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Nonlinearity, Nonstationarity, and Spurious Forecasts

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  • Marmer, Vadim

Abstract

Implications of nonlinearity, nonstationarity and misspecification are considered from a forecasting perspective. Our model allows for small departures from the martingale difference sequence hypothesis by including a nonlinear component, formulated as a general, integrable transformation of the I(1) predictor. We assume that the true generating mechanism is unknown to the econometrician and he is therefore forced to use some approximating functions. It is shown that in this framework the linear regression techniques lead to spurious forecasts. Improvements of the forecast accuracy are possible with properly chosen nonlinear transformations of the predictor. The paper derives the limiting distribution of the forecasts' MSE. In the case of square integrable approximants, it depends on the Lâ‚‚-distance between the nonlinear component and approximating function. Optimal forecasts are available for a given class of approximants.

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Bibliographic Info

Paper provided by Vancouver School of Economics in its series Microeconomics.ca working papers with number vadim_marmer-2009-60.

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Length: 44 pages
Date of creation: 03 Nov 2009
Date of revision: 03 Nov 2009
Handle: RePEc:ubc:pmicro:vadim_marmer-2009-60

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Web page: http://www.economics.ubc.ca/

Related research

Keywords: Forecasting; integrated time series; misspecified models; nonlinear transformations; stock returns;

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  1. Chang, Yoosoon & Park, Joon Y., 2003. "Index models with integrated time series," Journal of Econometrics, Elsevier, vol. 114(1), pages 73-106, May.
  2. Yoosoon Chang & Joon Y. Park & Peter C. B. Phillips, 2001. "Nonlinear econometric models with cointegrated and deterministically trending regressors," Econometrics Journal, Royal Economic Society, vol. 4(1), pages 1-36.
  3. Peter C.B. Phillips & Sainan Jin & Ling Hu, 2005. "Nonstationary Discrete Choice: A Corrigendum and Addendum," Cowles Foundation Discussion Papers 1516, Cowles Foundation for Research in Economics, Yale University.
  4. West, Kenneth D & McCracken, Michael W, 1998. "Regression-Based Tests of Predictive Ability," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 817-40, November.
  5. Ivo Welch & Amit Goyal, 2008. "A Comprehensive Look at The Empirical Performance of Equity Premium Prediction," Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1455-1508, July.
  6. John H. Cochrane, 1997. "Where is the market going? Uncertain facts and novel theories," Economic Perspectives, Federal Reserve Bank of Chicago, issue Nov, pages 3-37.
  7. Ross Williams, 2013. "Introduction," Australian Economic Review, The University of Melbourne, Melbourne Institute of Applied Economic and Social Research, vol. 46(4), pages 460-461, December.
  8. Kilian, Lutz & Taylor, Mark P., 2003. "Why is it so difficult to beat the random walk forecast of exchange rates?," Journal of International Economics, Elsevier, vol. 60(1), pages 85-107, May.
  9. Francis X. Diebold & Robert S. Mariano, 1994. "Comparing Predictive Accuracy," NBER Technical Working Papers 0169, National Bureau of Economic Research, Inc.
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  11. Seung Hyun Hong & Peter C. B. Phillips, 2005. "Testing Linearity in Cointegrating Relations with an Application to Purchasing Power Parity," Cowles Foundation Discussion Papers 1541, Cowles Foundation for Research in Economics, Yale University.
  12. Lewellen, Jonathan, 2004. "Predicting returns with financial ratios," Journal of Financial Economics, Elsevier, vol. 74(2), pages 209-235, November.
  13. Phillips, Peter C B & Hansen, Bruce E, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," Review of Economic Studies, Wiley Blackwell, vol. 57(1), pages 99-125, January.
  14. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June.
  15. Fama, Eugene F, 1991. " Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-617, December.
  16. Ling Hu & Peter C.B. Phillips, 2002. "Nonstationary Discrete Choice," Cowles Foundation Discussion Papers 1364, Cowles Foundation for Research in Economics, Yale University.
  17. Joon Y. Park & Peter C.B. Phillips, 1998. "Nonlinear Regressions with Integrated Time Series," Cowles Foundation Discussion Papers 1190, Cowles Foundation for Research in Economics, Yale University.
  18. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
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Citations

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Cited by:
  1. Katsumi Shimotsu & Alex Maynard, 2004. "Covariance-based orthogonality tests for regressors with unknown persistence," Econometric Society 2004 Far Eastern Meetings 518, Econometric Society.
  2. Kasparis, Ioannis & Phillips, Peter C.B., 2012. "Dynamic misspecification in nonparametric cointegrating regression," Journal of Econometrics, Elsevier, vol. 168(2), pages 270-284.
  3. Andreou, Elena & Kasparis, Ioannis & Phillips, Peter C. B., 2013. "Nonparametric Predictive Regression," CEPR Discussion Papers 9570, C.E.P.R. Discussion Papers.
  4. repec:wyi:journl:002203 is not listed on IDEAS
  5. Haiqiang Chen, 2013. "Robust Estimation and Inference for Threshold Models with Integrated Regressors," SFB 649 Discussion Papers SFB649DP2013-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  6. Liew, Venus Khim-Sen & Ling, Tai-Hu & Chia, Ricky Chee-Jiun & Yoon, Gawon, 2012. "On the application of the rank tests for nonlinear cointegration to PPP: The case of Papua New Guinea," Economic Modelling, Elsevier, vol. 29(2), pages 326-332.
  7. Kasparis, Ioannis, 2010. "The Bierens test for certain nonstationary models," Journal of Econometrics, Elsevier, vol. 158(2), pages 221-230, October.
  8. Chaohua Dong & Jiti Gao & Dag Tjostheim & Jiying Yin, 2014. "Specification Testing for Nonlinear Multivariate Cointegrating Regressions," Monash Econometrics and Business Statistics Working Papers 8/14, Monash University, Department of Econometrics and Business Statistics.
  9. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2013. "Some thoughts on accurate characterization of stock market indexes trends in conditions of nonlinear capital flows during electronic trading at stock exchanges in global capital markets," MPRA Paper 49921, University Library of Munich, Germany.
  10. repec:wyi:wpaper:002206 is not listed on IDEAS

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