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.

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 Fixed and Long Time Span Jump Tests: New Monte Carlo and Empirical Evidence

Econometrics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 13 ◽  
Author(s):  
Mingmian Cheng ◽  
Norman Swanson
Keyword(s):  
Monte Carlo ◽  
Fixed Time ◽  
Time Span ◽  
Finite Sample ◽  
Long Span ◽  
Finite Sample Properties ◽  
Jump Intensity ◽  
Data Generating Process ◽  
Long Time ◽  
Robust Tests

Numerous tests designed to detect realized jumps over a fixed time span have been proposed and extensively studied in the financial econometrics literature. These tests differ from “long time span tests” that detect jumps by examining the magnitude of the jump intensity parameter in the data generating process, and which are consistent. In this paper, long span jump tests are compared and contrasted with a variety of fixed span jump tests in a series of Monte Carlo experiments. It is found that both the long time span tests of Corradi et al. (2018) and the fixed span tests of Aït-Sahalia and Jacod (2009) exhibit reasonably good finite sample properties, for time spans both short and long. Various other tests suffer from finite sample distortions, both under sequential testing and under long time spans. The latter finding is new, and confirms the “pitfall” discussed in Huang and Tauchen (2005), of using asymptotic approximations associated with finite time span tests in order to study long time spans of data. An empirical analysis is carried out to investigate the implications of these findings, and “time-span robust” tests indicate that the prevalence of jumps is not as universal as might be expected.

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.

scholarly journals ASYMPTOTIC INFERENCE FOR NONSTATIONARY FRACTIONALLY INTEGRATED AUTOREGRESSIVE MOVING-AVERAGE MODELS

2001 ◽  
Vol 17 (4) ◽  
pp. 738-764 ◽  
Author(s):  
Shiqing Ling ◽  
W.K. Li
Keyword(s):  
Moving Average ◽  
Unit Roots ◽  
Asymptotic Distributions ◽  
Autoregressive Moving Average ◽  
Finite Sample ◽  
Asymptotic Inference ◽  
Moving Average Models ◽  
Special Cases ◽  
Finite Sample Properties ◽  
Memory Time

This paper considers nonstationary fractional autoregressive integrated moving-average (p,d,q) models with the fractionally differencing parameter d ∈ (− 1/2,1/2) and the autoregression function with roots on or outside the unit circle. Asymptotic inference is based on the conditional sum of squares (CSS) estimation. Under some suitable conditions, it is shown that CSS estimators exist and are consistent. The asymptotic distributions of CSS estimators are expressed as functions of stochastic integrals of usual Brownian motions. Unlike results available in the literature, the limiting distributions of various unit roots are independent of the parameter d over the entire range d ∈ (− 1/2,1/2). This allows the unit roots and d to be estimated and tested separately without loss of efficiency. Our results are quite different from the current asymptotic theories on nonstationary long memory time series. The finite sample properties are examined for two special cases through simulations.

scholarly journals ADAPTIVE LONG MEMORY TESTING UNDER HETEROSKEDASTICITY

2016 ◽  
Vol 33 (3) ◽  
pp. 755-778 ◽  
Author(s):  
David Harris ◽  
Hsein Kew
Keyword(s):  
Long Memory ◽  
Score Test ◽  
Monte Carlo Experiment ◽  
Finite Sample ◽  
Large Power ◽  
Finite Sample Properties ◽  
Weighted Score ◽  
Unknown Form ◽  
Arfima Model ◽  
Asymptotically Efficient

This paper considers adaptive hypothesis testing for the fractional differencing parameter in a parametric ARFIMA model with unconditional heteroskedasticity of unknown form. A weighted score test based on a nonparametric variance estimator is proposed and shown to be asymptotically equivalent, under the null and local alternatives, to the Neyman-Rao effective score test constructed under Gaussianity and known variance process. The proposed test is therefore asymptotically efficient under Gaussianity. The finite sample properties of the test are investigated in a Monte Carlo experiment and shown to provide potentially large power gains over the usual unweighted long memory test.

FULLY MODIFIED ESTIMATION OF SEASONALLY COINTEGRATED PROCESSES

2010 ◽  
Vol 26 (5) ◽  
pp. 1491-1528 ◽  
Author(s):  
Stéphane Gregoir
Keyword(s):  
Test Procedure ◽  
Unit Roots ◽  
Ordinary Least Squares ◽  
Convergence Result ◽  
Covariance Matrices ◽  
Finite Sample ◽  
Sample Covariance ◽  
Finite Sample Properties ◽  
Seasonal Cointegration ◽  
Asymptotic Normal

We extend the framework of the fully modified, ordinary least squares (OLS) estimator introduced by Phillips and Hansen (1990) to the case of seasonally cointegrated processes at a given frequency. First we extend a weak convergence result of sample covariance matrices (Phillips, 1988) to the case of seasonal unit roots. Using a complex number framework, we then show that we can take into account the constraints that exist in a situation of seasonal cointegration as illustrated in Gregoir (1999a) and derive estimates of the cointegration vectors that allow for asymptotic normal inference. This allows us to propose a test whose null hypothesis is the existence of seasonal cointegration. A Monte Carlo exercise investigates the finite sample properties of this test procedure. The paper closes with the analysis of situations in which there exist more than one frequency at which seasonal cointegration can be observed.

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.

Finite-Sample Properties of a Two-Stage Single Equation Estimator in the SUR Model

1986 ◽  
Vol 2 (1) ◽  
pp. 66-74 ◽  
Author(s):  
G. H. Hillier ◽  
S. E. Satchell
Keyword(s):  
Least Squares ◽  
Linear Combination ◽  
Density Function ◽  
Generalized Least Squares ◽  
Single Equation ◽  
Exact Results ◽  
Finite Sample ◽  
Two Stage ◽  
Special Cases ◽  
Finite Sample Properties

Exact expressions are derived for the density function, variance, and kurtosis of a linear combination of the elements of a two-stage estimator for the coefficients in a single equation of a SUR system. The estimator is the first iterate in the iterative generalized least squares procedure described by Telser [14]. Our results generalize all previously known results for this estimator and, in certain special cases, also generalize some earlier exact results for Zellner's unrestricted covariance matrix estimator, to which it reduces in these special cases.

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