Strong approximation for a class of stationary processes

By Weidong Liu, Zhengyan Lin. 2009

78 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/d1dbcfa5cd692664dd4abdee22f09affc678a77a

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Citations in the corpus

Identifying Cointegration by Eigenanalysis (2015, background): “εt = Ctεt−1 +et (5.1) and {(Ct,et)} are i.i.d random variables with E||C 1|| q 2 < 1 and E||e||q < ∞ for some q > 2, then (ii) of Condition 3 holds with s < min{q,4}, see Corollary 3.4 of Liu and Lin (2009). Similarly, (i) follows by ergodicity. Theorem 5. Let r be known. Under Condition”
Measuring nonlinear dependence in time‐series, a distance correlation approach (2012, unknown): “(i) in Liu and Lin (2009) with q ¼ 4 and Lemma 1 with q ¼ 4 and g ¼ 1, we have ffiffiffiffiffiffiffiffiffiffi l k p kS1ðu; lÞ S1;mðu; lÞk4 CðpÞ X1 j¼m fjtjdðj; 4Þ þ jsjdðj þ k; 4Þg CðpÞm 2 c ð52Þ for any (t,s) 2 D(c), where C(p) is a constant which only depends on p and can vary from place to place.”
Asymptotic theory for stationary processes (2011, unknown): “Theorem 6 (Liu and Lin, 2009a).”
GAUSSIAN APPROXIMATIONS FOR NON-STATIONARY MULTIPLE TIME SERIES (2011, methodology): “Earlier, Wu (2007) and Liu and Lin (2009) considered stationary one-dimensional and higher-dimensional processes, respectively.”
Split invariance principles for stationary processes. (2011, methodology): “1), but, in contrast to the very restrictive condition of m-dependence, weak M-dependence holds for a huge class of stationary sequences, including those studied in Wu [49, 50] and Liu and Lin [28].”
Simultaneous inference of linear models with time varying coefficients (2010, methodology): “It also suggests a bootstrap procedure for the construction of the SCT and non-parametric supremum-type tests; see Section 4.2.”
Komlós–Major–Tusnády approximation under dependence (2014, background): “Liu and Lin (2009) removed the logarithmic term from (1.3), reaching the KMT bound o(n1/p).”