Nonparametric estimation of structural change points in volatility models for time series

Chen, Gongmeng; Choi, Yoon Jung; Zhou, Yong

doi:10.1016/j.jeconom.2004.02.008

Cited by 42 publications

(30 citation statements)

References 35 publications

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“…When g (s) = 0 for s ≤ s 0 and g (s) = c = 0 for s > s 0 , (3.2) includes a one-time level shift of the regression function at time k 0 = s 0 n as a special case. This is analogous to the one-time scale change of volatility function in Chen et al (2005).…”

Section: Asymptotic Local Powermentioning

confidence: 77%

“…Delgado and Hidalgo (2000) proposed estimators of location and size of structural breaks in nonparametric regression models when the regressors are strictly stationary and when lagged dependent variables are present and the break is explained by the regressor "time". Recently, Chen et al (2005) proposed a hybrid test and estimation procedure for change points in volatility based on the least squares method in nonparametric time series models where there is a scale change in the volatility function at a certain time.…”

Section: Introductionmentioning

confidence: 99%

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Testing structural change in time-series nonparametric regression models

Zhang

2008

Statistics and Its Interface

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We propose a CUSUM type of test for structural change in dynamic nonparametric regression models. It is based upon the cumulative sums of weighted residuals from a single nonparametric regression and complements the conventional parameter instability tests in parametric models. We derive the limiting distributions of the test under both the null hypothesis and sequences of local alternatives. A bootstrap procedure is also proposed and its validity is justified. Finally, simulation experiments are conducted to investigate the finite sample properties of our test.

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Section: Asymptotic Local Powermentioning

confidence: 77%

Section: Introductionmentioning

confidence: 99%

Testing structural change in time-series nonparametric regression models

Zhang

2008

Statistics and Its Interface

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“…The technique of using a combination of the left and right kernels has been previously reported, for instance: (i) Hamrouni (1999) uses it to locate the breaks of the conditional mean function, (ii) Perron (2001), Delgado and Hidalgo (2000), Chen et al (2005) and Gao et al (2008) use it to find the location of the volatility breaks and their magnitude and (iii) Qiu (2003) and Gijbels et al (2007) use it to estimate the conditional mean with breaks. These two estimators alone are not consistent in every point in the support of X t however, as we will see in Section 3, the proper combination of them will result in a consistent estimator everywhere.…”

Section: The Left Right and Centred Estimatorsmentioning

confidence: 99%

“…The BPLL Downloaded by [UNAM Ciudad Universitaria] at 01:57 20 December 2014 estimator uses the LL for the continuous parts, and an extension of Qiu (2003) estimator at the breaks and their neighbourhoods. There is a vast literature involved with finding the location and size of the breaks (Hamrouni 1999, Delgado and Hidalgo 2000, Perron 2001Chen, Choi, and Zhou 2005;Gao, Gijbels, and Van Bellegem 2008). The most interesting feature of the BPLL is that the testing of whether a point is a break or not is done simultaneously to the estimation.…”

Section: Introductionmentioning

confidence: 99%

Unstable volatility: the break-preserving local linear estimator

Casas

Gijbels

2012

Journal of Nonparametric Statistics

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The objective of this paper is to introduce the break-preserving local linear (BPLL) estimator for the estimation of unstable volatility functions for independent and asymptotically independent processes. Breaks in the structure of the conditional mean and/or the volatility functions are common in Finance. Nonparametric estimators are well suited for these events due to the flexibility of their functional form and their good asymptotic properties. However, the local polynomial kernel estimators are not consistent at points where the volatility function has a break. The estimator presented in this paper generalises the classical local linear (LL). The BPLL estimator maintains the desirable properties of the LL estimator with regard to the bias and the boundary estimation while it estimates the breaks consistently. An extensive Monte Carlo study is shown as well as detailed proofs of the estimator asymptotic behaviour.

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“…For details about the change point estimator for the conditional variance function under a dependence assumption, we refer to Chen et al [4].…”

Section: Remarkmentioning

confidence: 99%

Change point estimators by local polynomial fits under a dependence assumption

Zhang

Chen

2008

Journal of Multivariate Analysis

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We study a random design regression model generated by dependent observations, when the regression function itself (or its ν-th derivative) may have a change or discontinuity point. A method based on the local polynomial fits with one-sided kernels to estimate the location and the jump size of the change point is applied in this paper. When the jump location is known, a central limit theorem for the estimator of the jump size is established; when the jump location is unknown, we first obtain a functional limit theorem for a local dilated-rescaled version estimator of the jump size and then give the asymptotic distributions for the estimators of the location and the jump size of the change point. The asymptotic results obtained in this paper can be viewed as extensions of corresponding results for independent observations. Furthermore, a simulated example is given to show that our theory and method perform well in practice.

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Nonparametric estimation of structural change points in volatility models for time series

Cited by 42 publications

References 35 publications

Testing structural change in time-series nonparametric regression models

Testing structural change in time-series nonparametric regression models

Unstable volatility: the break-preserving local linear estimator

Change point estimators by local polynomial fits under a dependence assumption

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