A flexible semiparametric model for time series
We consider approximating a multivariate regression function by an affine combination of one-dimensional conditional component regression functions. The weight parameters involved in the approximation are estimated by least squares on the first-stage nonparametric kernel estimates. We establish asymptotic normality for the estimated weights and the regression function in two cases: the number of the covariates is finite, and the number of the covariates is diverging. As the observations are assumed to be stationary and near epoch dependent, the approach in this paper is applicable to estimation and forecasting issues in time series analysis. Furthermore, the methods and results are augmented by a simulation study and illustrated by application in the analysis of the Australian annual mean temperature anomaly series. We also apply our methods to high frequency volatility forecasting, where we obtain superior results to parametric methods.
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- Linton, Oliver & Sancetta, Alessio, 2009. "Consistent estimation of a general nonparametric regression function in time series," Journal of Econometrics, Elsevier, vol. 152(1), pages 70-78, September.
- Linton, Oliver B., 2000.
"Efficient Estimation Of Generalized Additive Nonparametric Regression Models,"
Cambridge University Press, vol. 16(04), pages 502-523, August.
- Oliver Linton, 2000. "Efficient estimation of generalized additive nonparametric regression models," LSE Research Online Documents on Economics 314, London School of Economics and Political Science, LSE Library.
- Terasvirta, Timo & Tjostheim, Dag & Granger, Clive W. J., 2010. "Modelling Nonlinear Economic Time Series," OUP Catalogue, Oxford University Press, number 9780199587155, March.
- Oliver Linton & Enno Mammen, 2006.
"Nonparametric transformation to white noise,"
LSE Research Online Documents on Economics
4426, London School of Economics and Political Science, LSE Library.
- Oliver Linton & Enno Mammen & N Nielsen, 2000.
"The Existence and Asymptotic Properties of a Backfitting Projection Algorithm under Weak Conditions,"
STICERD - Econometrics Paper Series
386, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
- Enno Mammen & Oliver Linton & J Nielsen, 2000. "The existence and asymptotic properties of a backfitting projection algorithm under weak conditions," LSE Research Online Documents on Economics 2315, London School of Economics and Political Science, LSE Library.
- Oliver Linton & E. Mammen & J. Nielsen, 1999. "The existence and asymptotic properties of a backfitting projection algorithm under weak conditions," LSE Research Online Documents on Economics 300, London School of Economics and Political Science, LSE Library.
- Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
- Zudi Lu, 2001. "Asymptotic Normality of Kernel Density Estimators under Dependence," Annals of the Institute of Statistical Mathematics, Springer, vol. 53(3), pages 447-468, September.
- Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
- Liang, Hua & Zou, Guohua & Wan, Alan T. K. & Zhang, Xinyu, 2011. "Optimal Weight Choice for Frequentist Model Average Estimators," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1053-1066.
- Bruce E. Hansen, 2007. "Least Squares Model Averaging," Econometrica, Econometric Society, vol. 75(4), pages 1175-1189, 07.
- Yongmiao Hong, 2000. "Generalized spectral tests for serial dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(3), pages 557-574.
- Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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