Nonparametric regression for locally stationary time series
By Michael Vogt. 2012
178 citations recorded by the source corpus.
In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We introduce a kernel-based method to estimate the time-varying regression function and provide asymptotic theory for our estimates. Moreover, we show that the main conditions of the theory are satisfied for a large class of nonlinear autoregressive processes with a time-varying regression function. Finally, we examine structured models where the regression function splits up into time-varying additive components. As will be seen, estimation in these models does not suffer from the curse of dimensionality. We complement the technical analysis of the paper by an application to financial data.
Subfields: Artificial Intelligence, Finance, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/f4425935b69ddd173b04eef0bb03f3425fd5dfaf
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Artificial Intelligence
- Holger Dette
- Michael Eichler
- Marc Hallin
- Rainer Dahlhaus
- Stanislav Volgushev
- Tobias Kley
- Stefan Birr
- Carsten Jentsch
In Finance
- Carsten Jentsch
- Holger Dette
- S. Rao
- Michael Vogt
- Rainer Dahlhaus
- Anne van Delft
- Michael Eichler
- Stanislav Volgushev
In Statistics and Probability
- Marc Hallin
- Stanislav Volgushev
- Holger Dette
- S. Rao
- Michael Vogt
- Carsten Jentsch
- Anne van Delft
- Rainer Dahlhaus
Citations in the corpus
- Locally Stationary Functional Time Series (2016, background): “Similarly as Dahlhaus and Subba Rao (2006) and Vogt (2012) in the case of ordinary time series, we call a functional time series locally stationary if it can be locally approximated by a stationary functional time series.”
- A test for second order stationarity of a multivariate time series (2015, background): “Fryzlewicz and Subba Rao (2011) and Vogt (2012) who derive sufficient conditions for α-mixing of a general class of nonstationary time series).”
- Time-varying model averaging (2020, unknown): “The third model setting we consider involves lagged dependent variables with i.i.d. regression errors, here we prove the asymptotic optimality of the TVJMA estimator by allowing the regressors to be locally stationary, in he sense of Ing and Wei (2003) and Vogt (2012).”
- Locally Stationary Processes (2011, background): “Vogt (2011) investigates nonlinear nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time.”
- Quantile spectral analysis for locally stationary time series (2014, background): “Contrary to Dahlhaus and Polonik (2006) and Zhou and Wu (2009a, b), who dealt with time varying (linear or non-linear) moving averages, to Dahlhaus (1997), which is based on time varying second-order spectra, to Vogt (2012), where the approximation is in terms of random variables and requires finite”
- Detecting gradual changes in locally stationary processes (2013, background): “Specifically, we work with the following concept of local stationarity, which was introduced in Vogt (2012).”