Hostname: page-component-6b989bf9dc-mbg9n Total loading time: 0 Render date: 2024-04-13T06:24:28.031Z Has data issue: false hasContentIssue false


Published online by Cambridge University Press:  11 August 2020

Jinyong Hahn
University of California, Los Angeles
Guido Kuersteiner*
University of Maryland
Maurizio Mazzocco
University of California, Los Angeles
Address correspondence to Guido Kuersteiner, Department of Economics, University of Maryland, Tydings Hall 3145, College Park, MD 20742, USA; e-mail:


In this paper, we complement joint time-series and cross-section convergence results derived in a companion paper Hahn, Kuersteiner, and Mazzocco (2016, Central Limit Theory for Combined Cross-Section and Time Series) by allowing for serial correlation in the time-series sample. The implications of our analysis are limiting distributions that have a well-known form of long-run variances for the time-series limit. We obtain these results at the cost of imposing strict stationarity for the time-series model and conditional independence between the time-series and cross-section samples. Our results can be applied to estimators that combine time-series and cross-section data in the presence of aggregate uncertainty in models with rationally forward-looking agents.

© The Author(s), 2020. Published by Cambridge University Press

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.)


We thank Peter C.B. Phillips for his enormous contributions to the field of econometrics, both intellectually through his impressive research record and his time and effort with countless professional activities, not least starting this journal and running it as the lead editor for decades. Guido Kuersteiner is particularly grateful for Peter’s guidance and support as his Ph.D. advisor at Yale and ever since. We thank the Co-Editor Don Andrews and two anonymous referees for their careful reading of the manuscript and numerous helpful suggestions.



Aldous, D.J. & Eagleson, G.K. (1978) On mixing and stability of limit theorems. The Annals of Probability 6, 325331.CrossRefGoogle Scholar
Andrews, D.W.K. (1991) Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica 59, 817858.CrossRefGoogle Scholar
Barndorff-Nielsen, O.E., Hansen, P.R., Lunde, A., & Shephard, N. (2008) Designing realized kernels to measure the ex post variation of equity prices in the presence of noise. Econometrica 76, 14811536.Google Scholar
Billingsley, P. (1995) Probability and Measure. Wiley.Google Scholar
Breiman, L. (1992) Probability. SIAM Classics in Applied Mathematics.CrossRefGoogle Scholar
Dedecker, J. & Doukhan, P. (2003) A new covariance inequality and applications. Stochastic Processes and their Applications 106, 6380.CrossRefGoogle Scholar
Dedecker, J. & Merlevède, F. (2002) Necessary and sufficient conditions for the conditional central limit theorem. Annals of Probability 30, 10441081.CrossRefGoogle Scholar
Dedecker, J. & Rio, E. (2000) On the functional central limit theorem for stationary processes. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques 36, 134.CrossRefGoogle Scholar
Eagleson, G.K. (1975) Martingale convergence to mixtures of infinitely divisible laws. The Annals of Probability 3, 557562.CrossRefGoogle Scholar
Gordin, M.I. (1973) Abstracts of Communication, T.1: A-K. International Conference on Probability Theory, Vilnius.Google Scholar
Hahn, J., Kuersteiner, G., & Mazzocco, M. (2015) Estimation with Aggregate Shocks. Working paper, arXiv:1507.04415v1 [stat.ME].Google Scholar
Hahn, J., Kuersteiner, G., & Mazzocco, M. (2016) Central Limit Theory for Combined Cross-Section and Time Series. arXiv:1610.01697.Google Scholar
Hahn, J., Kuersteiner, G., & Mazzocco, M. (2019) Estimation with aggregate shocks. Review of Economic Studies 87, 180.Google Scholar
Hall, P. & Heyde, C.C. (1980) Martingale Limit Theory and Its Application. Academic Press.Google Scholar
Halmos, P.R. (1956) Lectures on Ergodic Theory. AMS Chelsea Publishing.Google Scholar
Ikeda, S.S. (2017) A note on mixingale limit theorems and stable convergence in law. Communications in Statistics—Theory and Methods 46, 93779387.CrossRefGoogle Scholar
Kuersteiner, G. & Prucha, I. (2013) Limit theory for panel data models with cross sectional dependence and sequential exogeneity. Journal of Econometrics 174, 107126.CrossRefGoogle ScholarPubMed
McLeish, D.L. (1974) Dependent central limit theorems and invariance principles. The Annals of Probability 2, 620628.CrossRefGoogle Scholar
McLeish, D.L. (1975) A maximal inequality and dependent strong laws. The Annals of Probability 3, 829839.CrossRefGoogle Scholar
Newey, W.K. & West, K.D. (1987) A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703708.CrossRefGoogle Scholar
Newey, W.K. & West, K.D. (1994) Automatic lag selection in covariance matrix estimation. The Review of Economic Studies 61, 631653.CrossRefGoogle Scholar
Phillips, P.C.B. (2005) HAC estimation by automated regression. Econometric Theory 21, 116142.CrossRefGoogle Scholar
Phillips, P.C.B. & Ouliaris, S. (1990) Asymptotic properties of residual based tests for cointegration. Econometrica 58, 165193.CrossRefGoogle Scholar
Renyi, A. (1963) On stable sequences of events. Sankya Series A 25, 293302.Google Scholar
Rosenzweig, M.R. & Udry, C. (2019) External validity in a stochastic world: Evidence from low-income countries. Review of Economic Studies 87, 343.CrossRefGoogle Scholar
Shiryaev, A.N. (1995) Probability. Springer.Google Scholar
van der Vaart, A.W. & Wellner, J.A. (1996) Weak Convergence and Empirical Processes: With Applications to Statistics. Springer.CrossRefGoogle Scholar