On detection of outliers in symmetric normal models

Extensions of recent results for detection of mean slippage type outliers from i.i.d. multivariate normal and elliptically symmetric distributions are made to symmetric case, that is, when the observations are equicorrelated. The main tool used is Wijsman's (1967) representation theorem. The results obtained can be viewed as a robustness property of the use of Mardia's multivariate kurtosis as a locally optimal test statistic to detect outliers against equicorrelated distributions.     

On influence diagnostics in elliptical multivariate regression models with equicorrelated random errors

In this paper we discuss estimation and diagnostic procedures in elliptical multivariate regression models with equicorrelated random errors. Two procedures are proposed for the parameter estimation and the local influence curvatures are derived under some usual perturbation schemes to assess the sensitivity of the maximum likelihood estimates (MLEs). Two motivating examples preliminarily analyzed under normal errors are reanalyzed considering appropriate elliptical distributions. The local influence approach is used to compare the sensitivity of the model estimates.     

Dynamic Equicorrelation

A new covariance matrix estimator is proposed under the assumption that at every time period all pairwise correlations are equal. This assumption, which is pragmatically applied in various areas of finance, makes it possible to estimate arbitrarily large covariance matrices with ease. The model, called DECO, involves first adjusting for individual volatilities and then estimating correlations. A quasi-maximum likelihood result shows that DECO provides consistent parameter estimates even when the equicorrelation assumption is violated. We demonstrate how to generalize DECO to block equicorrelation structures. DECO estimates for U.S. stock return data show that (block) equicorrelated models can provide a better fit of the data than DCC. Using out-of-sample forecasts, DECO and Block DECO are shown to improve portfolio selection compared to an unrestricted dynamic correlation structure.     

Optimal testing for equicorrelated linear regression models

Recently, Knautz and Trenkler (1993) considered Christensen’s (1987) equicorrelated linear regression model as an example to show that S² and are independent even though the disturbances are equicorrelated. This paper addresses the issue of testing for the equicorrelation coefficient in the linear regression model based on survey data. It computes exact and approximate critical values using Point optimal and F-test statistics, respectively. An empirical comparison of these critical values at five percent nominal level are presented to demonstrate the performance of the new tests.