lynx   »   [go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v235y2023i2p1447-1463.html
   My bibliography  Save this article

The distribution of rolling regression estimators

Author

Listed:
  • Cai, Zongwu
  • Juhl, Ted
Abstract
We establish the asymptotic distribution for rolling linear regression models using various window widths. The limiting distribution depends on the width of the rolling window and on a “bias process” that is typically ignored in practice. Based on the asymptotic distribution, we tabulate critical values used to find uniform confidence intervals for the average values of regression parameters over the windows. We propose a corrected rolling regression technique that removes the bias process by rolling over smoothed parameter estimates. The procedure is illustrated using a series of Monte Carlo experiments. The paper includes an empirical example to show how the confidence bands suggest alternative conclusions about the persistence of inflation.

Suggested Citation

  • Cai, Zongwu & Juhl, Ted, 2023. "The distribution of rolling regression estimators," Journal of Econometrics, Elsevier, vol. 235(2), pages 1447-1463.
    • Handle: RePEc:eee:econom:v:235:y:2023:i:2:p:1447-1463
    DOI: 10.1016/j.jeconom.2022.12.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407622002068
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2022.12.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Eric T. Swanson & John C. Williams, 2014. "Measuring the Effect of the Zero Lower Bound on Medium- and Longer-Term Interest Rates," American Economic Review, American Economic Association, vol. 104(10), pages 3154-3185, October.
    2. Olivier Blanchard, 2018. "Should We Reject the Natural Rate Hypothesis?," Journal of Economic Perspectives, American Economic Association, vol. 32(1), pages 97-120, Winter.
    3. Adrian, Tobias & Crump, Richard K. & Moench, Emanuel, 2015. "Regression-based estimation of dynamic asset pricing models," Journal of Financial Economics, Elsevier, vol. 118(2), pages 211-244.
    4. Todd E. Clark & Michael W. McCracken, 2009. "Improving Forecast Accuracy By Combining Recursive And Rolling Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 50(2), pages 363-395, May.
    5. Juhani T Linnainmaa & Michael R Roberts, 2018. "The History of the Cross-Section of Stock Returns," The Review of Financial Studies, Society for Financial Studies, vol. 31(7), pages 2606-2649.
    6. David López-Salido & Jeremy C. Stein & Egon Zakrajšek, 2017. "Credit-Market Sentiment and the Business Cycle," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(3), pages 1373-1426.
    7. Atsushi Inoue & Lu Jin & Denis Pelletier, 2021. "Local-Linear Estimation of Time-Varying-Parameter GARCH Models and Associated Risk Measures [Modelling Volatility by Variance Decomposition]," Journal of Financial Econometrics, Oxford University Press, vol. 19(1), pages 202-234.
    8. Georgiev, Iliyan & Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2018. "Testing for parameter instability in predictive regression models," Journal of Econometrics, Elsevier, vol. 204(1), pages 101-118.
    9. Gerard O'Reilly & Karl Whelan, 2005. "Has Euro-Area Inflation Persistence Changed Over Time?," The Review of Economics and Statistics, MIT Press, vol. 87(4), pages 709-720, November.
    10. Jiménez, Gabriel & Ongena, Steven & Peydró, José-Luis & Saurina, Jesús, 2017. "Macroprudential policy, countercyclical bank capital buffers and credit supply: evidence from the spanish dynamic provisioning experiments," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 125(6), pages 2126-2177.
    11. Murillo Campello & Antonio F. Galvao & Ted Juhl, 2019. "Testing for Slope Heterogeneity Bias in Panel Data Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(4), pages 749-760, October.
    12. Cai, Zongwu, 2007. "Trending time-varying coefficient time series models with serially correlated errors," Journal of Econometrics, Elsevier, vol. 136(1), pages 163-188, January.
    13. Perron, P, 1993. "Erratum [The Great Crash, the Oil Price Shock and the Unit Root Hypothesis]," Econometrica, Econometric Society, vol. 61(1), pages 248-249, January.
    14. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, February.
    15. Donald W. K. Andrews, 2003. "Tests for Parameter Instability and Structural Change with Unknown Change Point: A Corrigendum," Econometrica, Econometric Society, vol. 71(1), pages 395-397, January.
    16. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    17. James H. Stock & Mark W. Watson, 2007. "Erratum to “Why Has U.S. Inflation Become Harder to Forecast?”," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(7), pages 1849-1849, October.
    18. Bin Chen & Yongmiao Hong, 2012. "Testing for Smooth Structural Changes in Time Series Models via Nonparametric Regression," Econometrica, Econometric Society, vol. 80(3), pages 1157-1183, May.
    19. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    20. Cai, Zongwu & Xiao, Zhijie, 2012. "Semiparametric quantile regression estimation in dynamic models with partially varying coefficients," Journal of Econometrics, Elsevier, vol. 167(2), pages 413-425.
    21. Jia Li & Zhipeng Liao & Mengsi Gao, 2020. "Uniform nonparametric inference for time series using Stata," Stata Journal, StataCorp LLC, vol. 20(3), pages 706-720, September.
    22. Johnston, Gordon J., 1982. "Probabilities of maximal deviations for nonparametric regression function estimates," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 402-414, September.
    23. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    24. Zhou Zhou & Wei Biao Wu, 2010. "Simultaneous inference of linear models with time varying coefficients," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 513-531, September.
    25. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Kato, Kengo, 2015. "Some new asymptotic theory for least squares series: Pointwise and uniform results," Journal of Econometrics, Elsevier, vol. 186(2), pages 345-366.
    26. Perron, Pierre, 1997. "Further evidence on breaking trend functions in macroeconomic variables," Journal of Econometrics, Elsevier, vol. 80(2), pages 355-385, October.
    27. Raffaella Giacomini & Barbara Rossi, 2010. "Forecast comparisons in unstable environments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 595-620.
    28. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, February.
    29. Li, Jia & Liao, Zhipeng, 2020. "Uniform nonparametric inference for time series," Journal of Econometrics, Elsevier, vol. 219(1), pages 38-51.
    30. James H. Stock & Mark W. Watson, 2007. "Why Has U.S. Inflation Become Harder to Forecast?," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(s1), pages 3-33, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zambrano-Monserrate, Manuel A., 2024. "Labor dynamics and unions: An empirical analysis through Okun's Law," Economic Analysis and Policy, Elsevier, vol. 82(C), pages 613-628.
    2. Grobys, Klaus, 2024. "On co-dependent power-law behavior across cryptocurrencies," Finance Research Letters, Elsevier, vol. 63(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zongwu Cai & Ted Juhl, 2020. "The Distribution Of Rolling Regression Estimators," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202218, University of Kansas, Department of Economics, revised Dec 2022.
    2. Sun, Yuying & Hong, Yongmiao & Wang, Shouyang & Zhang, Xinyu, 2023. "Penalized time-varying model averaging," Journal of Econometrics, Elsevier, vol. 235(2), pages 1355-1377.
    3. Casini, Alessandro & Perron, Pierre, 2024. "Prewhitened long-run variance estimation robust to nonstationarity," Journal of Econometrics, Elsevier, vol. 242(1).
    4. Inoue, Atsushi & Jin, Lu & Rossi, Barbara, 2017. "Rolling window selection for out-of-sample forecasting with time-varying parameters," Journal of Econometrics, Elsevier, vol. 196(1), pages 55-67.
    5. Rossi, Barbara, 2013. "Advances in Forecasting under Instability," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1203-1324, Elsevier.
    6. Rossi, Barbara & Inoue, Atsushi & Jin, Lu, 2014. "Window Selection for Out-of-Sample Forecasting with Time-Varying Parameters," CEPR Discussion Papers 10168, C.E.P.R. Discussion Papers.
    7. Joseph P. Byrne & Alexandros Kontonikas & Alberto Montagnoli, 2010. "The Time‐Series Properties Of Uk Inflation: Evidence From Aggregate And Disaggregate Data," Scottish Journal of Political Economy, Scottish Economic Society, vol. 57(1), pages 33-47, February.
    8. Yu, Deshui & Chen, Li & Li, Luyang, 2023. "Nonparametric modeling for the time-varying persistence of inflation," Economics Letters, Elsevier, vol. 225(C).
    9. Ekşi Ozan & Orman Cüneyt & Taş Bedri Kamil Onur, 2017. "Has the forecasting performance of the Federal Reserve’s Greenbooks changed over time?," The B.E. Journal of Macroeconomics, De Gruyter, vol. 17(2), pages 1-25, June.
    10. Joshy Easaw & Roberto Golinelli, 2022. "Professionals Inflation Forecasts: The Two Dimensions Of Forecaster Inattentiveness [“Sectoral and aggregate inflation dynamics in the euro area”]," Oxford Economic Papers, Oxford University Press, vol. 74(3), pages 701-720.
    11. Chen, Qitong & Hong, Yongmiao & Li, Haiqi, 2024. "Time-varying forecast combination for factor-augmented regressions with smooth structural changes," Journal of Econometrics, Elsevier, vol. 240(1).
    12. Andersen, Torben G. & Varneskov, Rasmus T., 2022. "Testing for parameter instability and structural change in persistent predictive regressions," Journal of Econometrics, Elsevier, vol. 231(2), pages 361-386.
    13. Petrenko, Victoria (Петренко, ВИктория) & Skrobotov, Anton (Скроботов, Антон) & Turuntseva, Maria (Турунцева, Мария), 2016. "Testing of Changes in Persistence and Their Effect on the Forecasting Quality [Тестирование Изменения Инерционности И Влияние На Качество Прогнозов]," Working Papers 542, Russian Presidential Academy of National Economy and Public Administration.
    14. Pablo Guerróon‐Quintana & Molin Zhong, 2023. "Macroeconomic forecasting in times of crises," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(3), pages 295-320, April.
    15. Mohitosh Kejriwal & Claude Lopez, 2013. "Unit Roots, Level Shifts, and Trend Breaks in Per Capita Output: A Robust Evaluation," Econometric Reviews, Taylor & Francis Journals, vol. 32(8), pages 892-927, November.
    16. Ramzi Issa & Robert Lafrance & John Murray, 2008. "The turning black tide: energy prices and the Canadian dollar," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 41(3), pages 737-759, August.
    17. Giorgio Canarella & Rangan Gupta & Stephen M. Miller & Stephen K. Pollard, 2019. "Unemployment rate hysteresis and the great recession: exploring the metropolitan evidence," Empirical Economics, Springer, vol. 56(1), pages 61-79, January.
    18. Bańbura, Marta & Bobeica, Elena, 2023. "Does the Phillips curve help to forecast euro area inflation?," International Journal of Forecasting, Elsevier, vol. 39(1), pages 364-390.
    19. Travaglini, Guido, 2007. "The U.S. Dynamic Taylor Rule With Multiple Breaks, 1984-2001," MPRA Paper 3419, University Library of Munich, Germany, revised 15 Jun 2007.
    20. Nguyen Duc Do, 2025. "Using a Wage–Price‐Setting Model to Forecast US Inflation," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 44(2), pages 803-832, March.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:235:y:2023:i:2:p:1447-1463. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.
    Лучший частный хостинг