Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-13T10:17:07.125Z Has data issue: false hasContentIssue false
  • English
  • Français

Adaptive Estimation in Time Serise Regression Models With Heteroskedasticity of Unknown Form

Published online by Cambridge University Press:  18 October 2010

Javier Hidalgo
Javier Hidalgo
Affiliation:
London School of Economics
Get accessRights & Permissions [Opens in a new window]

Abstract

In a multiple time series regression model the residuals are heteroskedastic and serially correlated of unknown form. GLS estimates of the regression coefficients using kernel regression and spectral methods are shown to be adaptive, in the sense of having the same asymptotic distribution, to the first order, as GLS estimates based on knowledge of the actual heteroskedasticity and serial correlation. A Monte Carlo experiment about the performance of our estimator is described.

Information

Type
Articles
Information
Econometric Theory , Volume 8 , Issue 2 , June 1992, pp. 161 - 187
Copyright
Copyright © Cambridge University Press 1992

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.)

Article purchase

Temporarily unavailable

References

REFERENCES

1.Amemiya, T.Generalized least squares with an estimated autocovariance matrix. Econometrica 41 (1973):723–732.Google Scholar
2.Beltrao, K.I. & Bloomfield, P.. Determining the bandwidth of a kernel spectrum estimate. Journal of Time Series Analysis 8 (1987):21–38.Google Scholar
3.Bickel, P.On adaptive estimation. Annals of Statistics 10(1982):647–671.CrossRefGoogle Scholar
4.Carroll, R.D.Adapting for heteroscedasticity in linear models. Annals of Statistics 10 (1982): 1224–1233.Google Scholar
5.Doukhan, P. & Ghindes, M. Estimations dans le processus (Xn+1 =f(Xn)+EnComptes Rendus de L'Academie des Sciences. Paris, 291 (1980):61–64.Google Scholar
6.Duncan, R.B. & Jones, R.Multiple regression with stationary errors. Journal of the American Statistical Association 61 (1966):917–923.CrossRefGoogle Scholar
7.Eicker, F. Limit theorems for regression with unequal and dependent errors. Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability Vol. I Berkeley: University of California Press (1967):59–82.Google Scholar
8.Engle, R.F. & Gardner, R.Some finite sample properties of spectral estimators of a linear regression. Econometrica 44 (1976): 149–165.CrossRefGoogle Scholar
9.Hannae, E.J.Testing for a jump in the spectral function. Journal of the Royal Statistical Association Ser. B 23 (1961):394–404.Google Scholar
10.Hannan, E.J. Regression for time series. In Rosenblatt, M. (ed.) Time Series Analysis. New York: Wiley, 1963, pp. 17–37.Google Scholar
11.Hannan, E.J.Multiple time series analysis. New York: Wiley, 1970.Google Scholar
12.Hannan, E.J.Non-linear time series regression. Journal of Applied Probability 8 (1971):767–780.CrossRefGoogle Scholar
13.Harrison, M.J. & McCabe, B.P.M.. Autocorrelation with heteroscedasticity: A note on the robustness of Durbin-Watson, Geary, and Henshaw tests. Biometrika 62 (1975):214–216.Google Scholar
14.Harvey, A.C. & Robinson, P.M.. Efficient estimation of nonstationary time series regression.Journal of Time Series Analysis 9 (1988):201–214.Google Scholar
15.Hidalgo, J.Adaptive semiparametric estimation in the presence of autocorrelation of unknown form. Journal of Time Series Analysis (1992) forthcoming.Google Scholar
16.Hidalgo, J. Adaptive Estimation in Time Series Regression Models With Heteroscedasticity of Unknown Form. Preprint. Texas A&M University (1991).Google Scholar
17.Levine, D.A remark on serial correlation in maximum likelihood. Journal ofEconometrics 23 (1983): 145–194.Google Scholar
18.Manski, C.F.Adaptive estimation of non-linear regression models (with comment). Econometric Reviews 3 (1984): 145–194.Google Scholar
19.Nadaraya, E.A.On estimating regression. Theory of Probability and Its Applications 9 (1964):141–142.Google Scholar
20.Naimark, M.A.Normed rings. Groningen: Noordhoff, 1960.Google Scholar
21.Newey, W.K. & West, K.D.. A simple, positive, semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix. Econometrica 55 (1987):703–708.CrossRefGoogle Scholar
22.Parzen, E.On consistent estimates of the spectrum of a stationary time series. Annals of Mathematical Statistics 28 (1957):329–348.CrossRefGoogle Scholar
23.Pham, D.T. & Tran, L.T.. Some mixing properties of time series models. Stochastic Processes and Their Applications 19 (1986):297–303.CrossRefGoogle Scholar
24.Robinson, P.M.Instrumental variable estimation of differential equations. Econometrica 44 (1976):765–776.Google Scholar
25.Robinson, P.M.Asymptotically efficient estimation in the presence of heteroscedasticity of unknown form. Econometrica 55 (1987):875–891.CrossRefGoogle Scholar
26.Robinson, P.M. Hypothesis Testing in Semiparametric and Nonparametri c Models for Econometric Time Series. Preprint (1987).Google Scholar
27.Robinson, P.M.Root-N-consistent semiparametric regression. Econometrica 56 (1988): 931–954.Google Scholar
28.Robinson, P.M.Automatic Generalized Least Squares. Manuscript (1988).Google Scholar
29.Volkonskii, V.A. & Rozanov, Y.A..Some limit theorems for random functions II. Theory of Probability and Its Applications 6 (1961): 186–198.CrossRefGoogle Scholar
30.Watson, G.S.Smooth regression analysis. Sankhya, Ser. A 26 (1964):359–372.Google Scholar
31.White, H. & Domowitz, I.. Nonlinear regression with dependent observations. Econometrica 52 (1984): 143–161.Google Scholar
32.Yoshihara, K.Limiting behavior of U-statistics for stationary absolutely regular processes. Zeitschrift fur WahrscheinUchkeitstheorie und Verwandte Gebiete 35 (1976):237–252.Google Scholar