Testing for Structural Change in Time-Varying Nonparametric Regression Models

Vogt, Michael

doi:10.1017/s0266466614000565

Cited by 16 publications

(9 citation statements)

References 43 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Moreover, the author also established the convergence rates for their estimation on any compact set and the point-wise normality for their estimators. Moreover, the results and ideas have been used to study the structural changes problem in [60]. Later on, in [69], the authors advanced the kernel estimation theory under a general setting using the physical representation [63].…”

Section: Some Related Resultsmentioning

confidence: 99%

“…Moreover, m j 's are some smooth functions that map the time and covariates to the conditional mean. (1.1) has been employed in the literature, for instance, see [37,55,59,60,69]. It provides a more flexible and general framework and a wide range of models can fit into it.…”

Section: Introductionmentioning

confidence: 99%

“…Assuming that m j has a multiplicative separability form in the time t and the covariate, the time varying linear model has been studied in [10,26,27,35,48,75,77] among others and the general multiplicative form has been recently studied in [12,34,70]. Moreover, when X j,i,n = Y i−j,n in (1.1), it becomes the nonparametric and nonlinear autoregressive process [60,Section 3.1]. Finally, we point out that (1.1) can be regarded as a discretized version of the Langevin equation…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Simultaneous Sieve Inference for Time-Inhomogeneous Nonlinear Time Series Regression

Ding¹,

Zhou²

2021

Preprint

View full text Add to dashboard Cite

In this paper, we consider the time-inhomogeneous nonlinear time series regression for a general class of locally stationary time series. On one hand, we propose sieve nonparametric estimators for the time-varying regression functions which can achieve the min-max optimal rate as in [52]. On the other hand, we develop a unified simultaneous inferential theory which can be used to conduct both structural and exact form testings on the functions. Our proposed statistics are powerful even under locally weak alternatives. We also propose a multiplier bootstrapping procedure for practical implementation. Our methodology and theory do not require any structural assumptions on the regression functions and we also allow the functions to be supported in an unbounded domain. We also establish sieve approximation theory for 2-D functions in unbounded domain and a Gaussian approximation result for affine and quadratic forms for high dimensional locally stationary time series, which can be of independent interest. Numerical simulations and a real financial data analysis are provided to support our results.

show abstract

Section: Some Related Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Simultaneous Sieve Inference for Time-Inhomogeneous Nonlinear Time Series Regression

Ding¹,

Zhou²

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…observations via a permutation principle. Apart from these works, to some extent related problems have also been considered by Vogt [32] and by Juhl and Xiao [18]. Note that our procedure could be combined with that of Schmidt et al [30] to yield a test for stationarity of the first two moments.…”

mentioning

confidence: 80%

Detecting changes in the trend function of heteroscedastic time series

Schmidt¹

2021

Preprint

View full text Add to dashboard Cite

We propose a new asymptotic test to assess the stationarity of a time series' mean that is applicable in the presence of both heteroscedasticity and short-range dependence. Our test statistic is composed of Gini's mean difference of local sample means. To analyse its asymptotic behaviour, we develop new limit theory for U-statistics of strongly mixing triangular arrays under non-stationarity. Most importantly, we show asymptotic normality of the test statistic under the hypothesis of a constant mean and prove the test's consistency against a very general class of alternatives, including both smooth and abrupt changes in the mean. We propose estimators for all parameters involved, including an adapted subsampling estimator for the long run variance, and show their consistency. Our procedure is practically evaluated in an extensive simulation study and in two data examples.

show abstract

“…is symmetric about zero, bounded and twice continuously differentiable with K(x)dx = 1 and square-integrable with k(0 Vogt (2015) to relieve this condition. The β-mixing condition is widely adopted in the literature.…”

Section: Asymptotic Theorymentioning

confidence: 99%

Testing and Modelling for the Structural Change in Covariance Matrix Time Series With Multiplicative Form

Jiang¹,

Liu²,

Li³

et al. 2023

STAT SINICA

View full text Add to dashboard Cite

We first construct a new generalized Hausman test for detecting the structural change in a multiplicative form of covariance matrix time series model. This generalized Hausman test is asymptotically pivotal, and it has non-trivial power in detecting a broad class of alternatives. Moreover, we propose a new semiparametric covariance matrix time series model, which has a time-varying long run component to take the structural change into account, and a BEKKtype short run component to capture the temporal dependence. A two-step estimation procedure is proposed to estimate this semiparametric model, and the asymptotics of the related estimators are established. Finally, the importance of the generalized Hausman test and the semiparametric model is illustrated by simulations and an application to realized covariance matrix data.1. Introduction. Matrix-variate observations are often encountered in statistical applications with structured information. An important example is the realized covariance (RCOV) matrix, which is calculated from intraday high-frequency returns and able to enhance the prediction ability for the covariance matrix of the underly-Keywords and phrases: Covariance matrix time series model; Profiled quasi maximum likelihood estimation; Realized covariance matrix; Semiparametric time series model; Structural change testing.

show abstract

Testing for Structural Change in Time-Varying Nonparametric Regression Models

Cited by 16 publications

References 43 publications

Simultaneous Sieve Inference for Time-Inhomogeneous Nonlinear Time Series Regression

Simultaneous Sieve Inference for Time-Inhomogeneous Nonlinear Time Series Regression

Detecting changes in the trend function of heteroscedastic time series

Testing and Modelling for the Structural Change in Covariance Matrix Time Series With Multiplicative Form

Contact Info

Product

Resources

About