Nonparametric regression for locally stationary time series

Vogt, Michael

doi:10.1920/wp.cem.2012.2212

Cited by 34 publications

(62 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There, theory for smooth backfitting estimators of the time‐varying functions m j was developed. The results from the work of Vogt () could be used as a starting point to generalize our theoretical results to models and . This is however far from trivial.…”

Section: Extensionsmentioning

confidence: 98%

“…innovations. The locally stationary model (without a periodic component m θ ) was studied by Vogt (). There, theory for smooth backfitting estimators of the time‐varying functions m j was developed.…”

Section: Extensionsmentioning

confidence: 99%

“…To do so, we would have to derive a uniform stochastic expansion of the smooth backfitting estimators in the time‐varying regression model , which parallels the expansion from Theorem in Appendix . (Such an expansion has not been provided in the work of Vogt ().) With such an expansion at hand, one could attempt to extend the theoretical results of this paper and to derive the asymptotic distribution of the estimated AR parameters

{\overset{ϕ}{true}}_{i} false(u false)

at a given rescaled time point u .…”

Section: Extensionsmentioning

confidence: 99%

See 2 more Smart Citations

Estimating nonlinear additive models with nonstationarities and correlated errors

Vogt

Walsh

2018

Scandinavian J Statistics

Self Cite

View full text Add to dashboard Cite

In this paper, we study a nonparametric additive regression model suitable for a wide range of time series applications. Our model includes a periodic component, a deterministic time trend, various component functions of stochastic explanatory variables, and an AR(p) error process that accounts for serial correlation in the regression error. We propose an estimation procedure for the nonparametric component functions and the parameters of the error process based on smooth backfitting and quasimaximum likelihood methods. Our theory establishes convergence rates and the asymptotic normality of our estimators. Moreover, we are able to derive an oracle‐type result for the estimators of the AR parameters: Under fairly mild conditions, the limiting distribution of our parameter estimators is the same as when the nonparametric component functions are known. Finally, we illustrate our estimation procedure by applying it to a sample of climate and ozone data collected on the Antarctic Peninsula.

show abstract

Section: Extensionsmentioning

confidence: 98%

Section: Extensionsmentioning

confidence: 99%

{\overset{ϕ}{true}}_{i} false(u false)

at a given rescaled time point u .…”

Section: Extensionsmentioning

confidence: 99%

See 1 more Smart Citation

Estimating nonlinear additive models with nonstationarities and correlated errors

Vogt

Walsh

2018

Scandinavian J Statistics

Self Cite

View full text Add to dashboard Cite

show abstract

“…Motivated by the possibly time varying stock return–inflation relationship and the drawbacks of change point analysis, we propose to use the recently emerged locally stationary models (Dahlhaus, ; Dahlhaus and Subba Rao, ; Subba Rao, ; Wu and Zhou, ; Vogt, ; Zhao, ) to model stock return and inflation. By allowing the model dynamics to change smoothly in time, locally stationary models can provide flexible and tractable alternatives over stationary models.…”

Section: Introductionmentioning

confidence: 97%

A Time Varying Approach to the Stock Return–Inflation Puzzle

Zhao

2019

Journal of the Royal Statistical Society Series C: Applied Statistics

View full text Add to dashboard Cite

Summary In the large literature on the stock return–inflation puzzle, existing works have used constant coefficient linear regression models or change point analysis with abrupt change points. Motivated by the time varying stock return–inflation relationship and the drawbacks of change point analysis, we propose to use the recently emerged locally stationary models to model stock return and inflation. Although the model exhibits non‐parametric time varying dependence structure over a long time span, it has local stationarity within each small time interval. Detailed empirical analysis is conducted and comparisons are made between various approaches. We find that the stock return–inflation correlation is negative during early sample periods and turns positive during late sample periods, but the turning time point is different for the total inflation rate and core inflation rate.

show abstract

“…There is an increasing need for non‐stationary time series regression in statistics and various related fields (Starica and Granger (), Fan et al . (), Mikosch and Starica (), Mercurio and Spokoiny (), Koo and Linton () and Vogt (), among others). Meanwhile, because of prior knowledge or mathematical requirements, in various applications the regression coefficient β 0 is known to belong to a subset of

{double-struckR}^{p}

.…”

Section: Introductionmentioning

confidence: 99%

Inference for Non-Stationary Time Series Regression With or Without Inequality Constraints

Zhou

2014

Journal of the Royal Statistical Society Series B: Statistical Methodology

View full text Add to dashboard Cite

We consider statistical inference for time series linear regression where the response and predictor processes may experience general forms of abrupt and smooth non-stationary behaviours over time. Meanwhile, the regression parameters may be subject to linear inequality constraints. A simple and unified procedure for structural stability checks and parameter inference is proposed. In the case where the regression parameters are constrained, the methodology proposed is shown to be consistent whether or not the true regression parameters are on the boundary of the restricted parameter space via utilizing an asymptotically invariant geometric property of polyhedral cones.

show abstract

Nonparametric regression for locally stationary time series

Cited by 34 publications

References 0 publications

Estimating nonlinear additive models with nonstationarities and correlated errors

Estimating nonlinear additive models with nonstationarities and correlated errors

A Time Varying Approach to the Stock Return–Inflation Puzzle

Inference for Non-Stationary Time Series Regression With or Without Inequality Constraints

Contact Info

Product

Resources

About