Estimation of semiparametric locally stationary diffusion models

Koo, Bonsoo; Linton, Oliver

doi:10.1016/j.jeconom.2012.05.003

Cited by 43 publications

(22 citation statements)

References 57 publications

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“…This definition of locally stationarity accommodates a variety of financial datasets. Koo and Linton [20] give sufficient conditions under which a time-inhomogeneous diffusion process is locally stationary and meanwhile, Vogt [41] studies nonparametric regression for locally stationary time series. Certainly, each stationary process is locally stationary.…”

Section: Definition 21 (Locally Stationary Process)mentioning

confidence: 99%

Additive nonparametric models with time variable and both stationary and nonstationary regressions

Dong

Linton

2017

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This paper considers nonparametric additive models that have a deterministic time trend and both stationary and integrated variables as components. The diverse nature of the regressors caters for applications in a variety of settings. In addition, we extend the analysis to allow the stationary regressor to be instead locally stationary, and we allow the models to include a linear form of the integrated variable. Heteroscedasticity is allowed for in all models. We propose an estimation strategy based on orthogonal series expansion that takes account of the different type of stationarity/nonstationarity possessed by each covariate. We establish pointwise asymptotic distribution theory jointly for all estimators of unknown functions and also show the conventional optimal convergence rates jointly in the L 2 sense. In spite of the entanglement of different kinds of regressors, we can separate out the distribution theory for each estimator. We provide Monte Carlo simulations that establish the favourable properties of our procedures in moderate sized samples. Finally, we apply our techniques to the study of a pairs trading strategy.

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Section: Definition 21 (Locally Stationary Process)mentioning

confidence: 99%

Additive nonparametric models with time variable and both stationary and nonstationary regressions

Dong

Linton

2017

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“…That is, there exists a linear time-varying structural model for y t given x t as in e.g. Robinson (1989), Cai (2007), and Koo and Linton (2012).…”

Section: Asymptotic Distributionmentioning

confidence: 99%

Structural-break models under mis-specification: Implications for forecasting

Koo

Seo

2015

Journal of Econometrics

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a b s t r a c tThis paper revisits the least squares estimator of the linear regression with a structural break. We view the model as an approximation to the true data generating process whose exact nature is unknown but perhaps changing over time either continuously or with some jumps. This view is widely held in the forecasting literature and under this view, the time series dependence property of all the observed variables is unstable as well. We establish that the rate of convergence of the estimator to a properly defined limit is at most the cube root of T , where T is the sample size, which is much slower than the standard super consistent rate. We also provide an asymptotic distribution of the estimator and that of the Gaussian quasi likelihood ratio statistic for a certain class of true data generating processes. We relate our finding to current forecast combination methods and propose a new averaging scheme. Our method compares favourably with various contemporary forecasting methods in forecasting a number of macroeconomic series.

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“…Intuitively speaking, it says that the process {X t,T } can be approximated locally around each time point u by a strictly stationary process, namely the process {X t (u)}. Similar definitions can be found, e.g., in Dahlhaus and Subba Rao (2006) or Koo and Linton (2012). (c) The error process {ε t,T : t = 1,..., T } is assumed to have the martingale difference property that…”

Section: The Modelmentioning

confidence: 99%

Testing for Structural Change in Time-Varying Nonparametric Regression Models

Vogt

2014

Econom. Theory

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In this paper, we consider a nonparametric model with a time-varying regression function and locally stationary regressors. We are interested in the question whether the regression function has the same shape over a given time span. To tackle this testing problem, we propose a kernel-based L 2 -test statistic. We derive the asymptotic distribution of the statistic both under the null and under fixed and local alternatives. To improve the small sample behavior of the test, we set up a wild bootstrap procedure and derive the asymptotic properties thereof. The theoretical analysis of the paper is complemented by a simulation study and a real data example.

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Estimation of semiparametric locally stationary diffusion models

Cited by 43 publications

References 57 publications

Additive nonparametric models with time variable and both stationary and nonstationary regressions

Additive nonparametric models with time variable and both stationary and nonstationary regressions

Structural-break models under mis-specification: Implications for forecasting

Testing for Structural Change in Time-Varying Nonparametric Regression Models

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