Surveillance of the covariance matrix of multivariate nonlinear time series

In this paper, sequential procedures for the surveillance of the covariance matrices of multivariate nonlinear time series are introduced. Two different types of control charts are proposed. The first type is based on the exponential smoothing of each component of a local measure for the covariances. The control statistic is equal to the Mahalanobis distance of this quantity with its in-control mean. In our second approach, the Mahalanobis distance is first determined and after that it is exponentially smoothed. We discuss three examples of local measures.

Several properties of the proposed schemes are discussed assuming the target process to be generated by a multivariate GARCH(1, 1) model. The generalization to the family of spherical distributions allows the modelling of frequently observed fat tails in financial data. Some results of an extensive Monte Carlo simulation study are provided in order to judge the performance of the presented control schemes. As a performance measure we use the average run length. An empirical example illustrates the importance of the fast detection of the changes in the covariance structure of the returns of financial assets.     

Improved ridge estimators in a linear regression model

In this paper, the notion of the improved ridge estimator (IRE) is put forward in the linear regression model y=X β+e. The problem arises if augmenting the equation 0=c′α+ε instead of 0=C α+? to the model. Three special IREs are considered and studied under the mean-squared error criterion and the prediction error sum of squares criterion. The simulations demonstrate that the proposed estimators are effective and recommendable, especially when multicollinearity is severe.     

A simulation study of the stochastic ridge k

A simulation of regressions is used to generate estimates by iteration of the generalized ridge parameter.The simulation results indicate that generalized ridge parameters estimated by iteration from near collinear data may be quite different from unknown optimal values.     

Ridge estimation in regression problems with autocorrelated errors: A monte carlo study

This paper presents the results of a Monte Carlo study of OLS and GLS based adaptive ridge estimators for regression problems in which the independent variables are collinear and the errors are autocorrelated. It studies the effects of degree of collinearity, magnitude of error variance, orientation of the parameter vector and serial correlation of the independent variables on the mean squared error performance of these estimators. Results suggest that such estimators produce greatly improved performance in favorable portions of the parameter space. The GLS based methods are best when the independent variables are also serially correlated.     

Comparisons of the Unbiased Ridge Estimation to the Other Estimations

In this article, we employ the method of empirical likelihood to construct confidence intervals of conditional density for a left-truncation model. It is proved that the empirical likelihood ratio admits a limiting chi-square distribution with one degree of freedom when the lifetime observations with multivariate covariates form a stationary α-mixing sequence.     

A comparison of mixed and minimax estimators of linear models

In this paper the stochastic properties of two estimators of linear models, mixed and minimax, based on different types of prior information, are compared using quadratic risk as the criterion for superiority. A necessary and sufficient condition for the minimax estimator to be superior to the comparable mixed estimator is derived as well as a simpler necessary but not sufficient condition.     

Superiority comparisons of heterogeneous linear estimators

In this paper conditions for strong and weak superiority of a heterogeneous linear estimator over another are derived. The general results are applied to some special cases: in particular, two restricted least squares estimators are compared using the superiority conditions obtained. The weak superiority criterion is used as a basis in forming a generalization of an optimal se-quence of tests (Anderson, 1962) for searching for the best estimator when the alternative linear restrictions form a nested se-quence of hypotheses. An application of this is the determination of the correct length of lag and appropriate degree of polynomial in the estimation of polynomial distributed lag models.     

On small sample properties of the almost unbiased generalized ridge estimator

The purpose of this paper is to examine small sample properties of the operational almost unbiased generalized ridge estimator (E) . The exact first two moments of theAUGRE are derived. It is shown that although the reduction of the bias of the AUGRE is substantial, the AUGRE is rather inefficient than the generalized ridge estimator without the bias correction in a wide range of a noncen-trality parameter in terms of the mean square error.     

A test of the mean square error criterion for linear admissible estimators

A test for choosing between a linear admissible estimator and the least squares estimator (LSE) is developed. A characterization of linear admissible estimators useful for comparing estimators is presented and necessary and sufficient conditions for superiority of a linear admissible estimator over the LS estimetor is derived for the test. The test is based on the MSE matrix superiority, but also new resl?!ts concerning covariance matrix comparisons of linear estimators are derived. Further,shown that the test of Toro - Vizcarrondo and Wailace applies iioi only the restricted least squares estimators but also to certain estimators outside this class.