Currently, oil is the key element of energy sustainability, and its prices and economy have a strong mutual influence. Modeling a good method to accurately predict oil prices over long future horizons is challenging and of great interest to investors and policymakers. This paper forecasts oil prices using many predictor variables with a new time-varying weight combination approach. In doing so, we first use five single-variable time-varying parameter models to predict crude oil prices separately. Second, every special model is assigned a time-varying weight by the new combination approach. Finally, the forecasting results of oil prices are calculated. The results show that the paper's method is robust and performs well compared to random walk.

Abstract. e thickness of a graph G is the minimum number of planar subgraphs whose union is G. A t-minimal graph is a graph of thickness t which contains no proper subgraph of thickness t. In this paper, upper and lower bounds are obtained for the thickness, t(G ◻ H), of the Cartesian product of two graphs G and H, in terms of the thickness t(G) and t(H). Furthermore, the thickness of the Cartesian product of two planar graphs and of a t-minimal graph and a planar graph are determined. By using a new planar decomposition of the complete bipartite graph K k, k , the thickness of the Cartesian product of two complete bipartite graphs K n,n and K n,n is also given, for n ≠ k + .