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.

A NONPARAMETRIC TEST OF SIGNIFICANT VARIABLES IN GRADIENTS

2020 ◽  
pp. 1-45
Author(s):  
Feng Yao ◽  
Taining Wang
Keyword(s):  
Null Distribution ◽  
Monte Carlo Study ◽  
Nonparametric Test ◽  
Hedonic Price ◽  
Finite Sample ◽  
Test Statistic ◽  
Bootstrap Test ◽  
Local Polynomial Estimation ◽  
Polynomial Estimation ◽  
Mean Function

We propose a nonparametric test of significant variables in the partial derivative of a regression mean function. The derivative is estimated by local polynomial estimation and the test statistic is constructed through a variation-based measure of the derivative in the direction of variables of interest. We establish the asymptotic null distribution of the test statistic and demonstrate that it is consistent. Motivated by the null distribution, we propose a wild bootstrap test, and show that it exhibits the same null distribution, whether the null is valid or not. We perform a Monte Carlo study to demonstrate its encouraging finite sample performance. An empirical application is conducted showing how the test can be applied to infer certain aspects of regression structures in a hedonic price model.

A NEW CHARACTERIZATION OF THE NORMAL DISTRIBUTION AND TEST FOR NORMALITY

2015 ◽  
Vol 32 (5) ◽  
pp. 1216-1252 ◽  
Author(s):  
Anil K. Bera ◽  
Antonio F. Galvao ◽  
Liang Wang ◽  
Zhijie Xiao
Keyword(s):  
Normal Distribution ◽  
Testing Procedure ◽  
Finite Sample ◽  
Omnibus Test ◽  
Sample Mean ◽  
Underlying Distribution ◽  
Asymptotic Covariance ◽  
Finite Sample Properties ◽  
Test For Normality

We study the asymptotic covariance function of the sample mean and quantile, and derive a new and surprising characterization of the normal distribution: the asymptotic covariance between the sample mean and quantile is constant across all quantiles,if and only ifthe underlying distribution is normal. This is a powerful result and facilitates statistical inference. Utilizing this result, we develop a new omnibus test for normality based on the quantile-mean covariance process. Compared to existing normality tests, the proposed testing procedure has several important attractive features. Monte Carlo evidence shows that the proposed test possesses good finite sample properties. In addition to the formal test, we suggest a graphical procedure that is easy to implement and visualize in practice. Finally, we illustrate the use of the suggested techniques with an application to stock return datasets.

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.

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 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 ESTIMATION OF INTEGRATED COVARIANCES IN THE SIMULTANEOUS PRESENCE OF NONSYNCHRONICITY, MICROSTRUCTURE NOISE AND JUMPS

2015 ◽  
Vol 32 (3) ◽  
pp. 533-611 ◽  
Author(s):  
Yuta Koike
Keyword(s):  
High Frequency ◽  
Monte Carlo Study ◽  
Jump Processes ◽  
Observation Data ◽  
Observation Error ◽  
Microstructure Noise ◽  
Finite Sample ◽  
Sampling Schemes ◽  
Integrated Covariance ◽  
Asymptotic Mixed Normality

We propose a new estimator for the integrated covariance of two Itô semimartingales observed at a high frequency. This new estimator, which we call the pre-averaged truncated Hayashi–Yoshida estimator, enables us to separate the sum of the co-jumps from the total quadratic covariation even in the case that the sampling schemes of two processes are nonsynchronous and the observation data are polluted by some noise. We also show the asymptotic mixed normality of this estimator under some mild conditions allowing infinite activity jump processes with finite variations, some dependency between the sampling times and the observed processes as well as a kind of endogenous observation error. We examine the finite sample performance of this estimator using a Monte Carlo study and we apply our estimators to empirical data, highlighting the importance of accounting for jumps even in an ultra-high frequency framework.

A Test for Functional Form Against Nonparametric Alternatives

1992 ◽  
Vol 8 (4) ◽  
pp. 452-475 ◽  
Author(s):  
Jeffrey M. Wooldridge
Keyword(s):  
Alternative Model ◽  
Regression Models ◽  
Functional Form ◽  
Parametric Model ◽  
Finite Sample ◽  
Test Statistic ◽  
Sieve Estimation ◽  
Finite Sample Properties ◽  
Standard Normal ◽  
Nonparametric Alternatives

A test for neglected nonlinearities in regression models is proposed. The test is of the Davidson-MacKinnon type against an increasingly rich set of non-nested alternatives, and is based on sieve estimation of the alternative model. For the case of a linear parametric model, the test statistic is shown to be asymptotically standard normal under the null, while rejecting with probability going to one if the linear model is misspecified. A small simulation study suggests that the test has adequate finite sample properties, but one must guard against over fitting the nonparametric alternative.

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