**6. Conclusions**

In this paper, we proposed the shrinkage and preliminary test estimation methods in a system of regression models when the disturbances were dependent and correlations existed among regressors in each equation. To build the model, we first multiplied both sides of Model (1) by the inverse variance–covariance matrix of the disturbances and transformed the values using spectral decomposition. We defined the full model estimator by following Alkhamisi and Shukur (2008) and the restricted estimator by assuming a UNPI on the vector of parameters. Finally, we combined them in an optimal way by applying the shrinkage and preliminary test strategies. To illustrate and compare the relative performance of these methods, we conducted a Monte Carlo simulation. The simulated results demonstrated that the RE outperformed all other estimators when there was sufficient evidence that the vector nuisance parameters were a zero vector, that is Δ = 0. However, the RE lost its efficiency as Δ increased and became unbounded when Δ was large. The PSE dominated the FME at the small values of Δ, while the SE and PSE outshone the FME in the entire parametric space. However, the PSE was better than the SE because it controlled for the over-shrinking problem in SE. We also investigated the performance of the suggested estimations via a real-world example using financial data for the "Fragile Five" countries. The results of our data analysis were consistent with the simulated results.

For further research, one can use the other penalized techniques for the SUR model such as the smoothly clipped absolute deviation (SCAD) by Fan and Li (2001), the least absolute shrinkage and selection operator (LASSO) by Tibshirani (1996), and the adaptive LASSO estimators by Zou (2006), as well as our preliminary and shrinkage estimations.

**Author Contributions:** Conceptualization, B.Y. and S.E.A.; methodology, S.E.A.; software, B.Y.; validation, B.Y. and S.E.A.; formal analysis, B.Y.; investigation, S.E.A.; resources, S.E.A; data curation, B.Y.; writing-original draft preparation, B.Y.; writing-review and editing, B.Y. and S.E.A.; visualization, B.Y.; supervision, S.E.A.; project administration, B.Y.; funding acquisition, S.E.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** The research of S. Ejaz Ahmed is supported by the Natural Sciences and the Engineering Research Council of Canada (NSERC).

**Acknowledgments:** The authors thank Guest Editors Shuangzhe Liu and Milind Sathye and the three reviewers for their detailed reading of the manuscript and their valuable comments and suggestions that led to a considerable improvement of the paper.

**Conflicts of Interest:** The authors declare no conflict of interest.
