Hostname: page-component-8448b6f56d-c4f8m Total loading time: 0 Render date: 2024-04-23T10:29:42.624Z Has data issue: false hasContentIssue false
  • English
  • Français

On diagnostics in conditionally heteroskedastic time series models under elliptical distributions

Part of: Linear inference, regression

Published online by Cambridge University Press:  14 July 2016

Shuangzhe Liu
Shuangzhe Liu*
Affiliation:
Mathematical Sciences Institute, Australian National University, Canberra ACT 0200, Australia. Email address: lius@maths.anu.edu.au
Get access Rights & Permissions [Opens in a new window]

Abstract

In statistical diagnostics and sensitivity analysis, the local influence method plays an important rôle. In the present paper, we use this method to study financial time series data and conditionally heteroskedastic models under elliptical distributions. We start with a likelihood displacement, and consider data- and model-perturbation schemes. We obtain corresponding matrices of derivatives, and measures of slope and normal curvature, and then discuss the assessment of local influence.

Keywords

Statistical diagnosticslikelihood displacementobserved information matrixmatrices of derivativesmatrix differential

MSC classification

Primary: 62J05: Linear regression
Type
Part 7. Time series analysis
Information
Journal of Applied Probability , Volume 41 , Issue A: Stochastic Methods and their Applications , 2004 , pp. 393 - 405
Copyright
Copyright © Applied Probability Trust 2004 

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

Bera, A. K. and Higgins, M. L. (1995). On ARCH models: properties, estimation and testing. In Surveys in Econometrics , eds Oxley, L., George, D. A. R., Roberts, C. J. and Sayer, S., Blackwell, Oxford, pp. 215–272.Google Scholar
Chatterjee, S. and Hadi, A. S. (1988). Sensitivity Analysis in Linear Regression. John Wiley, New York.Google Scholar
Billor, N. and Loynes, R. M. (1993). Local influence: anew approach. Commun. Statist. Theory Meth. 22, 1595–1611.Google Scholar
Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity. J. Econometrics 31, 307–327.Google Scholar
Brockwell, P. J. (2000). Heavy-tailed and non-linear continuous-time ARMA models for financial time series. In Statistics and Finance: an Interface , eds Chan, W. S., Li, W. K. and Tong, H., Imperial College Press, London, pp. 3–22.Google Scholar
Brockwell, P. J. and Davis, R. A. (2002). Introduction to Time Series and Forecasting , 2nd edn. Springer, New York.Google Scholar
Cook, R. D. (1986). Assessment of local influence (with discussion). J. R. Statist. Soc. B 48, 133–169.Google Scholar
Cook, R. D. (1997). Local influence. In Encyclopedia of Statistical Sciences , Vol. 1 Update, eds Kotz, S., Read, C. B. and Banks, D. L., John Wiley, New York, pp. 380–385.Google Scholar
Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50, 987–1007.Google Scholar
Fang, K. T. and Zhang, Y. T. (1990). Generalized Multivariate Analysis. Springer, Berlin.Google Scholar
Farebrother, R. W. (1992). Relative local influence and the condition number. Commun. Statist. Simul. Comput. 21, 707–710.Google Scholar
Galea, M., Paula, G. A. and Bolfarine, H. (1997). Local influence in elliptical linear regression models. Statistician 46, 71–79.Google Scholar
Gourieroux, C. and Jasiak, J. (2001). Financial Econometrics. Problems, Models, and Methods. Princeton University Press.Google Scholar
Heyde, C. C. (1999). A risky asset model with strong dependence through fractal activity time. J. Appl. Prob. 36, 1234–1239.Google Scholar
Heyde, C. C. and Kou, S. G. (2002). On the controversy over tailweight of distributions.Google Scholar
Heyde, C. C. and Liu, S. (2001). Empirical realities for a minimal description risky asset model. The need for fractal features. J. Korean Math. Soc. 38, 1047–1059.Google Scholar
Heyde, C. C., Liu, S. and Gay, R. (2001). Fractal scaling and Black-Scholes: the full story. A new view of long-range dependence in stock prices. J. Austral. Soc. Security Anal. 1, 29–32.Google Scholar
Jung, K. M., Kim, M. G. and Kim, B. C. (1997). Second order local influence in linear discriminant analysis. J. Japan. Soc. Comput. Statist. 10, 1–11.Google Scholar
Liu, S. (2000). On local influence in elliptical linear regression models. Statist. Papers 41, 211–224.Google Scholar
Liu, S. (2002a). Local influence in multivariate elliptical linear regression models. Linear Algebra Appl. 354, 159–174.CrossRefGoogle Scholar
Liu, S. (2002b). On regression diagnostics in multivariate models under elliptical distributions. Research Division, National Center for University Entrance Examinations, Tokyo, November 2002.Google Scholar
Liu, S. and Heyde, C. C. (2002). On estimation in conditionally heteroskedastic time series models under non-normal distributions (talk). 16th Austral. Statist. Conf., Canberra, July 2002.Google Scholar
Magnus, J. R. and Neudecker, H. (1999). Matrix Differential Calculus with Applications in Statistics and Econometrics. John Wiley, Chichester.Google Scholar
Pan, J. X. and Fang, K. T. (2002). Growth Curve Models with Statistical Diagnostics. Springer, New York.Google Scholar
Peña, D. (2001). Outliers, influential observations, and missing data. In A Course in Time Series Analysis , eds Peña, D., Tiao, G. C. and Tsay, R. S., John Wiley, New York, pp. 136–170.Google Scholar
Poon, W. Y. and Poon, Y. S. (1999). Conformal normal curvature and assessment of local influence. J. R. Statist. Soc. B 61, 51–61.Google Scholar
Praetz, P. D. (1972). The distribution of share price changes. J. Business 45, 49–55.Google Scholar
Rachev, S. T. and Mittnik, S. (2000). Stable Paretian Models in Finance. John Wiley, New York.Google Scholar
Schall, R. and Dunne, T. T. (1991). Diagnostics for regression-ARMA time series, in Directions in Robust Statistics and Diagnostics , Part II, eds Stahel, W. and Weisberg, S., Springer, New York, pp. 205–221.Google Scholar
Tsay, R. S. (2002). Analysis of Financial Time Series. John Wiley, New York.Google Scholar