Local Linear Fitting Under Near Epoch Dependence: Uniform Consistency With Convergence Rates

Li, Degui; Lu, Zudi; Linton, Oliver

doi:10.1017/s0266466612000011

Cited by 30 publications

(22 citation statements)

References 42 publications

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“…The simultaneous confidence bands are useful for assessing the overall variability of the estimated curves. Recently Lu and Linton (2007) and Li, Lu and Linton (2010) obtained asymptotic normality and uniform bounds for local linear estimates under near-epoch dependence. It seems not easy to apply their framework to establish the Gumbel type of convergence for maximum deviations of local linear estimates.…”

Section: Dependence Measuresmentioning

confidence: 99%

Asymptotic theory for stationary processes

2011

Statistics and Its Interface

104

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We present a systematic asymptotic theory for statistics of stationary time series. In particular, we consider properties of sample means, sample covariance functions, covariance matrix estimates, periodograms, spectral density estimates, U -statistics, kernel density and regression estimates of linear and nonlinear processes. The asymptotic theory is built upon physical and predictive dependence measures, a new measure of dependence which is based on nonlinear system theory. Our dependence measures are particularly useful for dealing with complicated statistics of time series such as eigenvalues of sample covariance matrices and maximum deviations of nonparametric curve estimates.

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Section: Dependence Measuresmentioning

confidence: 99%

Asymptotic theory for stationary processes

2011

Statistics and Its Interface

104

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“…Assumption 4 gives some conditions on the bandwidths and stability coefficient of the NED process. In particular, the technical conditions in Assumption 4(ii) are similar to the corresponding conditions in Lu and Linton (2007) and Li et al (2012), and they can be satisfied by some interesting time series models under mild conditions. More discussion can be found in Section 4.1 of Lu and Linton (2007) and Remark 2.1 of Li et al (2012).…”

Section: Assumptionmentioning

confidence: 69%

A Flexible Semiparametric Model for Time Series

Li¹,

Linton²,

Lu³

2012

SSRN Journal

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We consider approximating a multivariate regression function by an affine combination of one-dimensional conditional component regression functions. The weight parameters involved in the approximation are estimated by least squares on the first-stage nonparametric kernel estimates. We establish asymptotic normality for the estimated weights and the regression function in two cases: the number of the covariates is finite, and the number of the covariates is diverging. As the observations are assumed to be stationary and near epoch dependent, the approach in this paper is applicable to estimation and forecasting issues in time series analysis. Furthermore, the methods and results are augmented by a simulation study and illustrated by application in the analysis of the Australian annual mean temperature anomaly series. We also apply our methods to high frequency volatility forecasting, where we obtain superior results to parametric methods. JEL subject classifications: C14, C22.

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“…However, they provided only a sketch proof of this result in the case where the process is assumed to have compact support and to be strong mixing with geometric decay. A recent paper by Li et al (2012) provided a more rigorous and complete proof of this result. Linton and Mammen (2008) generalized this class of models to allow for exogenous regressors and more complicated dynamics.…”

Section: Introductionmentioning

confidence: 76%