This article presents the advantages of multivariate GARCH models. Multivariate GARCH models are identified as the best and flexible models in econometrics. Also, the interest of these models is to be able to examine and analyze the various relations which the various series maintain between them. In order to be able to estimate several financial series to analyze their correlations and transfers of volatility. We present an application on the relationship between the existing volatility in the oil market and the energy market, which we found that the assembly performance of the BEKK-GARCH form is better than that of other models.
In this work, we study the famous model of volatility; called model of conditional heteroscedastic autoregressive with mixed memory MMGARCH for modeling nonlinear time series. The MMGARCH model has two mixing components, one is a GARCH short memory and the other is GARCH long memory. the main objective of this search for finds the best model between mixtures of the models we made (long memory with long memory, short memory with short memory and short memory with long memory) Also, the existence of its stationary solution is discussed. The Monte Carlo experiments demonstrate we discovered theoretical. In addition, the empirical application of the MMGARCH model (1, 1) to the daily index DOW and NASDAQ illustrates its capabilities; we find that for the mixture between APARCH and EGARCH is superior to any other model tested because it produces the smallest errors.
We define the rest of a vertex v in a graph as the number of geodesics passing through v minus the degree of v. The total rest of a graph is the sum of rests of all the vertices in that graph. We made some observations, compute rest of vertices in some standard graphs and obtain some interesting results. 1 corresponding author 2020 Mathematics Subject Classification. Geodesic, stress of a vertex, k-rest regular, total rest of a graph.
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