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Interaction between Autocorrelation and Conditional Heteroscedasticity: A Random-Coefficient Approach

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  • Bera, Anil K
  • Higgins, Matthew L
  • Lee, Sangkyu

Abstract

In applied econometrics, the authors tend to tackle specification problems one at a time rather than considering them jointly. This has serious consequences for statistical inference. One example of this is considering autocorrelation and autoregressive conditional heteroscedasticity separately. In this article, the authors consider a linear regression model with random coefficient autoregressive disturbances that provides a convenient framework to analyze autocorrelation and autoregressive conditional heteroscedasticity simultaneously. Their stationarity conditions and testing results reveal the strong interaction between autoregressive conditional heteroscedasticity and autocorrelation. An empirical example of testing the unbiasedness of experts' expectations of inflation demonstrates that neglecting conditional heteroscedasticity or misspecifying the autocorrelation structure might result in unreliable inference.

Suggested Citation

  • Bera, Anil K & Higgins, Matthew L & Lee, Sangkyu, 1992. "Interaction between Autocorrelation and Conditional Heteroscedasticity: A Random-Coefficient Approach," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 133-142, April.
    • Handle: RePEc:bes:jnlbes:v:10:y:1992:i:2:p:133-42
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    Cited by:

    1. J. Peter Ferderer, 1999. "Credibility of the Interwar Gold Standard, Uncertainty, and the Great Depression," Macroeconomics 9907002, University Library of Munich, Germany.
    2. Arouri, Mohamed El Hedi & Hammoudeh, Shawkat & Lahiani, Amine & Nguyen, Duc Khuong, 2013. "On the short- and long-run efficiency of energy and precious metal markets," Energy Economics, Elsevier, vol. 40(C), pages 832-844.
    3. H. Wong & W. Li, 2002. "Detecting and Diagnostic Checking Multivariate Conditional Heteroscedastic Time Series Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 45-59, March.
    4. McDonald, A.David & Hurn, A.Stan, 1995. "Unobservable cyclical components in term premia of fixed-term financial instruments," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 39(3), pages 403-409.
    5. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    6. Aknouche, Abdelhakim & Guerbyenne, Hafida, 2009. "On some probabilistic properties of double periodic AR models," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 407-413, February.
    7. Marc Sáez & Robert M. Kunst, 1995. "ARCH patterns in cointegrated systems," Economics Working Papers 110, Department of Economics and Business, Universitat Pompeu Fabra.
    8. Stefan Mittnik & Marc Paolella & Svetlozar Rachev, 1998. "Unconditional and Conditional Distributional Models for the Nikkei Index," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 5(2), pages 99-128, May.
    9. A. DAVID McDONALD & JON D. KENDALL & TIM LA. RIDLEY, 1993. "GARCH‐M Estimates of Variable Risk Premia for 180‐day Australian Bank Bills," The Economic Record, The Economic Society of Australia, vol. 69(1), pages 10-19, March.
    10. Blake, Andrew P. & Kapetanios, George, 2007. "Testing for ARCH in the presence of nonlinearity of unknown form in the conditional mean," Journal of Econometrics, Elsevier, vol. 137(2), pages 472-488, April.
    11. Tzavalis, Elias & Wickens, M. R., 1996. "Forecasting inflation from the term structure," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 103-122, May.
    12. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521770415.
    13. Christos Agiakloglou & Anil Bera & Emmanouil Deligiannakis, 2022. "Evaluating measures of dependence for linearly generated nonlinear time series along with spurious correlation," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 46(3), pages 535-552, July.
    14. De Arce Borda, R., 2004. "20 años de modelos ARCH: una visión de conjunto de las distintas variantes de la familia/20 Years of Arch Modelling: a Survey of Different Models in the Family," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 22, pages 1-27, Abril.
    15. James D. Hamilton, 2008. "Macroeconomics and ARCH," NBER Working Papers 14151, National Bureau of Economic Research, Inc.
    16. Robert Kunst, 1997. "Augmented ARCH models for financial time series: stability conditions and empirical evidence," Applied Financial Economics, Taylor & Francis Journals, vol. 7(6), pages 575-586.
    17. Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2000. "Diagnosing and treating the fat tails in financial returns data," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 389-416, November.
    18. Jacek Kwiatkowski, 2008. "Bayesian Analysis of Polish Inflation Rates Using RCA and GLL Models," Dynamic Econometric Models, Uniwersytet Mikolaja Kopernika, vol. 8, pages 129-138.
    19. Furno, Marilena, 2001. "LAD estimation with random coefficient autocorrelated errors," Computational Statistics & Data Analysis, Elsevier, vol. 36(4), pages 511-523, June.
    20. He, Changli & Teräsvirta, Timo, 2002. "An application of the analogy between vector ARCH and vector random coefficient autoregressive models," SSE/EFI Working Paper Series in Economics and Finance 516, Stockholm School of Economics.
    21. Kyrtsou, Catherine, 2008. "Re-examining the sources of heteroskedasticity: The paradigm of noisy chaotic models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(27), pages 6785-6789.
    22. Niklas Ahlgren & Paul Catani, 2017. "Wild bootstrap tests for autocorrelation in vector autoregressive models," Statistical Papers, Springer, vol. 58(4), pages 1189-1216, December.
    23. J. Peter Ferderer, 1994. "Credibility of the Interwar Gold Standard, Uncertainty, and the Great Depression," Economics Working Paper Archive wp_102, Levy Economics Institute.
    24. Hurn, A Stan & Moody, Terry & Muscatelli, V Anton, 1995. "The Term Structure of Interest Rates in the London Interbank Market," Oxford Economic Papers, Oxford University Press, vol. 47(3), pages 419-436, July.
    25. Edmonds, Radcliffe Jr. & So, Jacky Y. C., 2004. "Is exchange rate volatility excessive? An ARCH and AR approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 44(1), pages 122-154, February.

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