Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-27T17:56:02.306Z Has data issue: false hasContentIssue false
  • English
  • Français

Estimation in Dynamic Linear Regression Models with Infinite Variance Errors

Published online by Cambridge University Press:  11 February 2009

Keith Knight
Keith Knight
Affiliation:
University of Toronto
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper considers the asymptotic behavior of M-estimates in a dynamic linear regression model where the errors have infinite second moments but the exogenous regressors satisfy the standard assumptions. It is shown that under certain conditions, the estimates of the parameters corresponding to the exogenous regressors are asymptotically normal and converge to the true values at the standard n−½ rate.

Type
Articles
Information
Econometric Theory , Volume 9 , Issue 4 , August 1993 , pp. 570 - 588
Copyright
Copyright © Cambridge University Press 1993

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

1.Akgiray, V. & Booth, G.G.. The stable-law model of stock returns. Journal of Business and Economic Statistics 6 (1988): 51–57.Google Scholar
2.Andrews, D.W.K.Least squares regression with integrated or dynamic regressors under weak error assumptions. Econometric Theory 3 (1987): 98–116.CrossRefGoogle Scholar
3.Booth, P. & Glassman, D.. The statistical distribution of exchange rates: empirical evidence and economic implications. Journal of International Economics 22 (1987): 297–319.CrossRefGoogle Scholar
4.Davis, R.A., Knight, K., & Liu, J.. M-estimation for autoregressions with infinite variance. Stochastic Processes and Their Applications 40 (1992): 145–180.CrossRefGoogle Scholar
5.Fama, E.F.The behavior of stock-market prices. Journal of Business 38 (1965): 34–105.CrossRefGoogle Scholar
6.Feller, W.An Introduction to Probability Theory and its Applications, Vol. 2 (second edition). New York: Wiley, 1971.Google Scholar
7.Fielitz, B.D. & Rozelle, J.P.. Stable distributions and mixtures of distributions for common stock returns. Journal of the American Statistical Association 78 (1982): 28–36.CrossRefGoogle Scholar
8.Hall, J.A., Brorsen, B.W. & Irwin, S.H.. The distribution of futures prices: a test of the stable-Paretian and mixtures of normal hypothesis. Journal of Financial and Quantitative Analysis 24 (1989): 105–116.CrossRefGoogle Scholar
9.Huber, P.J.Robust Statistics. New York: Wiley, 1981.CrossRefGoogle Scholar
10.Knight, K.Rate of convergence of centred estimates of autoregressive parameters for infinite variance autoregressions. Journal of Time Series Analysis 8 (1987): 51–60.CrossRefGoogle Scholar
11.Knight, K.Limit theory for autoregressive-parameter estimates in an infinite variance random walk. Canadian Journal of Statistics 17 (1989): 261–278.CrossRefGoogle Scholar
12.Lau, A.H.L., Lau, H.S., & Wingender, J.R.. The distribution of stock returns: new evidence against the stable model. Journal of Business and Economic Statistics 8 (1990): 217–223.Google Scholar
13.Mandelbrot, B.The variation of certain speculative prices. Journal of Business 36 (1963): 394–419.CrossRefGoogle Scholar
14.Mandelbrot, B.The variation of some other speculative prices. Journal of Business 40 (1967): 393–413.CrossRefGoogle Scholar
15.Pollard, D.Asymptotics for least absolute deviations regression estimators. Econometric Theory 7 (1991): 186–199.CrossRefGoogle Scholar
16.So, J.The sub-Gaussian distribution of currency futures: stable Paretian or nonstationary? Review of Economics and Statistics 69 (1987): 100–107.CrossRefGoogle Scholar