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90
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 184 (19 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.
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 113 (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,
Testing for Linearity
 Journal of Economic Surveys
, 1999
"... Abstract. The problem of testing for linearity and the number of regimes in the context of selfexciting threshold autoregressive (SETAR) models is reviewed. We describe leastsquares methods of estimation and inference. The primary complication is that the testing problem is nonstandard, due to th ..."
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Cited by 92 (1 self)
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Abstract. The problem of testing for linearity and the number of regimes in the context of selfexciting threshold autoregressive (SETAR) models is reviewed. We describe leastsquares methods of estimation and inference. The primary complication is that the testing problem is nonstandard, due to the presence of parameters which are only defined under the alternative, so the asymptotic distribution of the test statistics is nonstandard. Simulation methods to calculate asymptotic and bootstrap distributions are presented. As the sampling distributions are quite sensitive to conditional heteroskedasticity in the error, careful modeling of the conditional variance is necessary for accurate inference on the conditional mean. We illustrate these methods with two applications Ð annual sunspot means and monthly U.S. industrial production. We find that annual sunspots and monthly industrial production are SETAR(2) processes. Keywords. SETAR models; Thresholds; Nonstandard asymptotic theory; Bootstrap
Predictive density evaluation
, 2005
"... This chapter discusses estimation, specification testing, and model selection of predictive density models. In particular, predictive density estimation is briefly discussed, and a variety of different specification and model evaluation tests due to various ..."
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Cited by 49 (8 self)
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This chapter discusses estimation, specification testing, and model selection of predictive density models. In particular, predictive density estimation is briefly discussed, and a variety of different specification and model evaluation tests due to various
Improved Rates and Asymptotic Normality for Nonparametric Neural Network Estimators
, 1997
"... Barron (1993) obtained a deterministic approximation rate (in L2norm) of rm for a class of single hid den layer feedforward artificial neural networks (ANN) with r hidden units and sigmoid activation func tions when the target function satisfies certain smoothness conditions. Hornik, Stinchcom ..."
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Cited by 33 (10 self)
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Barron (1993) obtained a deterministic approximation rate (in L2norm) of rm for a class of single hid den layer feedforward artificial neural networks (ANN) with r hidden units and sigmoid activation func tions when the target function satisfies certain smoothness conditions. Hornik, Stinchcombe, White, and Auer (HSWA, 1994) extended Barron's result to a class of ANNs with possibly nonsigmoid activation approximating the target function and its derivatives simultaneously. Recently Makovoz (1996) obtained an improved degree of approximation rate ro+/a for Barron's ANNs with sigmoid activation func tion where d is the dimension of the domain of the target function.
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 29 (14 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.
Model selection in neural networks
 Neural Networks
, 1999
"... Die ZBW räumt Ihnen als Nutzerin/Nutzer das unentgeltliche, räumlich unbeschränkte und zeitlich auf die Dauer des Schutzrechts beschränkte einfache Recht ein, das ausgewählte Werk im Rahmen der unter ..."
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Cited by 28 (0 self)
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Die ZBW räumt Ihnen als Nutzerin/Nutzer das unentgeltliche, räumlich unbeschränkte und zeitlich auf die Dauer des Schutzrechts beschränkte einfache Recht ein, das ausgewählte Werk im Rahmen der unter
2003), “Generalized Spectral Tests for Conditional Mean Models in Time Series with Conditional Heteroskedasticity of Unknown Form”,mimeo
"... Economic theories in time series contexts usually have implications on and only on the conditional mean dynamics of underlying economic variables. We propose a new class of specification tests for time series conditional mean models, where the dimension of the conditioning information set may be inf ..."
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Cited by 27 (8 self)
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Economic theories in time series contexts usually have implications on and only on the conditional mean dynamics of underlying economic variables. We propose a new class of specification tests for time series conditional mean models, where the dimension of the conditioning information set may be infinite. Both linear and nonlinear conditional mean specifications are covered. The tests can detect a wide range of model misspecifications in mean while being robust to conditional heteroscedasticity and higher order timevarying moments of unknown form. They check a large number of lags, but naturally discount higher order lags, which is consistent with the stylized fact that economic behaviours are more affected by the recent past events than by the remote past events. No specific estimation method is required, and the tests have the appealing “nuisance parameter free ” property that parameter estimation uncertainty has no impact on the limit distribution of the tests. A simulation study shows that it is important to take into account the impact of conditional heteroscedasticity; failure to do so will cause overrejection of a correct conditional mean model. In a horse race competition on testing linearity in mean, our tests have omnibus and robust power against a variety of alternatives relative to some existing tests. In an application, we find that after removing significant but possibly spurious autocorrelations due to nonsynchronous trading, there still exists significant predictable nonlinearity in mean for S&P 500 and NASDAQ daily returns.