IDEAS home Printed from https://ideas.repec.org/p/chb/bcchwp/376.html
   My bibliography  Save this paper

Shrinkage Based Tests of the Martingale Difference Hypothesis

Author

Listed:
  • Pablo Pincheira

Abstract

In this paper we define a family of tests for the Martingale Difference Hypothesis (MDH) based upon a shrinkage principle. Tests within this family are such that rejection of the null implies that forecasts from the alternative model, adjusted by a shrinkage factor, will display lower Mean Square Prediction Error (MSPE) than forecasts from the null model. This generalizes most previous tests which compare forecast errors of one model, the null, to errors of the plain alternative model, not allowing for shrinkage. We argue that tests derived from this shrinkage approach display in general better small sample properties than MSPE based tests of the MDH. This occurs because the shrinkage based tests implicitly consider the reduced variance benefits of shrinkage estimators. Finally, we illustrate the use of our tests in an empirical application within the exchange rate literature

Suggested Citation

  • Pablo Pincheira, 2006. "Shrinkage Based Tests of the Martingale Difference Hypothesis," Working Papers Central Bank of Chile 376, Central Bank of Chile.
    • Handle: RePEc:chb:bcchwp:376
    as

    Download full text from publisher

    File URL: https://www.bcentral.cl/documents/33528/133326/DTBC_376.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Chao, John & Corradi, Valentina & Swanson, Norman R., 2001. "Out-Of-Sample Tests For Granger Causality," Macroeconomic Dynamics, Cambridge University Press, vol. 5(4), pages 598-620, September.
    2. Cheung, Yin-Wong & Chinn, Menzie David & Garcia Pascual, Antonio, 2003. "Empirical Exchange Rate Models of the Nineties: Are Any Fit to Survive?," Santa Cruz Department of Economics, Working Paper Series qt12z9x4c5, Department of Economics, UC Santa Cruz.
    3. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    4. Clemen, Robert T., 1989. "Combining forecasts: A review and annotated bibliography," International Journal of Forecasting, Elsevier, vol. 5(4), pages 559-583.
    5. Skouras, Spyros, 2001. "Financial returns and efficiency as seen by an artificial technical analyst," Journal of Economic Dynamics and Control, Elsevier, vol. 25(1-2), pages 213-244, January.
    6. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    7. Cheung, Yin-Wong & Chinn, Menzie D. & Pascual, Antonio Garcia, 2005. "Empirical exchange rate models of the nineties: Are any fit to survive?," Journal of International Money and Finance, Elsevier, vol. 24(7), pages 1150-1175, November.
    8. Miller, Don M. & Williams, Dan, 2003. "Shrinkage estimators of time series seasonal factors and their effect on forecasting accuracy," International Journal of Forecasting, Elsevier, vol. 19(4), pages 669-684.
    9. Donald Brown & Rustam Ibragimov, 2005. "Sign Tests for Dependent Observations and Bounds for Path-Dependent Options," Yale School of Management Working Papers amz2581, Yale School of Management, revised 01 Jul 2005.
    10. Anatolyev, Stanislav & Gerko, Alexander, 2005. "A Trading Approach to Testing for Predictability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 455-461, October.
    11. Avramov, Doron, 2002. "Stock return predictability and model uncertainty," Journal of Financial Economics, Elsevier, vol. 64(3), pages 423-458, June.
    12. Meese, Richard A. & Rogoff, Kenneth, 1983. "Empirical exchange rate models of the seventies : Do they fit out of sample?," Journal of International Economics, Elsevier, vol. 14(1-2), pages 3-24, 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. Pablo Pincheira, 2008. "Combining Tests of Predictive Ability Theory and Evidence for Chilean and Canadian Exchange Rates," Working Papers Central Bank of Chile 459, Central Bank of Chile.
    2. Pablo Pincheira B., 2007. "Hidden Predictability in Economics: The Case of the Chilean Exchange Rate," Working Papers Central Bank of Chile 435, Central Bank of Chile.
    3. Pablo Pincheira & Jorge Selaive, 2011. "External imbalance, valuation adjustments and real Exchange rate: evidence of predictability in an emerging economy," Revista de Analisis Economico – Economic Analysis Review, Universidad Alberto Hurtado/School of Economics and Business, vol. 26(1), pages 107-125, Junio.
    4. Ana María Abarca G. & Felipe Alarcón G. & Pablo Pincheira B. & Jorge Selaive C., 2007. "Nominal Exchange Rate in Chile: Predictions based on technical analysis," Journal Economía Chilena (The Chilean Economy), Central Bank of Chile, vol. 10(2), pages 57-80, August.
    5. Ana María Abarca & Felipe Alarcón & Pablo Pincheira & Jorge Selaive, 2007. "Chilean Nominal Exchange Rate: Forecasting Based Upon Technical Analysis," Working Papers Central Bank of Chile 425, Central Bank of Chile.
    6. Pablo Pincheira, 2012. "A Joint Test of Superior Predictive Ability for Chilean Inflation Forecasts," Journal Economía Chilena (The Chilean Economy), Central Bank of Chile, vol. 15(3), pages 04-39, December.
    7. Pablo Pincheira B., 2008. "Predictibilidad Encubierta en Economía: El Caso del Tipo de Cambio Nominal Chileno," Notas de Investigación Journal Economía Chilena (The Chilean Economy), Central Bank of Chile, vol. 11(1), pages 137-142, April.

    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. Pablo Pincheira, 2008. "Combining Tests of Predictive Ability Theory and Evidence for Chilean and Canadian Exchange Rates," Working Papers Central Bank of Chile 459, Central Bank of Chile.
    2. West, Kenneth D., 2006. "Forecast Evaluation," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 3, pages 99-134, Elsevier.
    3. Barbara Rossi & Atsushi Inoue, 2012. "Out-of-Sample Forecast Tests Robust to the Choice of Window Size," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(3), pages 432-453, April.
    4. Todd E. Clark & Kenneth D. West, 2005. "Using Out-of-Sample Mean Squared Prediction Errors to Test the Martingale Difference," NBER Technical Working Papers 0305, National Bureau of Economic Research, Inc.
    5. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.
    6. Nicolás Magner & Nicolás Hardy, 2022. "Cryptocurrency Forecasting: More Evidence of the Meese-Rogoff Puzzle," Mathematics, MDPI, vol. 10(13), pages 1-27, July.
    7. Clark, Todd E. & West, Kenneth D., 2006. "Using out-of-sample mean squared prediction errors to test the martingale difference hypothesis," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 155-186.
    8. Carlo Altavilla & Paul De Grauwe, 2010. "Forecasting and combining competing models of exchange rate determination," Applied Economics, Taylor & Francis Journals, vol. 42(27), pages 3455-3480.
    9. Barbara Rossi, 2013. "Exchange Rate Predictability," Journal of Economic Literature, American Economic Association, vol. 51(4), pages 1063-1119, December.
    10. Tanya Molodtsova & Alex Nikolsko-Rzhevskyy & David H. Papell, 2011. "Taylor Rules and the Euro," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43, pages 535-552, March.
    11. Joseph P. Byrne & Dimitris Korobilis & Pinho J. Ribeiro, 2018. "On The Sources Of Uncertainty In Exchange Rate Predictability," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(1), pages 329-357, February.
    12. Ahmed, Shamim & Liu, Xiaoquan & Valente, Giorgio, 2016. "Can currency-based risk factors help forecast exchange rates?," International Journal of Forecasting, Elsevier, vol. 32(1), pages 75-97.
    13. Kenneth S. Rogoff & Vania Stavrakeva, 2008. "The Continuing Puzzle of Short Horizon Exchange Rate Forecasting," NBER Working Papers 14071, National Bureau of Economic Research, Inc.
    14. Jian Wang & Jason J. Wu, 2012. "The Taylor Rule and Forecast Intervals for Exchange Rates," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 44(1), pages 103-144, February.
    15. Ince, Onur & Molodtsova, Tanya & Papell, David H., 2016. "Taylor rule deviations and out-of-sample exchange rate predictability," Journal of International Money and Finance, Elsevier, vol. 69(C), pages 22-44.
    16. Pincheira-Brown, Pablo & Neumann, Federico, 2020. "Can we beat the Random Walk? The case of survey-based exchange rate forecasts in Chile," Finance Research Letters, Elsevier, vol. 37(C).
    17. Alessandro Casini, 2018. "Tests for Forecast Instability and Forecast Failure under a Continuous Record Asymptotic Framework," Papers 1803.10883, arXiv.org, revised Dec 2018.
    18. Domenico Ferraro & Kenneth S. Rogoff & Barbara Rossi, 2011. "Can oil prices forecast exchange rates?," Working Papers 11-34, Federal Reserve Bank of Philadelphia.
    19. Brooks, Chris & Burke, Simon P. & Stanescu, Silvia, 2016. "Finite sample weighting of recursive forecast errors," International Journal of Forecasting, Elsevier, vol. 32(2), pages 458-474.
    20. Amat, Christophe & Michalski, Tomasz & Stoltz, Gilles, 2018. "Fundamentals and exchange rate forecastability with simple machine learning methods," Journal of International Money and Finance, Elsevier, vol. 88(C), pages 1-24.

    More about this item

    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:chb:bcchwp:376. 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: Alvaro Castillo (email available below). General contact details of provider: https://edirc.repec.org/data/bccgvcl.html .

    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.