Hostname: page-component-8448b6f56d-gtxcr Total loading time: 0 Render date: 2024-04-23T09:48:55.068Z Has data issue: false hasContentIssue false
  • English
  • Français

INFERENCE ON NONSTATIONARY TIME SERIES WITH MOVING MEAN

Published online by Cambridge University Press:  29 December 2014

Jiti Gao  and
Peter M. Robinson
Jiti Gao
Affiliation:
Monash University and London School of Economics
Peter M. Robinson*
Affiliation:
Monash University and London School of Economics
*
*Address correspondence to Peter Robinson, Department of Economics, London School of Economics, Houghton Street, London WC2A 2AE, UK; e-mail: p.m.robinson@lse.ac.uk.
Get access Rights & Permissions [Opens in a new window]

Abstract

A semiparametric model is proposed in which a parametric filtering of a nonstationary time series, incorporating fractionally differencing with short memory correction, removes correlation but leaves a nonparametric deterministic trend. Estimates of the memory parameter and other dependence parameters are proposed, and shown to be consistent and asymptotically normally distributed with parametric rate. Tests with standard asymptotics for I(1) and other hypotheses are thereby justified. Estimation of the trend function is also considered. We include a Monte Carlo study of finite-sample performance.

Type
ARTICLES
Information
Econometric Theory , Volume 32 , Issue 2 , April 2016 , pp. 431 - 457
Copyright
Copyright © Cambridge University Press 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Benedetti, J.K. (1977) On the nonparametric estimation of regression functions. Journal of the Royal Statistical Society, Series B 39, 248–253.Google Scholar
Beran, J. & Feng, Y. (2002) Local polynomial fitting with long memory, short memory and antipersistent errors. Annals of the Institute of Statistical Mathematics 54, 291–311.CrossRefGoogle Scholar
Csorgo, S. & Mielniczuk, J. (1995) Nonparametric regression under long-range dependent normal errors. Annals of Statistics 23, 1000–1014.CrossRefGoogle Scholar
Deo, R. (1997) Nonparametric regression with long-memory errors. Statistics and Probability Letters 33, 89–94.CrossRefGoogle Scholar
Fox, R. & Taqqu, M.S. (1986) Large-sample properties of parameter estimates for strongly dependent processes. Annals of Statistics 14, 517–532.CrossRefGoogle Scholar
Gasser, Th. & Mueller, H.G. (1979) Kernel estimation of regression functions. In Gasser, Th. & Rosenblatt, M. (eds.), Smoothing Techniques for Curve Estimation, pp. 23–68. Springer.CrossRefGoogle Scholar
Guo, H. & Koul, H.L. (2007) Nonparametric regression with heteroscedastic long memory errors. Journal of Statistical Planning and Inference 137, 379–404.Google Scholar
Hannan, E.J. (1973) The asymptotic theory of linear time-series models. Journal of Applied Probability 10, 130–145.CrossRefGoogle Scholar
Hualde, J. & Robinson, P.M. (2011) Gaussian pseudo-maximum likelihood estimation of fractional time series models. Annals of Statistics 39, 3152–3181.Google Scholar
Phillips, P.C.B. (2007) Regression with slowly varying regressors and nonlinear trends. Econometric Theory 23, 557–614.Google Scholar
Phillips, P.C.B. & Sul, D. (2007) Transition modeling and econometric convergence tests. Econometrica 75, 1771–1855.CrossRefGoogle Scholar
Priestley, M.B. & Chao, M.T. (1972) Non-parametric function fitting. Journal of the Royal Statistical Society, Series B 34, 385–392.Google Scholar
Robinson, P.M. (1994) Efficient tests of nonstationary hypotheses. Journal of the American Statistical Association 89, 1420–1437.Google Scholar
Robinson, P.M. (1997) Large-sample inference for nonparametric regression with dependent errors. Annals of Statistics 25, 2054–2083.Google Scholar
Robinson, P.M. (2012a) Inference on power law spatial trends. Bernoulli 18, 644–677.CrossRefGoogle Scholar
Robinson, P.M. (2012b) Nonparametric trending regression with cross-sectional dependence. Journal of Econometrics 169, 4–14.CrossRefGoogle Scholar
Roussas, G., Tran, L.T., & Ioannides, O.A. (1992) Fixed design regression for time series: Asymptotic normality. Journal of Multivariate Analysis 40, 262–291.CrossRefGoogle Scholar
Starica, C. & Granger, C. (2005) Nonstationarities in stock returns. Review of Economics and Statistics 87, 503–522.Google Scholar
Tran, L.T., Roussas, G., Yakowitz, S., & Truong Van, B. (1996) Fixed-design regression for linear time series. Annals of Statistics 24, 975–991.Google Scholar
Zhao, Z., Zhang, Y., & Li, R. (2014) Non-parametric estimation under strong dependence. Journal of Time Series Analysis 35, 4–15.Google Scholar
Zygmund, A. (1979) Trigonometric Series. Cambridge University Press.Google Scholar