Automatic positive semidefinate HAC covariance matrix and GMM estimation

This paper proposes a new class of heteroskedastic and autocorrelation consistent (HAC) covariance matrix estimators. The standard HAC estimation method reweights estimators of the autocovariances. Here we initially smooth the data observations themselves using kernel function–based weights. The resultant HAC covariance matrix estimator is the normalized outer product of the smoothed random vectors and is therefore automatically positive semidefinite. A corresponding efficient GMM criterion may also be defined as a quadratic form in the smoothed moment indicators whose normalized minimand provides a test statistic for the overidentifying moment conditions

Robust Covariance Matrix Estimation with Data-Dependent VAR Prewhitening Order

This paper analyzes the performance of heteroskedasticity-and-autocorrelation-consistent (HAC) covariance matrix estimators in which the residuals are prewhitened using a vector autoregressive (VAR) filter. We highlight the pitfalls of using an arbitrarily fixed lag order for the VAR filter, and we demonstrate the benefits of using a model selection criterion (either AIC or BIC) to determine its lag structure. Furthermore, once data-dependent VAR prewhitening has been utilized, we find negligible or even counter-productive effects of applying standard kernel-based methods to the prewhitened residuals; that is, the performance of the prewhitened kernel estimator is virtually indistinguishable from that of the VARHAC estimator.

Spectral Density Bandwidth Choice and Prewhitening in the Generalized Method of Moments Estimators for the Asset Pricing Model

This paper investigates the performances of GMM estimates using kernel methods with and without prewhitening and the VARHAC method in a representative agent exchange economy. A Monte Carlo study is conducted to evaluate the issues of estimating the spectral density functions, e.g., parametric vs. nonparametric, data-based bandwidth selection, and prewhitening procedures. The Monte Carlo results show that kernel methods with prewhitening procedure outperform others in terms of statistical inferences. The deviations from true parameter values, however, are larger for kernel methods with prewhitening procedure. Therefore, there exists efficiency/bias trade-off when choosing HAC covariance estimation method.Asset Pricing

Computing Generalized Method of Moments and Generalized Empirical Likelihood with R

This paper shows how to estimate models by the generalized method of moments and the generalized empirical likelihood using the R package gmm. A brief discussion is offered on the theoretical aspects of both methods and the functionality of the package is presented through several examples in economics and finance.

A Two-Stage Plug-In Bandwidth Selection and Its Implementation in Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation

The performance of a kernel HAC estimator depends on the accuracy of the estimation of the normalized curvature, an unknown quantity in the optimal bandwidth represented as the spectral density and its derivative. This paper proposes to estimate it with a general class of kernels. The AMSE of the kernel estimator and the AMSE-optimal bandwidth are derived. It is shown that the optimal bandwidth for the kernel estimator should grow at a much slower rate than the one for the HAC estimator with the same kernel. A solve-the-equation implementation method is also proposed. Finite sample performances are assessed through simulations.Covariance matrix estimation, Kernel estimator, Bandwidth selection, Spectral density, Asymptotic mean squared error

Finite Sample Properties of Tests Based on Prewhitened Nonparametric Covariance Estimators

We analytically investigate size and power properties of a popular family of procedures for testing linear restrictions on the coefficient vector in a linear regression model with temporally dependent errors. The tests considered are autocorrelation-corrected F-type tests based on prewhitened nonparametric covariance estimators that possibly incorporate a data-dependent bandwidth parameter, e.g., estimators as considered in Andrews and Monahan (1992), Newey and West (1994), or Rho and Shao (2013). For design matrices that are generic in a measure theoretic sense we prove that these tests either suffer from extreme size distortions or from strong power deficiencies. Despite this negative result we demonstrate that a simple adjustment procedure based on artificial regressors can often resolve this problem.Comment: Some material adde

Fixed-B Asymptotics in Single Equation Cointegration Models with Endogenous Regressors

This note uses fixed bandwidth (fixed-b) asymptotic theory to suggest a new approach to testing cointegration parameters in a single-equation cointegration environment. It is shown that the standard tests still have asymptotic distributions that are free of serial correlation nuisance parameters regardless of the bandwidth or kernel used, even if the regressors in the cointegration relationship are endogenous.

Advances in forecast evaluation

This paper surveys recent developments in the evaluation of point forecasts. Taking West's (2006) survey as a starting point, we briefly cover the state of the literature as of the time of West's writing. We then focus on recent developments, including advancements in the evaluation of forecasts at the population level (based on true, unknown model coefficients), the evaluation of forecasts in the finite sample (based on estimated model coefficients), and the evaluation of conditional versus unconditional forecasts. We present original results in a few subject areas: the optimization of power in determining the split of a sample into in-sample and out-of-sample portions; whether the accuracy of inference in evaluation of multi-step forecasts can be improved with judicious choice of HAC estimator (it can); and the extension of West's (1996) theory results for population-level, unconditional forecast evaluation to the case of conditional forecast evaluation.Forecasting

Advances in forecast evaluation

This paper surveys recent developments in the evaluation of point forecasts. Taking West’s (2006) survey as a starting point, we briefly cover the state of the literature as of the time of West’s writing. We then focus on recent developments, including advancements in the evaluation of forecasts at the population level (based on true, unknown model coefficients), the evaluation of forecasts in the finite sample (based on estimated model coefficients), and the evaluation of conditional versus unconditional forecasts. We present original results in a few subject areas: the optimization of power in determining the split of a sample into in-sample and out-of-sample portions; whether the accuracy of inference in evaluation of multistep forecasts can be improved with the judicious choice of HAC estimator (it can); and the extension of West’s (1996) theory results for population-level, unconditional forecast evaluation to the case of conditional forecast evaluation.Forecasting ; Time-series analysis

The use of semi-parametric methods in achieving robust inference

Doutoramento em MatemáticaThis thesis focuses on some topics in semi-parametric econometrics, particularly the use of semi-parametric methods of estimation to obtain robust inference. Chapter two proposes a study of the finite-sample performance of the heteroskedastic and autocorrelation consistent covariance matrix estimators (HAC). This performance is accessed through the bias of the first moment of HAC type estimators and the quality of the asymptotic normal approximation to the exact finite-sample distributions of HAC type Wald statistics of scalar linear hypothesis. In Chapter three, the use of the non-overlapping deleted-l jackknife is used to propose a new approach to estimate the covariance matrix of the least square estimator in a linear regression model. This estimator is robust to the presence of heteroskedastldty and autocorrelation in the errors. Chapter four deals with improved estimation of regression coefficients through an alternative and efficient method of estimation regression models under heteroskedasticity of tmknown form. Kernel and average derivative estimation are used to estimate the conditional variance of the response variable where this conditional variance is assumed to be in an index form. Chapter five is concerned with the estimation of duration models under unobserved heterogeneity. This is a typical problem in mlcroer.onometrics and is in general due to differences among individuals. It is suggested a method of estimation based on a roughness penalty approach