KERNEL AND BANDWIDTH SELECTION, PREWHITENING, AND THE PERFORMANCE OF THE FULLY MODIFIED LEAST SQUARES ESTIMATION METHOD

2002 ◽  
Vol 18 (4) ◽  
pp. 948-961 ◽  
Author(s):  
Christina Christou ◽  
Nikitas Pittis
Keyword(s):  
Least Squares ◽  
Estimation Method ◽  
Bandwidth Selection ◽  
Kernel Estimation ◽  
Kernel Estimator ◽  
Monte Carlo Study ◽  
Finite Sample ◽  
Cointegrating Vector ◽  
Bandwidth Parameter ◽  
Finite Sample Properties

This paper examines several practical issues regarding the implementation of the Phillips and Hansen fully modified least squares (FMLS) method for the estimation of a cointegrating vector. Various versions of this method arise by selecting between standard and prewhitened kernel estimation and between parametric and nonparametric automatic bandwidth estimators and also among alternative kernels. A Monte Carlo study is conducted to investigate the finite-sample properties of the alternative versions of the FMLS procedure. The results suggest that the prewhitened kernel estimator of Andrews and Monahan (1992, Econometrica 60, 953–966) in which the bandwidth parameter is selected via the nonparametric procedure of Newey and West (1994, Review of Economic Studies 61, 631–653) minimizes the second-order asymptotic bias effects.

SPATIAL DEPENDENCE IN OPTION OBSERVATION ERRORS

2020 ◽  
pp. 1-43
Author(s):  
Torben G. Andersen ◽  
Nicola Fusari ◽  
Viktor Todorov ◽  
Rasmus T. Varneskov
Keyword(s):  
Spatial Dependence ◽  
Option Price ◽  
Monte Carlo Study ◽  
Nonparametric Test ◽  
Testing Procedure ◽  
Observation Error ◽  
Finite Sample ◽  
Finite Sample Properties ◽  
Observation Times ◽  
Index Option

In this paper, we develop the first formal nonparametric test for whether the observation errors in option panels display spatial dependence. The panel consists of options with different strikes and tenors written on a given underlying asset. The asymptotic design is of the infill type—the mesh of the strike grid for the observed options shrinks asymptotically to zero, while the set of observation times and tenors for the option panel remains fixed. We propose a Portmanteau test for the null hypothesis of no spatial autocorrelation in the observation error. The test makes use of the smoothness of the true (unobserved) option price as a function of its strike and is robust to the presence of heteroskedasticity of unknown form in the observation error. A Monte Carlo study shows good finite-sample properties of the developed testing procedure and an empirical application to S&P 500 index option data reveals mild spatial dependence in the observation error, which has been declining in recent years.

scholarly journals Indirect Inference Estimation of Spatial Autoregressions

Econometrics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 34
Author(s):  
Yong Bao ◽  
Xiaotian Liu ◽  
Lihong Yang
Keyword(s):  
Monte Carlo ◽  
Least Squares ◽  
Asymptotic Distribution ◽  
Monte Carlo Study ◽  
Ordinary Least Squares ◽  
Indirect Inference ◽  
Finite Sample ◽  
Spatial Unit ◽  
Asymptotically Normal ◽  
Distribution Result

The ordinary least squares (OLS) estimator for spatial autoregressions may be consistent as pointed out by Lee (2002), provided that each spatial unit is influenced aggregately by a significant portion of the total units. This paper presents a unified asymptotic distribution result of the properly recentered OLS estimator and proposes a new estimator that is based on the indirect inference (II) procedure. The resulting estimator can always be used regardless of the degree of aggregate influence on each spatial unit from other units and is consistent and asymptotically normal. The new estimator does not rely on distributional assumptions and is robust to unknown heteroscedasticity. Its good finite-sample performance, in comparison with existing estimators that are also robust to heteroscedasticity, is demonstrated by a Monte Carlo study.

Estimating cross-sectional regressions in event studies with conditional heteroskedasticity and regression designs that have leverage

2014 ◽  
Vol 10 (4) ◽  
pp. 418-431 ◽  
Author(s):  
Imre Karafiath
Keyword(s):  
Least Squares ◽  
Event Studies ◽  
Standard Errors ◽  
Conditional Heteroskedasticity ◽  
Test Statistics ◽  
Finite Sample ◽  
Cross Sectional ◽  
Content Type ◽  
Finite Sample Properties ◽  
Regression Design

Purpose – In the finance literature, fitting a cross-sectional regression with (estimated) abnormal returns as the dependent variable and firm-specific variables (e.g. financial ratios) as independent variables has become de rigueur for a publishable event study. In the absence of skewness and/or kurtosis the explanatory variable, the regression design does not exhibit leverage – an issue that has been addressed in the econometrics literature on the finite sample properties of heteroskedastic-consistent (HC) standard errors, but not in the finance literature on event studies. The paper aims to discuss this issue. Design/methodology/approach – In this paper, simulations are designed to evaluate the potential bias in the standard error of the regression coefficient when the regression design includes “points of high leverage” (Chesher and Jewitt, 1987) and heteroskedasticity. The empirical distributions of test statistics are tabulated from ordinary least squares, weighted least squares, and HC standard errors. Findings – None of the test statistics examined in these simulations are uniformly robust with regard to conditional heteroskedasticity when the regression includes “points of high leverage.” In some cases the bias can be quite large: an empirical rejection rate as high as 25 percent for a 5 percent nominal significance level. Further, the bias in OLS HC standard errors may be attenuated but not fully corrected with a “wild bootstrap.” Research limitations/implications – If the researcher suspects an event-induced increase in return variances, tests for conditional heteroskedasticity should be conducted and the regressor matrix should be evaluated for observations that exhibit a high degree of leverage. Originality/value – This paper is a modest step toward filling a gap on the finite sample properties of HC standard errors in the event methodology literature.

Adjustments of Rao’s Score Test for Distributional and Local Parametric Misspecifications

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Anil K. Bera ◽  
Yannis Bilias ◽  
Mann J. Yoon ◽  
Süleyman Taşpınar ◽  
Osman Doğan
Keyword(s):  
Test Procedure ◽  
Score Test ◽  
Score Function ◽  
Monte Carlo Study ◽  
Fundamental Principle ◽  
Finite Sample ◽  
Special Cases ◽  
Finite Sample Properties ◽  
Data Generating Process ◽  
Rao's Score Test

AbstractRao’s (1948) seminal paper introduced a fundamental principle of testing based on the score function and the score test has local optimal properties. When the assumed model is misspecified, it is well known that Rao’s score (RS) test loses its optimality. A model could be misspecified in a variety of ways. In this paper, we consider two kinds: distributional and parametric. In the former case, the assumed probability density function differs from the data generating process. Kent (1982) and White (1982) analyzed this case and suggested a modified version of the RS test that involves adjustment of the variance. In the latter case, the dimension of the parameter space of the assumed model does not match with that of the true one. Using the distribution of the RS test under this situation, Bera and Yoon (1993) developed a modified RS test that is valid under the local parametric misspecification. This involves adjusting both the mean and variance of the standard RS test. This paper considers the joint presence of the distributional and parametric misspecifications and develops a modified RS test that is valid under both types of misspecification. Earlier modified tests under either type of misspecification can be obtained as the special cases of the proposed test. We provide three examples to illustrate the usefulness of the suggested test procedure. In a Monte Carlo study, we demonstrate that the modified test statistics have good finite sample properties.

scholarly journals X-DIFFERENCING AND DYNAMIC PANEL MODEL ESTIMATION

2013 ◽  
Vol 30 (1) ◽  
pp. 201-251 ◽  
Author(s):  
Chirok Han ◽  
Peter C. B. Phillips ◽  
Donggyu Sul
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Limit Distribution ◽  
Fixed Effects ◽  
Generalized Method Of Moments ◽  
Estimation Method ◽  
Estimation Methods ◽  
Finite Sample ◽  
Dynamic Panel ◽  
Dynamic Panel Model

This paper introduces a new estimation method for dynamic panel models with fixed effects and AR(p) idiosyncratic errors. The proposed estimator uses a novel form of systematic differencing, called X-differencing, that eliminates fixed effects and retains information and signal strength in cases where there is a root at or near unity. The resulting “panel fully aggregated” estimator (PFAE) is obtained by pooled least squares on the system of X-differenced equations. The method is simple to implement, consistent for all parameter values, including unit root cases, and has strong asymptotic and finite sample performance characteristics that dominate other procedures, such as bias corrected least squares, generalized method of moments (GMM), and system GMM methods. The asymptotic theory holds as long as the cross section (n) or time series (T) sample size is large, regardless of then/Tratio, which makes the approach appealing for practical work. In the time series AR(1) case (n= 1), the FAE estimator has a limit distribution with smaller bias and variance than the maximum likelihood estimator (MLE) when the autoregressive coefficient is at or near unity and the same limit distribution as the MLE in the stationary case, so the advantages of the approach continue to hold for fixed and even smalln. Some simulation results are reported, giving comparisons with other dynamic panel estimation methods.

scholarly journals SPECIFICATION TESTING IN NONPARAMETRIC INSTRUMENTAL QUANTILE REGRESSION

2020 ◽  
Vol 36 (4) ◽  
pp. 583-625 ◽  
Author(s):  
Christoph Breunig
Keyword(s):  
Quantile Regression ◽  
Regression Model ◽  
Monte Carlo Study ◽  
Test Statistics ◽  
Finite Sample ◽  
Test Statistic ◽  
Specification Testing ◽  
Quantile Regression Model ◽  
Endogenous Regressors ◽  
Finite Sample Properties

There are many environments in econometrics which require nonseparable modeling of a structural disturbance. In a nonseparable model with endogenous regressors, key conditions are validity of instrumental variables and monotonicity of the model in a scalar unobservable variable. Under these conditions the nonseparable model is equivalent to an instrumental quantile regression model. A failure of the key conditions, however, makes instrumental quantile regression potentially inconsistent. This article develops a methodology for testing the hypothesis whether the instrumental quantile regression model is correctly specified. Our test statistic is asymptotically normally distributed under correct specification and consistent against any alternative model. In addition, test statistics to justify the model simplification are established. Finite sample properties are examined in a Monte Carlo study and an empirical illustration is provided.

scholarly journals Integral Least-Squares Inferences for Semiparametric Models with Functional Data

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Limian Zhao ◽  
Peixin Zhao
Keyword(s):  
Data Analysis ◽  
Asymptotic Normality ◽  
Least Squares ◽  
Confidence Intervals ◽  
Functional Data ◽  
Estimation Method ◽  
Real Data ◽  
Semiparametric Models ◽  
Simulation Studies ◽  
Finite Sample

The inferences for semiparametric models with functional data are investigated. We propose an integral least-squares technique for estimating the parametric components, and the asymptotic normality of the resulting integral least-squares estimator is studied. For the nonparametric components, a local integral least-squares estimation method is proposed, and the asymptotic normality of the resulting estimator is also established. Based on these results, the confidence intervals for the parametric component and the nonparametric component are constructed. At last, some simulation studies and a real data analysis are undertaken to assess the finite sample performance of the proposed estimation method.

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