An adjustment procedure for predicting systematic risk

This paper looks at the currently available beta adjustment techniques and suggests a multiple root-linear model to adjust for the regression tendency of betas. Our empirical investigate on indicates that cross-sectional betas are not normally distributed, but their distribution tends to normal after a square-root transformation. The evidence from the Box-Cox regression model and the multivariate normality observed among betas after the transformation, make the functional form of our model correct. Also, we observe that the disturbance term of the multiple root-linear model is well behaved. These findings make the ordinary least squares estimates unbiased and efficient. Finally, the mean square and extreme errors are found to be lower when our adjustment procedure is used vis-à-vis the existing procedures.     

CONDITIONAL HETEROSCEDASTICITY IN THE MARKET MODEL AND EFFICIENT ESTIMATES OF BETAS

Previous studies have investigated only unconditional heteroscedasticity in the market model. This paper tests for both conditional and unconditional heteroscedasticities as well as normality. Using the monthly stock rate of return data secured from the Center for Research in Security Prices (CRSP) tape for 1976 through 1983, this paper shows that conditional heteroscedasticity is more widespread than unconditional heteroscedasticity, suggesting the necessity of model refinements that take conditional heteroscedasticity into account. This paper provides an alternative estimation of betas of individual securities and portfolios based on the autoregressive conditional heteroscedastic (ARCH) model introduced by Engle. The efficiency of the market model coefficients is markedly improved across all firms in the sample through the ARCH technique.     

Heteroskedasticity-consistent covariance matrix estimators for spatial autoregressive models

In the presence of heteroskedasticity, conventional test statistics based on the ordinary least squares (OLS) estimator lead to incorrect inference results for the linear regression model. Given that heteroskedasticity is common in cross-sectional data, the test statistics based on various forms of heteroskedasticity-consistent covariance matrices (HCCMs) have been developed in the literature. In contrast to the standard linear regression model, heteroskedasticity is a more serious problem for spatial econometric models, generally causing inconsistent extremum estimators of model coefficients. This paper investigates the finite sample properties of the heteroskedasticity-robust generalized method of moments estimator (RGMME) for a spatial econometric model with an unknown form of heteroskedasticity. In particular, it develops various HCCM-type corrections to improve the finite sample properties of the RGMME and the conventional Wald test. The Monte Carlo results indicate that the HCCM-type corrections can produce more accurate results for inference on model parameters and the impact effects estimates in small samples.     

Testing spatial regression models under nonregular conditions

In time series context, estimation and testing issues with autoregressive and moving average (ARMA) models are well understood. Similar issues in the context of spatial ARMA models for the disturbance of the regression, however, remain largely unexplored. In this paper, we discuss the problems of testing no spatial dependence in the disturbances against the alternative of spatial ARMA process incorporating the possible presence of spatial dependence in the dependent variable. The problems of conducting such a test are twofold. First, under the null hypothesis, the nuisance parameter is not identified, resulting in a singular information matrix (IM), which is a nonregular case in statistical inference. To take account of singular IM, we follow Davies (Biometrika 64(2):247–254, 1977; Biometrika 74(1):33–43, 1987) and propose a test procedure based on the supremum of the Rao score test statistic. Second, the possible presence of spatial lag dependence will have adverse effect on the performance of the test. Using the general test procedure of Bera and Yoon (Econom Theory 9:649–658, 1993) under local misspecification, we avoid the explicit estimation of the spatial autoregressive parameter. Thus our suggested tests are entirely based on ordinary least squares estimation. Tests suggested here can be viewed as a generalization of Anselin et al. (Reg Sci Urban Econ 26:77–104, 1996). We conduct Monte Carlo simulations to investigate the finite sample properties of the proposed tests. Simulation results show that our tests have good finite sample properties both in terms of size and power, compared to other tests in the literature. We also illustrate the applications of our tests through several data sets.     

A new test for normality

Burr (1942) type XII distribution $\text{?(u)=kc u}{}^{\mathrm{c?1}}\text{(1+u}{}^{\mathrm{c}}\text{)}{}^{\mathrm{-(k+1)}}\text{u?0, k > 0, c > 0}$ is considered. Particular values of k and c give β₁ ? 0 and β₂ ? 3. Using this fact tests for normality of observations and regression disturbances are constructed.u.1. Introduction     

Model specification tests: A simultaneous approach

In econometrics, specification tests have been constructed to verify the validity of one specification at a time. It is argued that most of these tests are not, in general, robust in the presence of other misspecifications, so their application may result in misleading conclusions. Using the Lagrange Multiplier principle we develop efficient test procedures that are capable of testing a number of specifications simultaneously. These tests will ‘confirm’ the validity (or invalidity) of a general model requiring the estimates of the restricted model only. Through an extensive Monte Carlo experiment we study the performance of these tests and some commonly used one-directional tests. We also suggest a Multiple Comparison Procedure, to identify different sources of errors. This, we hope, will lead to a better specification of econometric models.     

Efficient tests for normality,homoscedasticity and serial independence of regression residuals: Monte Carlo Evidence

In this paper we study the performance of various tests for normality (N), homoscedasticity (H) and serial independence (I) of regression residuals (u) under one, two and three directional departures from H_O:u～NHI.     

Maximum entropy autoregressive conditional heteroskedasticity model

In many applications, it has been found that the autoregressive conditional heteroskedasticity (ARCH) model under the conditional normal or Student’s t distributions are not general enough to account for the excess kurtosis in the data. Moreover, asymmetry in the financial data is rarely modeled in a systematic way. In this paper, we suggest a general density function based on the maximum entropy (ME) approach that takes account of asymmetry, excess kurtosis and also of high peakedness. The ME principle is based on the efficient use of available information, and as is well known, many of the standard family of distributions can be derived from the ME approach. We demonstrate how we can extract information functional from the data in the form of moment functions. We also propose a test procedure for selecting appropriate moment functions. Our procedure is illustrated with an application to the NYSE stock returns. The empirical results reveal that the ME approach with a fewer moment functions leads to a model that captures the stylized facts quite effectively.     

Efficient specification tests for limited dependent variable models

The procedure of Jarque and Bera (1980a, b), consisting of the application of the Lagrange Multiplier (LM) test to the Pearson Family of distributions, is used to derive efficient normality and/or homoscedasticity tests for limited dependent variable (LDV) models.     

A Test for Symmetry with Leptokurtic Financial Data

Most of the tests for symmetry are developed under the (implicitor explicit) null hypothesis of normal distribution. As is wellknown, many financial data exhibit fat tails, and thereforecommonly used tests for symmetry (such as the standard test based on sample skewness) are not valid fortesting the symmetry of leptokurtic financial data. In particular,the test uses third moment, which may not be robust in presence of gross outliers. In this article wepropose a simple test for symmetry based on the Pearson typeIV family of distributions, which take account of leptokurtosisexplicitly. Our test is based on a function that is boundedover the real line, and we expect it to be more well behavedthan the test based on sample skewness (third moment). Resultsfrom our Monte Carlo study reveal that the suggested test performsvery well in finite samples both in terms of size and power.Simulation results also support our conjecture of the teststo be well behaved and robust to excess kurtosis. We apply thetest to some selected individual stock return data to illustrateits usefulness.