Nonlinear Time Series: Nonparametric and Parametric Methods

By Jay Breidt. 2005

797 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/7a8b689dc63c230684559ea4c31dfe41b1f6542c

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In Analytical Chemistry

Citations in the corpus

Coverage error optimal confidence intervals for local polynomial regression (2018, methodology): “, (Yn,Xn) of size n from F , we investigate the quality of statistical inference for μ(ν) when using kernel-based local polynomial regression methods [16, 17], focusing in particular on higher-order distributional properties of t statistics as well as on coverage error and length of Waldtype confide”
Local linear quantile estimation for nonstationary time series (2009, background): “Conditions (A1)–(A3) are needed in the sense that, without them, it might be impossible to estimate quantile curves of the series from its stochastic variation [see the discussions in Chapter 6 in Fan and Yao (2003)].”
NONPARAMETRIC ESTIMATION OF CONDITIONAL VALUE-AT-RISK AND EXPECTED SHORTFALL BASED ON EXTREME VALUE THEORY (2016, methodology): “2 δ, P∞ j=1 j aα(j)1−2 δ <∞, a fact that is needed in our proofs. We note that α-mixing is the weakest of the mixing concepts (Doukhan (1994)) and its use here is only possible due to Lemma A.2 in Gao (2007), which plays a critical role in the proof of Lemma 5. Assumption A3: 1) m(x) and all of i”
Modelling multivariate volatilities via conditionally uncorrelated components (2008, background): “1 of Fan and Yao (2003).) For an arbitrary set of n points {x1, . . . , xn}, there are 2 possible subsets. Say that B picks out a certain subset from {x1, . . . , xn} if this can be formed as a set of the form B ∩{x1, . . . , xn} for a set B in B. The collection B shatters {x1, . . . , xn} if each o”
Asymptotics for sliced average variance estimation (2007, methodology): “, βk), there are several proposed methods for estimating the projection directions B/space that is spanned by B , such as projection pursuit regression (PPR) [11], the alternating conditional expectation (ACE) method [1], principal Hessian directions (pHd) [17], minimum average variance estimation (”
Chapter 76 Large Sample Sieve Estimation of Semi-Nonparametric Models (2007, background): “30 See Fan and Yao (2003) for description of various nonparametric methods applied to nonlinear time series models.”
A Test for model specification of diffusion processes (2007, methodology): “Kernel-based tests have been shown to be effective in testing discrete time series models as demonstrated in Robinson [44], Fan and Li [24], Hjellvik, Yao and Tjøstheim [30], Li [38], Aït-Sahalia, Bickel and Stoker [4], Gozalo and Linton [27] and Chen, Härdle and Li [12]; see Hart [29] and Fan and Y”
Principal component analysis for second-order stationary vector time series (2014, background): “s. On the other hand, many time series including causal ARMA processes with continuously distributed innovations are α-mixing with exponentially decaying mixing coeﬃcients. See, e.g. Section 2.6.1 of Fan and Yao (2003) and the references within. 3.1 Asymptotics when n→ ∞ and p ﬁxed When the dimensio”
Factor modeling for high-dimensional time series: inference for the number of factors (2012, background): “6 of [7] gives a compact survey on the mixing properties of time series.”
Uniform change point tests in high dimension (2015, background): “Especially for nonlinear time series such as GARCH-models, iterated random functions and the like, we refer to [25, 29, 44] and the many references there.”
TESTING FOR THE MARKOV PROPERTY IN TIME SERIES (2011, methodology): “, local polynomial fits adapt automatically to the boundary regions when the order of polynomial r is odd (Ruppert and Wand; Fan and Yao, 2003); it is superior to the NW estimator in the context of estimating the derivatives of the regression function (Ruppert and Wand; Fan and Yao).”
Closed-loop and activity-guided optogenetic control. (2015, positive): “There is a strong precedent in the control and time series literatures for such procedures when switching dynamics are present (Fan and Yao, 2008; Liu and Gong, 2014; Zappavigna et al., 2010; Egerstedt et al., 2003; Xu and Antsaklis , 2002) as they allow for the fitting of several (often simpler;…”
Measuring nonlinear dependence in time‐series, a distance correlation approach (2012, background): “…0:546þ 1:032Xj 1 0:173Xj 2 þ 0:171Xj 3 0:431Xj 4 þ 0:332Xj 5 0:284Xj 6 þ 0:21Xj 7 þ eð1Þj ; if Xj 2 3:116; Xj ¼ 2:632þ 1:492Xj 1 1:324Xj 2 þ eð2Þj ; if Xj 2 > 3:116: ð20Þ Fan and Yao (2003) mentioned that the residuals of the above TAR model pass most residual-based tests of autocorrelation…”
Accurate Methods for Approximate Bayesian Computation Filtering (2015, methodology): “We show that using the optimal decay rate of the bandwidth, the root mean squared error of moments computed using the ﬁlter decays at the optimal rate N − 2 / ( n Y +4) , that is at the same rate as the kernel density estimator of a random vector on R n Y (Fan & Yao, 2003; Hall et al., 1995).”