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New bootstrap inference for spurious regression problems

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  • H.D. Vinod

Abstract

Phillips [11] provides asymptotic theory for regressions that relate nonstationary time series including those integrated of order 1, . A practical implication of the literature on spurious regression is that one cannot trust the usual confidence intervals (CIs). In the absence of prior knowledge that two series are cointegrated, it is therefore recommended that we abandon the specification in levels and work with differenced or detrended series. For situations when the specification in levels is sacrosanct we propose new CIs based on the Maximum Entropy bootstrap explained in Vinod and López-de-Lacalle ( Maximum entropy bootstrap for time series: The meboot R package , J. Statist. Softw. 29 (2009), pp. 1--19). An extensive Monte Carlo simulation shows that our proposal can provide more reliable conservative CIs than traditional and block bootstrap intervals.

Suggested Citation

  • H.D. Vinod, 2016. "New bootstrap inference for spurious regression problems," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(2), pages 317-335, February.
    • Handle: RePEc:taf:japsta:v:43:y:2016:i:2:p:317-335
    DOI: 10.1080/02664763.2015.1049939
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    References listed on IDEAS

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    1. Stock, James H & Watson, Mark W, 1993. "A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems," Econometrica, Econometric Society, vol. 61(4), pages 783-820, July.
    2. Phillips, P.C.B., 1986. "Understanding spurious regressions in econometrics," Journal of Econometrics, Elsevier, vol. 33(3), pages 311-340, December.
    3. Antonio E. Noriega & Daniel Ventosa‐Santaulària, 2006. "Spurious Regression Under Broken‐Trend Stationarity," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(5), pages 671-684, September.
    4. Andreas Koutris & Maria Heracleous & Aris Spanos, 2008. "Testing for Nonstationarity Using Maximum Entropy Resampling: A Misspecification Testing Perspective," Econometric Reviews, Taylor & Francis Journals, vol. 27(4-6), pages 363-384.
    5. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
    6. Vinod, Hrishikesh D. & Lopez-de-Lacalle, Javier, 2009. "Maximum Entropy Bootstrap for Time Series: The meboot R Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 29(i05).
    7. Vinod, H. D., 2004. "Ranking mutual funds using unconventional utility theory and stochastic dominance," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 353-377, June.
    8. Vinod, Hrishikesh D., 2006. "Maximum entropy ensembles for time series inference in economics," Journal of Asian Economics, Elsevier, vol. 17(6), pages 955-978, December.
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    2. Mariano Méndez-Suárez, 2021. "Marketing Mix Modeling Using PLS-SEM, Bootstrapping the Model Coefficients," Mathematics, MDPI, vol. 9(15), pages 1-12, August.

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