Mixing: Properties and Examples

By Paul Doukhan. 1994

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Citations in the corpus

A Kernel Independence Test for Random Processes (2014, background): “(4) Using covariance inequalities from (Doukhan, 1994, Section 1.2.2) we conclude that EeYo (Y1)eYp (Yj+1) = O(Λ(j) 1 2 ) and EeXu (Xπ(1))eXi (Xπ(j+1)) = O(Λ(|π(j) − π(1)”
Basic properties of strong mixing conditions. A survey and some open questions (2005, methodology): “For mixing properties of linear processes, see [71] and [143].”
A new semiparametric spatial model for panel time series (2001, unknown): “To establish � -mixing with exponential decay rates for {Z � t =( Yt; ln(Dt))}, we need to show (e.g. Doukhan, 1994 ):”
Inference for Observations of Integrated Diffusion Processes (2004, background): “Hence the theorem follows from a classical central limit result for strongly mixing processes, see e.g. Theorem 1 in Section 1.5 of Doukhan (1994).”
Inequalities and limit theorems for weakly dependent sequences (2013, methodology): “2, we give the extension of Ibragimov’s central limit theorem for partial sums of a strongly mixing sequence of bounded random variables to unbounded random variables, due to Doukhan, Massart and Rio (1994). We essentially follow the line of proof of Ibragimov and Linnik (1971) and Hall and Heyde (1”
Let's Fix It: Fixed-b Asymptotics versus Small-b Asymptotics in Heteroskedasticity and Autocorrelation Robust Inference (2010, unknown): “q = maxfq0 : q0 2 Z; gq0 = lim x!0 1 k(x) jxjq0 <1g (6)”
COPULAS AND TEMPORAL DEPENDENCE (2008, background): “Geometric α-mixing is sufficient for a range of inequalities and limit theorems that are useful in demonstrating the asymptotic validity of statistical methods; see e.g. Doukhan (1994).”
Estimating Space and Space-Time Covariance Functions for Large Data Sets: A Weighted Composite Likelihood Approach (2012, background): “Condition ( N 1) is satisfied if Z is a stationary Gaussian random field with correlation function that decays at a polynomial rate faster than d 1 and its spectral density is bounded below due to Corollary 2 of Doukhan ( 1994 , p.”
Least‐squares Estimation of an Unknown Number of Shifts in a Time Series (2000, background): “A maximal inequality for strongly mixing stationary processes We consider now that å is a strongly mixing stationary process (or á-mixing), see Doukhan (1994), or Rio (1995) for the de®nition of the sequence of strongly mixing coef®cient fá(n)gn .”
ASYMPTOTICS OF THE QMLE FOR A CLASS OF ARCH(q) MODELS (2005, background): “…ergodic+ Geometric ergodicity implies that the stationary version is b-mixing with exponentially decaying mixing coefficients ~see Davydov, 1973; Doukhan, 1994!+ Importantly, the strong law of large numbers ~LLN! holds for any given initial distribution of the geometrically ergodic process ~cf+…”
Sharp error terms and neccessary conditions for exponential hitting times in mixing processes (2004, background): “We refer to Doukhan (1995) for examples and references of α-mixing processes that are not φ-mixing, φ-mixing processes that are not ψ-mixing and ψ-mixing processes decaying at any rate.”
ROSENTHAL’S TYPE INEQUALITIES FOR NEGATIVELY ORTHANT DEPENDENT RANDOM VARIABLES (2006, background): “Doukhan [2] for more Key words and phrases: Negatively orthant dependent, Rosenthal’s type inequality.”
ERGODICITY, MIXING, AND EXISTENCE OF MOMENTS OF A CLASS OF MARKOV MODELS WITH APPLICATIONS TO GARCH AND ACD MODELS (2008, methodology): “…from its stationary distribution, Zt is stationary and b-mixing with geometrically decaying mixing numbers ~see Meyn and Tweedie, 1993, pp+ 230–231; Doukhan, 1994, pp+ 4, 89!+ Thus, Proposition 1 provides us with results similar to those stated in Proposition 4 of Carrasco and Chen…”
Entry and return times distribution (2013, unknown): “s a list of mixing properties arranged in decreasing order of strength. Except for the β-mixing case, Uis always in the σ-algebra generated by An and V lies in the σ-algebra generated by A∗ (see also [33, 16]). The limiting behaviour is as the length of the ‘gap’ ∆ → ∞: (1) ψ-mixing: sup n sup U,V µ”