6,399 research outputs found
Quotient algebra of compact-by-approximable operators on Banach spaces failing the approximation property
We initiate a study of structural properties of the quotient algebra
of the compact-by-approximable operators on
Banach spaces failing the approximation property. Our main results and
examples include the following: (i) there is a linear isomorphic embedding from
into , where belongs to the class of
Banach spaces constructed by Willis that have the metric compact approximation
property but fail the approximation property, (ii) there is a linear isomorphic
embedding from a non-separable space into , where is a universal compact
factorisation space arising from the work of Johnson and Figiel.Comment: 21 page
Transfer operators for coupled analytic maps
We consider analytically coupled circle maps (uniformly expanding and analytic) on the -lattice with exponentially decaying interaction. We introduce Banach spaces for the infinite-dimensional system that include measures whose finite-dimensional marginals have analytic, exponentially bounded densities. Using residue calculus and âcluster expansionâ-like techniques we define transfer operators on these Banach spaces. We get a unique (in the considered Banach spaces) probability measure that exhibits exponential decay of correlations
The Compass Rose Pattern of the Stock Market: How Does it Affect Parameter Estimates, Forecasts, and Statistical Tests?
A "compass rose" pattern sometimes appears when stock returns are plotted against themselves with a one-day lag, since stock prices move in discrete steps. In this paper, we perform a Monte Carlo study on simulated stock price series rounded in different ways to mirror the behavior of stocks on the Stockholm Stock Exchange. We find AR-GARCH parameter estimates to be affected by the discreteness imposed by rounding. Based on the compass rose and the discreteness, we investigate, theoretically and empirically, different possibilities of improving predictions of stock returns. The distributions of the BDS test as well as Savit and Green's dependability index are also influenced by the compass rose pattern. However, throughout the paper, we must impose unrealistically heavy rounding of the stock prices to find significant effects on our estimates, forecasts, and statistical tests.discrete prices; GARCH; forecasts; correlation integral statistics
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