In this article, the tests on parallelism, equal intercept and sets of lines in-tersected at a fixed value for a set of r simple linear Models or a set of r linearizable regression Models are generalized to the Multivariate case, r = 2; 3; : : :; R. Likewise, the normality hypothesis is replaced assuming an elliptical matrix variate distribution, concluding that the tests obtained under normality are valid and are invariant under the whole family of elliptical matrix variate distributions. Finally, an application in an agricultural acarology context is provided.

In this paper, the use of weighted pairwise likelihood instead of the full likelihood in estimating the parameters of the Multivariate AR (1) is investigated. A closed formula for typical elements of the Godambe information (sandwich information) is presented. Some efficiency calculations are also given to discuss the feasibility and computational advantages of the weighted pairwise likelihood approach relative to the full likelihood approach.

H igh price volatility and the risk are the main features of commodity markets. One way to reduce this risk is to apply the hedging policy by future contracts. In this regard, in this paper, we will calculate the optimal hedging ratios for OPEC oil. In this study, besides the Multivariate GARCH Models, for the first time we use conditional copula Models for modelling dependence structure between OPEC oil and WTI future contract with different maturities and estimating hedging ratio for OPEC oil by using WTI future contracts. The results of this study show that dependence structure between OPEC oil and WTI future contract in three maturities is asymmetric. In addition, results indicate that during the studied period (2003-2017), Copula-based Models have more efficiency in applying the hedging policy than Multivariate GARCH Models. With an increase in the maturity of contracts, the average optimal hedge ratio increases. On the other hand, the highest performance of hedging strategies achieved by using WTI futures contract with six months maturity...