31,884 research outputs found
Dynamic modeling of mean-reverting spreads for statistical arbitrage
Statistical arbitrage strategies, such as pairs trading and its
generalizations, rely on the construction of mean-reverting spreads enjoying a
certain degree of predictability. Gaussian linear state-space processes have
recently been proposed as a model for such spreads under the assumption that
the observed process is a noisy realization of some hidden states. Real-time
estimation of the unobserved spread process can reveal temporary market
inefficiencies which can then be exploited to generate excess returns. Building
on previous work, we embrace the state-space framework for modeling spread
processes and extend this methodology along three different directions. First,
we introduce time-dependency in the model parameters, which allows for quick
adaptation to changes in the data generating process. Second, we provide an
on-line estimation algorithm that can be constantly run in real-time. Being
computationally fast, the algorithm is particularly suitable for building
aggressive trading strategies based on high-frequency data and may be used as a
monitoring device for mean-reversion. Finally, our framework naturally provides
informative uncertainty measures of all the estimated parameters. Experimental
results based on Monte Carlo simulations and historical equity data are
discussed, including a co-integration relationship involving two
exchange-traded funds.Comment: 34 pages, 6 figures. Submitte
Cliques and duplication-divergence network growth
A population of complete subgraphs or cliques in a network evolving via
duplication-divergence is considered. We find that a number of cliques of each
size scales linearly with the size of the network. We also derive a clique
population distribution that is in perfect agreement with both the simulation
results and the clique statistic of the protein-protein binding network of the
fruit fly. In addition, we show that such features as fat-tail degree
distribution, various rates of average degree growth and non-averaging,
revealed recently for only the particular case of a completely asymmetric
divergence, are present in a general case of arbitrary divergence.Comment: 7 pages, 6 figure
Revlex-Initial 0/1-Polytopes
We introduce revlex-initial 0/1-polytopes as the convex hulls of
reverse-lexicographically initial subsets of 0/1-vectors. These polytopes are
special knapsack-polytopes. It turns out that they have remarkable extremal
properties. In particular, we use these polytopes in order to prove that the
minimum numbers f(d, n) of facets and the minimum average degree a(d, n) of the
graph of a d-dimensional 0/1-polytope with n vertices satisfy f(d, n) <= 3d and
a(d, n) <= d + 4. We furthermore show that, despite the sparsity of their
graphs, revlex-initial 0/1-polytopes satisfy a conjecture due to Mihail and
Vazirani, claiming that the graphs of 0/1-polytopes have edge-expansion at
least one.Comment: Accepted for publication in J. Comb. Theory Ser. A; 24 pages;
simplified proof of Theorem 1; corrected and improved version of Theorem 4
(the average degree is now bounded by d+4 instead of d+8); several minor
corrections suggested by the referee
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