712 research outputs found
Are foreign currency markets interdependent? evidence from data mining technologies
This study uses two data mining methodologies: Classification and Regression Trees (C&RT) and Generalized Rule Induction (GRI) to uncover patterns among daily cash closing prices of eight currency markets. Data from 2000 through 2009 is used, with the last year held out to test the robustness of the rules found in the previous nine years. Results from the two methodologies are contrasted. A number of rules which perform well in both the training and testing years are discussed as empirical evidence of interdependence among foreign currency markets. The mechanical rules identified in this paper can usefully supplement other types of financial modeling of foreign currencies.Foreign Currency Markets
Are oil, gold and the euro inter-related? time series and neural network analysis
This paper investigates inter-relationships among the price behavior of oil, gold and the euro using time series and neural network methodologies. Traditionally gold is a leading indicator of future inflation. Both the demand and supply of oil as a key global commodity are impacted by inflationary expectations and such expectations determine current spot prices. Inflation influences both short and long-term interest rates that in turn influence the value of the dollar measured in terms of the euro. Certain hypotheses are formulated in this paper and time series and neural network methodologies are employed to test these hypotheses. We find that the markets for oil, gold and the euro are efficient but have limited inter-relationships among themselves.Oil, Gold, the Euro, Relationships, Time-series Analysis, Neural Network Methodology
Existence of optimal ultrafilters and the fundamental complexity of simple theories
In the first edition of Classification Theory, the second author
characterized the stable theories in terms of saturation of ultrapowers. Prior
to this theorem, stability had already been defined in terms of counting types,
and the unstable formula theorem was known. A contribution of the ultrapower
characterization was that it involved sorting out the global theory, and
introducing nonforking, seminal for the development of stability theory. Prior
to the present paper, there had been no such characterization of an unstable
class. In the present paper, we first establish the existence of so-called
optimal ultrafilters on Boolean algebras, which are to simple theories as
Keisler's good ultrafilters are to all theories. Then, assuming a supercompact
cardinal, we characterize the simple theories in terms of saturation of
ultrapowers. To do so, we lay the groundwork for analyzing the global structure
of simple theories, in ZFC, via complexity of certain amalgamation patterns.
This brings into focus a fundamental complexity in simple unstable theories
having no real analogue in stability.Comment: The revisions aim to separate the set theoretic and model theoretic
aspects of the paper to make it accessible to readers interested primarily in
one side. We thank the anonymous referee for many thoughtful comment
Constructing regular ultrafilters from a model-theoretic point of view
This paper contributes to the set-theoretic side of understanding Keisler's
order. We consider properties of ultrafilters which affect saturation of
unstable theories: the lower cofinality \lcf(\aleph_0, \de) of
modulo \de, saturation of the minimum unstable theory (the random graph),
flexibility, goodness, goodness for equality, and realization of symmetric
cuts. We work in ZFC except when noted, as several constructions appeal to
complete ultrafilters thus assume a measurable cardinal. The main results are
as follows. First, we investigate the strength of flexibility, detected by
non-low theories. Assuming is measurable, we construct a
regular ultrafilter on which is flexible (thus: ok) but
not good, and which moreover has large \lcf(\aleph_0) but does not even
saturate models of the random graph. We prove that there is a loss of
saturation in regular ultrapowers of unstable theories, and give a new proof
that there is a loss of saturation in ultrapowers of non-simple theories.
Finally, we investigate realization and omission of symmetric cuts, significant
both because of the maximality of the strict order property in Keisler's order,
and by recent work of the authors on . We prove that for any , assuming the existence of measurable cardinals below ,
there is a regular ultrafilter on such that any -ultrapower of
a model of linear order will have alternations of cuts, as defined below.
Moreover, will -saturate all stable theories but will not
-saturate any unstable theory, where is the smallest
measurable cardinal used in the construction.Comment: 31 page
Saturating the random graph with an independent family of small range
Motivated by Keisler's order, a far-reaching program of understanding basic
model-theoretic structure through the lens of regular ultrapowers, we prove
that for a class of regular filters on , , the
fact that P(I)/\de has little freedom (as measured by the fact that any
maximal antichain is of size , or even countable) does not prevent
extending to an ultrafilter on which saturates ultrapowers of the
random graph. "Saturates" means that M^I/\de_1 is -saturated
whenever M is a model of the theory of the random graph. This was known to be
true for stable theories, and false for non-simple and non-low theories. This
result and the techniques introduced in the proof have catalyzed the authors'
subsequent work on Keisler's order for simple unstable theories. The
introduction, which includes a part written for model theorists and a part
written for set theorists, discusses our current program and related results.Comment: 14 page
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