1,497 research outputs found
The Hall algebra of a spherical object
We determine the Hall algebra, in the sense of Toen, of the algebraic
triangulated category generated by a spherical object.Comment: references added, generalization to ground ring in section 3, 14
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Quantile correlations and quantile autoregressive modeling
In this paper, we propose two important measures, quantile correlation (QCOR)
and quantile partial correlation (QPCOR). We then apply them to quantile
autoregressive (QAR) models, and introduce two valuable quantities, the
quantile autocorrelation function (QACF) and the quantile partial
autocorrelation function (QPACF). This allows us to extend the classical
Box-Jenkins approach to quantile autoregressive models. Specifically, the QPACF
of an observed time series can be employed to identify the autoregressive
order, while the QACF of residuals obtained from the fitted model can be used
to assess the model adequacy. We not only demonstrate the asymptotic properties
of QCOR, QPCOR, QACF, and PQACF, but also show the large sample results of the
QAR estimates and the quantile version of the Ljung-Box test. Simulation
studies indicate that the proposed methods perform well in finite samples, and
an empirical example is presented to illustrate usefulness
A localisation theorem for singularity categories of proper dg algebras
Given a recollement of three proper dg algebras over a noetherian commutative
ring, e.g. three algebras which are finitely generated over the base ring,
which extends one step downwards, it is shown that there is a short exact
sequence of their singularity categories. This allows us to recover and
generalise some known results on singularity categories of finite-dimensional
algebras.Comment: Section 3 is new, and in Section 4 the base ring is changed from a
field to a commutative noetherian ring and in Section 6 the base ring is
changed from a field to an arbitrary commutative rin
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