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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.

Suggested Citation

  • Marmer, Vadim, 2009. "Nonlinearity, Nonstationarity, and Spurious Forecasts," Microeconomics.ca working papers vadim_marmer-2009-60, Vancouver School of Economics, revised 03 Nov 2009.
    • Handle: RePEc:ubc:pmicro:vadim_marmer-2009-60
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    File URL: http://microeconomics.ca/vadim_marmer/nonlforc21.pdf
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    1. 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.
    2. John H. Cochrane, 1997. "Where is the market going? Uncertain facts and novel theories," Economic Perspectives, Federal Reserve Bank of Chicago, vol. 21(Nov), pages 3-37.
    3. Peter C. B. Phillips & Bruce E. Hansen, 1990. "Statistical Inference in Instrumental Variables Regression with I(1) Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(1), pages 99-125.
    4. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037, Decembrie.
    5. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(2), pages 241-257, June.
    6. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
    7. 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.
    8. 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.
    9. John Y. Campbell & Samuel B. Thompson, 2005. "Predicting the Equity Premium Out of Sample: Can Anything Beat the Historical Average?," Harvard Institute of Economic Research Working Papers 2084, Harvard - Institute of Economic Research.
    10. Sarno,Lucio & Taylor,Mark P., 2003. "The Economics of Exchange Rates," Cambridge Books, Cambridge University Press, number 9780521485845.
    11. 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.
    12. Chang, Yoosoon & Park, Joon Y., 2003. "Index models with integrated time series," Journal of Econometrics, Elsevier, vol. 114(1), pages 73-106, May.
    13. Phillips, Peter C.B. & Jin, Sainan & Hu, Ling, 2007. "Nonstationary discrete choice: A corrigendum and addendum," Journal of Econometrics, Elsevier, vol. 141(2), pages 1115-1130, December.
    14. 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 817-840, November.
    15. Lewellen, Jonathan, 2004. "Predicting returns with financial ratios," Journal of Financial Economics, Elsevier, vol. 74(2), pages 209-235, November.
    16. Atsushi Inoue & Lutz Kilian, 2005. "In-Sample or Out-of-Sample Tests of Predictability: Which One Should We Use?," Econometric Reviews, Taylor & Francis Journals, vol. 23(4), pages 371-402.
    17. Park, Joon Y & Phillips, Peter C B, 2001. "Nonlinear Regressions with Integrated Time Series," Econometrica, Econometric Society, vol. 69(1), pages 117-161, January.
    18. Fama, Eugene F, 1991. "Efficient Capital Markets: II," Journal of Finance, American Finance Association, vol. 46(5), pages 1575-1617, December.
    19. Hu, Ling & Phillips, Peter C. B., 2004. "Nonstationary discrete choice," Journal of Econometrics, Elsevier, vol. 120(1), pages 103-138, May.
    20. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(3), pages 269-298, June.
    21. Hong, Seung Hyun & Phillips, Peter C. B., 2010. "Testing Linearity in Cointegrating Relations With an Application to Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 96-114.
    22. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
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    2. Jia Chen & Jiti Gao & Degui Li & Zhengyan Lin, 2015. "Specification testing in nonstationary time series models," Econometrics Journal, Royal Economic Society, vol. 18(1), pages 117-136, February.
    3. Abdallah Abu Abdallah & Mousa Mohammad Abdullah Saleh & Sadam Al-Wadi & Firas Al Rawashdeh, 2019. "Improving the Estimation Accuracy Based on Wavelet Transform," Journal of Social Sciences (COES&RJ-JSS), , vol. 8(4), pages 544-557, October.
    4. repec:wyi:journl:002203 is not listed on IDEAS
    5. Biqing Cai & Chaohua Dong & Jiti Gao, 2015. "Orthogonal Series Estimation in Nonlinear Cointegrating Models with Endogeneity," Monash Econometrics and Business Statistics Working Papers 18/15, Monash University, Department of Econometrics and Business Statistics.
    6. 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.
    7. Kasparis, Ioannis, 2010. "The Bierens test for certain nonstationary models," Journal of Econometrics, Elsevier, vol. 158(2), pages 221-230, October.
    8. Kasparis, Ioannis & Phillips, Peter C.B., 2012. "Dynamic misspecification in nonparametric cointegrating regression," Journal of Econometrics, Elsevier, vol. 168(2), pages 270-284.
    9. 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.
    10. Maynard, Alex & Shimotsu, Katsumi, 2009. "Covariance-Based Orthogonality Tests For Regressors With Unknown Persistence," Econometric Theory, Cambridge University Press, vol. 25(1), pages 63-116, February.
    11. Kasparis, Ioannis & Andreou, Elena & Phillips, Peter C.B., 2015. "Nonparametric predictive regression," Journal of Econometrics, Elsevier, vol. 185(2), pages 468-494.
    12. Chen, Haiqiang, 2015. "Robust Estimation And Inference For Threshold Models With Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 31(4), pages 778-810, August.
    13. Jonghyeon Min, 2020. "Financial Market Trend Forecasting and Performance Analysis Using LSTM," Papers 2004.01502, arXiv.org.

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    More about this item

    Keywords

    Forecasting; integrated time series; misspecified models; nonlinear transformations; stock returns;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

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