Brazilian Journal of Probability and Statistics

Slope influence diagnostics in conditional heteroscedastic time series models

Mauricio Zevallos and Luiz Koodi Hotta

Full-text: Open access

Abstract

In this paper, we provide useful and simple expressions for slope influence diagnostics of several conditional heteroscedastic time series models under innovative model perturbations. These expressions are obtained by establishing a connection between the local influence and residual diagnostics. Monte Carlo experiments provided good results in terms of the size and power of the proposed statistics. To illustrate the results, we analyze the financial time series returns of the S&P500 and DJIA indexes.

Article information

Source
Braz. J. Probab. Stat., Volume 29, Number 1 (2015), 34-52.

Dates
First available in Project Euclid: 30 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1414674774

Digital Object Identifier
doi:10.1214/13-BJPS227

Mathematical Reviews number (MathSciNet)
MR3299106

Zentralblatt MATH identifier
1329.62386

Keywords
GARCH local influence outliers

Citation

Zevallos, Mauricio; Hotta, Luiz Koodi. Slope influence diagnostics in conditional heteroscedastic time series models. Braz. J. Probab. Stat. 29 (2015), no. 1, 34--52. doi:10.1214/13-BJPS227. https://projecteuclid.org/euclid.bjps/1414674774


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References

  • Abraham, B. and Yatawara, N. (1988). A score test for detection of time series outliers. Journal of Time Series Analysis 9, 109–119.
  • Billor, N. and Loynes, R. M. (1993). Local influence: A new approach. Communication in Statistics—Theory and Methods 22, 1595–1611.
  • Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 31, 307–327.
  • Charles, A. and Darné, O. (2005). Outliers and GARCH models in financial data. Economic Letters 86, 347–352.
  • Cook, R. D. (1986). Assessment of local influence (with discussion). Journal of the Royal Statistical Society B 48, 133–169.
  • Ding, Z., Granger, C. W. J. and Engle, R. F. (1993). A long memory property of stock market returns and a new model. Journal of Empirical Finance 1, 83–106.
  • Doornik, J. A. and Ooms, M. (2005). Outlier detection in GARCH models. Tinbergen Institute discussion paper TI 2005-092/4, Vrije Universiteit Amsterdam.
  • Engle, R. (2002). New frontiers for ARCH models. Journal of Applied Econometrics 17, 425–446.
  • Franses, P. H. and van Dijk, D. (1999). Outlier detection in the $\operatorname{GARCH}(1,1)$ model. Econometric Institute Research Report EI-9926/A, Erasmus Univ. Rotterdam.
  • Franses, P. H. and van Dijk, D. (2000). Non-Linear Time Series Models in Empirical Finance. Cambridge, UK: Cambridge Univ. Press.
  • Glosten, L., Jagannathan, R. and Runkle, D. (1993). On the relation between expected value and the volatility of the nominal excess returns on stocks. Journal of Finance 48, 1779–1801.
  • Hotta, L. K. and Tsay, R. (2012). Outliers in GARCH Processes. In Economic Time Series: Modeling and Seasonality (W. R. Bell, S. H. Holan and T. S. McElroy, eds.) 337–358. Boca Raton, FL: Chapman & Hall/CRC Press.
  • Johnson, N. L., Kotz, S. and Balakrishnan, N. (1995). Continuous Univariate Distributions, 2nd ed. New York: Wiley.
  • Leadbetter, M. R. (1983). Extremes and local dependence in stationary sequences. Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete 65, 291–306.
  • Liu, S. (2004). On diagnostics in conditionally heteroskedastic time series models under elliptical distributions. Journal of Applied Probability 41A, 393–405.
  • Nelson, D. B. (1991). Conditional heteroskedasticity in asset returns: A new approach. Econometrica 59, 347–370.
  • Schwarzmann, B. (1991). A connection between local-influence analysis and residual diagnostics. Technometrics 33, 103–104.
  • Zevallos, M., Santos, B. and Hotta, L. K. (2012). A note on influential diagnostics in AR(1) time series models. Journal of Statistical Planning and Inference 142, 2999–3007.
  • Zevallos, M. and Hotta, L. K. (2012). Influential observations in GARCH models. Journal of Statistical Computation and Simulation 82, 1571–1589.
  • Zhang, X. and King, M. L. (2005). Influence diagnostics in generalized autoregressive conditional heteroscedasticity processes. Journal of Business & Economic Statistics 23, 118–129.
  • Zivot, E. and Wang, J. (2006). Modeling Financial Time Series with S-PLUS, 2nd ed. New York: Springer.