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Some Limit Theory For Autocovariances Whose Order Depends On Sample Size

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  • Harris, David
  • McCabe, Brendan
  • Leybourne, Stephen

Abstract

In this paper we provide some weak convergence results for sample statistics of the product of a variable with its kth-order lag. We assume the variable is a stationary vector that can be represented by linear process, and the lag length k is allowed to be a function of the sample size. Employing the Beveridge–Nelson decomposition, we derive a new functional central limit theorem for this situation and establish related stochastic integral convergence results. We then consider the behavior of associated long-run variance estimators and also extend our analysis to the case where the sample statistics are based on regression residuals. We illustrate the potential range of application of these techniques in the context of (i) testing for I(0) versus I(1) behavior and (ii) estimation and testing in a heteroskedastically cointegrated regression model.We thank the co-editor and the referees for helpful comments on earlier drafts.

Suggested Citation

  • Harris, David & McCabe, Brendan & Leybourne, Stephen, 2003. "Some Limit Theory For Autocovariances Whose Order Depends On Sample Size," Econometric Theory, Cambridge University Press, vol. 19(5), pages 829-864, October.
    • Handle: RePEc:cup:etheor:v:19:y:2003:i:05:p:829-864_19
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    Cited by:

    1. Kaddour Hadri & Eiji Kurozumi & Yao Rao, 2015. "Novel panel cointegration tests emending for cross‐section dependence with N fixed," Econometrics Journal, Royal Economic Society, vol. 18(3), pages 363-411, October.
    2. Hassan B. Ghassan & Zakaria Boulanouar & Kabir M. Hassan, 2021. "Revisiting Banking Stability Using a New Panel Cointegration Test," IJFS, MDPI, vol. 9(2), pages 1-8, April.
    3. Harvey David I & Leybourne Stephen J & Xiao Bin, 2008. "A Powerful Test for Linearity When the Order of Integration is Unknown," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(3), pages 1-24, September.
    4. Brendan McCabe & Stephen Leybourne & David Harris, 2003. "Testing for Stochastic Cointegration and Evidence for Present Value Models," Econometrics 0311009, University Library of Munich, Germany.
    5. Kyung So Im & Junsoo Lee & Vladimir Arcabic & Mansik Hur, 2018. "DF-IV Unit Root Tests Using Stationary Instrument Variables," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 7(1), pages 1-1.
    6. Ayesh Ariyasinghe & N. S. Cooray, 2021. "The Nexus Of Foreign Reserves, Exchange Rate And Inflation: Recent Empirical Evidence From Sri Lanka," South Asia Economic Journal, Institute of Policy Studies of Sri Lanka, vol. 22(1), pages 29-72, March.
    7. Jirak, Moritz, 2011. "On the maximum of covariance estimators," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1032-1046, July.
    8. Gawon Yoon, 2010. "Nonlinearity in real exchange rates: an approach with disaggregated data and a new linearity test," Applied Economics Letters, Taylor & Francis Journals, vol. 17(11), pages 1125-1132.
    9. Hadri, Kaddour & Kurozumi, Eiji & 黒住, 英司, 2008. "A Simple Panel Stationarity Test in the Presence of Cross-Sectional Dependence," CCES Discussion Paper Series 7, Center for Research on Contemporary Economic Systems, Graduate School of Economics, Hitotsubashi University.
    10. Yoon, Gawon, 2009. "It's all the miners' fault: On the nonlinearity in U.S. unemployment rates," Economic Modelling, Elsevier, vol. 26(6), pages 1449-1454, November.
    11. Bob Nobay & Ivan Paya & David A. Peel, 2010. "Inflation Dynamics in the U.S.: Global but Not Local Mean Reversion," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(1), pages 135-150, February.
    12. Nobay, A. Robert & Paya, Ivan & Peel, David A., 2007. "Inflation dynamics in the US - a nonlinear perspective," LSE Research Online Documents on Economics 24499, London School of Economics and Political Science, LSE Library.
    13. Khraief, Naceur & Shahbaz, Muhammad & Heshmati, Almas & Azam, Muhammad, 2020. "Are unemployment rates in OECD countries stationary? Evidence from univariate and panel unit root tests," The North American Journal of Economics and Finance, Elsevier, vol. 51(C).
    14. Harris, David & McCabe, Brendan & Leybourne, Stephen, 2002. "Stochastic cointegration: estimation and inference," Journal of Econometrics, Elsevier, vol. 111(2), pages 363-384, December.
    15. Erdas Mehmet Levent, 2019. "Validity of Weak-Form Market Efficiency in Central and Eastern European Countries (CEECs): Evidence from Linear and Nonlinear Unit Root Tests," Review of Economic Perspectives, Sciendo, vol. 19(4), pages 399-428, December.
    16. Syed A. Basher & Josep Lluís Carrion-i-Silvestre, 2007. "Another Look at the Null of Stationary RealExchange Rates. Panel Data with Structural Breaks and Cross-section Dependence," IREA Working Papers 200710, University of Barcelona, Research Institute of Applied Economics, revised May 2007.
    17. Neifar, Malika, 2020. "Multivariate GARCH Approaches: case of major sectorial Tunisian stock markets," MPRA Paper 99658, University Library of Munich, Germany.
    18. Yavuz, Nilgün Çil & Yilanci, Veli, 2012. "Testing For Nonlinearity In G7 Macroeconomic Time Series," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(3), pages 69-79, September.
    19. Ghassan, Hassan & Abdullah, Abdelgader, 2009. "Does the entry of foreign investors influence the volatility of Doha Securities Market?," MPRA Paper 95620, University Library of Munich, Germany, revised 2010.
    20. Malika Neifar & Leila Gharbi, 2022. "Weak EMH and Canadian stock markets: evidence from linear and nonlinear unit root tests," Journal of Islamic Accounting and Business Research, Emerald Group Publishing Limited, vol. 14(4), pages 629-651, December.
    21. David Harris & Steve Leybourne & Brendan McCabe, 2003. "Panel Stationarity Tests with Cross-sectional Dependence," Econometrics 0311005, University Library of Munich, Germany.
    22. neifar, malika, 2020. "Efficient Markets Hypothesis in Canada:‎ a comparative study between Islamic and Conventional stock markets ‎," MPRA Paper 103175, University Library of Munich, Germany.
    23. Wu, Wei Biao, 2009. "An asymptotic theory for sample covariances of Bernoulli shifts," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 453-467, February.

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