Copula representation of bivariate L-moments: a new estimation method for multiparameter two-dimensional copula models

Serfling and Xiao [A contribution to multivariate L-moments, L-comoment matrices. J Multivariate Anal. 2007;98:1765–1781] extended the L-moment theory to the multivariate setting. In the present paper, we focus on the two-dimensional random vectors to establish a link between the bivariate L-moments (BLM) and the underlying bivariate copula functions. This connection provides a new estimate of dependence parameters of bivariate statistical data. Extensive simulation study is carried out to compare estimators based on the BLM, the maximum likelihood, the minimum distance and a rank approximate Z-estimation. The obtained results show that, when the sample size increases, BLM-based estimation performs better as far as the bias and computation time are concerned. Moreover, the root-mean-squared error is quite reasonable and less sensitive in general to outliers than those of the above cited methods. Further, the proposed BLM method is an easy-to-use tool for the estimation of multiparameter copula models. A generalization of the BLM estimation method to the multivariate case is discussed.     

Moment method estimation of first-order continuous-time bilinear processes

In the present paper, we propose an estimation method of the first order continuous-time bilinear (COBL) process based on Euler-Maruyama discretization of the Itô solution asociated with the stochastic differerential equation (SDE) defining the process, and we suggest a standard moment method (MM) estimates of the unknown parameters involving in COBL process. So, some relationships linking the parameters and the theoretical moments of the process and its quadratic version are given. These relationships we allow to construct two algorithms to estimate the parameters based on MM. Using the fact that the incremented processes are strongly mixing with exponential rate whenever certain conditions are fulfilled, we show that the resulting estimators are strongly consistent and asymptotically normal. The theory can be applied to the COGARCH(1, 1), Gaussian Ornstein-Uhlenbeck (OU) models and among other specifications. Finite sample properties are also considered throught Monte-Carlo experimencts. In end, this algorithm is then used to model the exchanges rate of the Algerian Dinar against the US-dollar and against the single European currency.