P. Doukhan

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In this paper I identify a condition on the finite dimensional copulas of a univariate time series that ensures the series is weakly dependent in the sense of Doukhan and Louhichi (1999). This condition relates to the Kolmogorov-Smirnov distance between the joint copula of a group of variables in the past and a group of variables in the future, and the(More)
We give an introduction to a notion of weak dependence which is more general than mixing and allows to treat for example processes driven by discrete innovations as they appear with time series bootstrap. As a typical example, we analyze autoregressive processes and their bootstrap analogues in detail and show how weak dependence can be easily derived from(More)
J o u r n a l o f P r o b a b i l i t y Electron. Abstract We give rates of convergence in the strong invariance principle for stationary sequences satisfying some projective criteria. The conditions are expressed in terms of conditional expectations of partial sums of the initial sequence. Our results apply to a large variety of examples. We present some(More)
In this paper, a very useful lemma (in two versions) is proved: it simplifies notably the essential step to establish a Lindeberg central limit theorem for dependent processes. Then, applying this lemma to weakly dependent processes introduced in Doukhan and Louhichi (1999), a new central limit theorem is obtained for sample mean or kernel density(More)
We establish rates of convergences in time series forecasting using the statistical learning approach based on oracle inequalities. A series of papers (e.g. [MM98, Mei00, BCV01, AW12]) extends the oracle inequalities obtained for iid observations to time series under weak dependence conditions. Given a family of predictors and n observations, oracle(More)
Doukhan and Louhichi (1999) introduced a new concept of weak dependence which is more general than mixing. Such conditions are particularly well suited for deriving estimates for the cumulants of sums of random variables. We employ such cumulant estimates to derive inequalities of Bernstein and Rosenthal type which both improve on previous results.(More)
  • Robert J. Shillera, Rafał M. Wojakowskib, +11 authors John Wilson
  • 2012
This paper models Continuous Workout Mortgages (CWMs) in an economic environment with refinancings and prepayments. CWMs are home loans whose balance and payments are indexed using a market-observable house price index of the pertaining locality. Our main results include: (a) explicit modelling of repayment and interest-only CWMs; (b) closed form formulae(More)
We prove uniform convergence results for the integrated periodogram of a weakly dependent time series, namely a law of large numbers and a central limit theorem. These results are applied to Whittle's parametric estimation. Under general weak-dependence assumptions we derive uniform limit theorems and asymptotic normality of Whittle's estimate for a large(More)
We introduce new models of stationary random fields, solutions of X t = F (X t−j) j∈Z d \{0} ; ξ t , the input random field ξ is stationary, e.g. ξ is independent and identically distributed (iid). Such models extend most of those used in statistics. The (nontrivial) existence of such models is based on a contraction principle and Lipschitz conditions are(More)
We consider a class of nonparametric time series regression models in which the regressor takes values in a sequence space. Technical challenges that hampered theoretical advances in these models include the lack of associated Lebesgue density and difficulties with regard to the choice of dependence structure in the autoregressive framework. We propose an(More)