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Unbounded heteroscedasticity in first-order autoregressive models and the Eicker-White asymptotic variance estimator


  • Kourogenis, Nikolaos
  • Pittis, Nikitas


This paper focuses on first-order autoregressive models in which the noise variance increases without bound. Although this specification violates a standard assumption made in the relevant literature, namely that of bounded noise variance, it is proved that the well-known Eicker-White estimator remains a consistent estimator of the asymptotic variance of the OLS estimator.

Suggested Citation

  • Kourogenis, Nikolaos & Pittis, Nikitas, 2010. "Unbounded heteroscedasticity in first-order autoregressive models and the Eicker-White asymptotic variance estimator," Economics Letters, Elsevier, vol. 106(2), pages 84-86, February.
  • Handle: RePEc:eee:ecolet:v:106:y:2010:i:2:p:84-86

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    References listed on IDEAS

    1. John Y. Campbell, 2001. "Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk," Journal of Finance, American Finance Association, vol. 56(1), pages 1-43, February.
    2. Hansen, Bruce E, 1992. "Consistent Covariance Matrix Estimation for Dependent Heterogeneous Processes," Econometrica, Econometric Society, vol. 60(4), pages 967-972, July.
    3. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    4. Margaret M. McConnell & Gabriel Perez-Quiros, 2000. "Output fluctuations in the United States: what has changed since the early 1980s?," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
    5. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-1153, December.
    6. Nicholls, D F & Pagan, A R, 1983. "Heteroscedasticity in Models with Lagged Dependent Variables," Econometrica, Econometric Society, vol. 51(4), pages 1233-1242, July.
    7. Robinson, P M, 1991. "Automatic Frequency Domain Inference on Semiparametric and Nonparametric Models," Econometrica, Econometric Society, vol. 59(5), pages 1329-1363, September.
    8. Robert M. De Jong & James Davidson, 2000. "Consistency of Kernel Estimators of Heteroscedastic and Autocorrelated Covariance Matrices," Econometrica, Econometric Society, vol. 68(2), pages 407-424, March.
    9. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(03), pages 458-467, December.
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    Cited by:

    1. Abdelkamel Alj & Rajae Azrak & Guy Melard, 2014. "On Conditions in Central Limit Theorems for Martingale Difference Arrays Long Version," Working Papers ECARES ECARES 2014-05, ULB -- Universite Libre de Bruxelles.


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