Abstract: Estimation of Covariance Matrices in Fixed and Mixed Effects Linear Models
The estimation of the covariance matrix or the multivariate components of variance is considered in the multivariate linear regression models with effects being fixed or random. In this paper, we propose a new method to show that usual unbiased estimators are improved on by the truncated estimators. The method is based on the Stein-Haff identity, namely the integration by parts in the Wishart distribution, and it allows us to handle the general types of scale-equivariant estimators as well as the general fixed or mixed effects linear models.
We model cross-market Bitcoin prices as long-memory processes and study dynamic interdependence in a fractionally cointegrated VAR framework. We find long-memory in both the individual markets and the system of markets depicting non-homogeneous informational inefficiency. Moreover, Bitcoin markets are found to be fractionally cointegrated, where uncertainty negatively impacts this type of cointegration relationship.