In a recent pilot study, errors in forecasts of future returns showed little differences when arithmetic and geometric mean calculations served as the basis for the projections. Using annual returns on the DJIA and S&P for 1954 to 2007, 1-year-, 5-year-ahead, and 10-year-ahead forecasts were made based on 5-, 10-, 15-, and 20-year histories based on both arithmetic and geometric averages. This ...

The second and third geometric-arithmetic indices GA2(G) and GA3(G) of a graph G are defined, respectively, as ∑ uv∈E(G) √ nu(e,G)nv(e,G) 1 2 [nu(e,G)+nv(e,G)] and ∑ uv∈E(G) √ mu(e,G)mv(e,G) 1 2 [mu(e,G)+mv(e,G)] , where e = uv is one edge in G, nu(e,G) denotes the number of vertices in G lying closer to u than to v andmu(e,G) denotes the number of edges in G lying closer to u than to v. The Sz...