 1. Introduction In testing whether or not a parametric statistical model is correctly specified, there are a number of apparently distinct approaches one might take. T...
Consistent Model Specification Tests
 Journal of Econometrics
, 1982
"... This paper reviews the literature on tests for the correct specification of the functional form of parametric conditional expectation and conditional distribution models. In particular I will discuss various versions of the Integrated Conditional Moment (ICM) test and the ideas behind them. 1 ..."
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Cited by 49 (10 self)
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This paper reviews the literature on tests for the correct specification of the functional form of parametric conditional expectation and conditional distribution models. In particular I will discuss various versions of the Integrated Conditional Moment (ICM) test and the ideas behind them. 1
Tests of conditional predictive ability
 Econometrica
, 2006
"... We argue that the current framework for predictive ability testing (e.g.,West, 1996) is not necessarily useful for realtime forecast selection, i.e., for assessing which of two competing forecasting methods will perform better in the future. We propose an alternative framework for outofsample com ..."
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Cited by 46 (1 self)
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We argue that the current framework for predictive ability testing (e.g.,West, 1996) is not necessarily useful for realtime forecast selection, i.e., for assessing which of two competing forecasting methods will perform better in the future. We propose an alternative framework for outofsample comparison of predictive ability which delivers more practically relevant conclusions. Our approach is based on inference about conditional expectations of forecasts and forecast errors rather than the unconditional expectations that are the focus of the existing literature. We capture important determinants of forecast performance that are neglected in the existing literature by evaluating what we call the forecasting method (the model and the parameter estimation procedure), rather than just the forecasting model. Compared to previous approaches, our tests are valid under more general data assumptions (heterogeneity rather than stationarity) and estimation methods, and they can handle comparison of both nested and nonnested models, which is not currently possible. To illustrate the usefulness of the proposed tests, we compare the forecast performance of three leading parameterreduction methods for macroeconomic forecasting using a large number of predictors: a sequential model selection approach,
Reversed Score and Likelihood Ratio Tests
, 2000
"... Two extensions of a parametric model are proposed, each one involving the score function of an alternative parametric model. We show that the encompassing hypothesis is equivalent to standard conditions on the score of each of the extended models. The condition on the first extension gives rise to t ..."
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Cited by 20 (0 self)
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Two extensions of a parametric model are proposed, each one involving the score function of an alternative parametric model. We show that the encompassing hypothesis is equivalent to standard conditions on the score of each of the extended models. The condition on the first extension gives rise to the standard score encompassing test, while the condition on the second extension induces a socalled reversed score encompassing test. A similar logic is applied to the likelihood ratio, generating a likelihood ratio and a reversed likelihood ratio encompassing test. The ensued test statistics can be based on simulations if certain calculations are too difficult to carry out analytically. We study the first order asymptotic properties of the proposed test statistics under general conditions.
Consistent Bootstrap Tests Of Parametric Regression Functions
, 2000
"... This paper introduces specification tests of parametric meanregression models. The null hypothesis of interest is that the parametric regression function is correctly specified. The proposed tests are generalizations of the KolmogorovSmirnov and Cramervon Mises tests to the regression framework. ..."
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Cited by 20 (7 self)
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This paper introduces specification tests of parametric meanregression models. The null hypothesis of interest is that the parametric regression function is correctly specified. The proposed tests are generalizations of the KolmogorovSmirnov and Cramervon Mises tests to the regression framework. They are consistent against all alternatives to the null hypothesis, powerful against 1= p n local alternatives, not dependent on any smoothing parameters and simple to compute. A wildbootstrap procedure is suggested to obtain critical values for the tests and is justified asymptotically. A small scale Monte Carlo experiment shows that our tests (especially Cramervon Mises test) have outstanding small sample performance compared to some of the existing tests.
Nonparametric Bootstrap Procedures for Predictive Inference Based on Recursive Estimation Schemes
, 2005
"... We introduce block bootstrap techniques that are (first order) valid in recursive estimation frameworks. Thereafter, we present two examples where predictive accuracy tests are made operational using our new bootstrap procedures. In one application, we outline a consistent test for outofsample n ..."
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Cited by 15 (6 self)
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We introduce block bootstrap techniques that are (first order) valid in recursive estimation frameworks. Thereafter, we present two examples where predictive accuracy tests are made operational using our new bootstrap procedures. In one application, we outline a consistent test for outofsample nonlinear Granger causality, and in the other we outline a test for selecting amongst multiple alternative forecasting models, all of which are possibly misspecified. In a Monte Carlo investigation, we compare the finite sample properties of our block bootstrap procedures with the parametric bootstrap due to Kilian (1999); within the context of encompassing and predictive accuracy tests. In the empirical illustration, it is found that unemployment has nonlinear marginal predictive content for inflation.
Nonlinear time series, complexity theory and finance
 Handbook of Statistics Volume 14: Statistical Methods in Finance
, 1995
"... ..."
An Out of Sample Test for Granger Causality
 Macroeconomic Dynamics
, 2000
"... Granger (1980) summarizes his personal viewpoint on testing for causality, and outlines what he considers to be a useful operational version of his original denition of causality (Granger (1969)), which he notes was partially alluded to in Wiener (1958). This operational version is based on a compar ..."
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Cited by 12 (5 self)
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Granger (1980) summarizes his personal viewpoint on testing for causality, and outlines what he considers to be a useful operational version of his original denition of causality (Granger (1969)), which he notes was partially alluded to in Wiener (1958). This operational version is based on a comparison of the 1step ahead predictive ability of competing models. However, Granger concludes his discussion by noting that it is common practice to test for Granger causality using insample Ftests. The practice of using insample type Granger causality tests continues to be prevalent. In this paper we develop simple (nonlinear) outofsample predictive ability tests of the Granger noncausality null hypothesis. In addition, Monte Carlo experiments are used to investigate the nite sample properites of the test. An empirical illustration shows that the choice of insample versus outofsample Granger causality tests can crucially aect the conclusions about the predictive content of money for ...
Approximate nonlinear forecasting methods
 Handbook of Economic Forecasting
, 2006
"... We review key aspects of forecasting using nonlinear models. Because economic models are typically misspecified, the resulting forecasts provide only an approximation to the best possible forecast. Although it is in principle possible to obtain superior approximations to the optimal forecast using n ..."
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Cited by 12 (6 self)
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We review key aspects of forecasting using nonlinear models. Because economic models are typically misspecified, the resulting forecasts provide only an approximation to the best possible forecast. Although it is in principle possible to obtain superior approximations to the optimal forecast using nonlinear methods, there are some potentially serious practical challenges. Primary among these are computational difficulties, the dangers of overfit, and potential difficulties of interpretation. In this chapter we discuss these issues in detail. Then we propose and illustrate the use of a new family of methods (QuickNet) that achieves the benefits of using a forecasting model that is nonlinear in the predictors while avoiding or mitigating the other challenges to the use of nonlinear forecasting methods. 1.