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Nonlinearity, Nonstationarity and Spurious Forecasts

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  • Vadim Marmer

    (Yale University)

Abstract

Implications of nonlinearity, nonstationarity and misspecification are considered from a forecasting perspective. My 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. I assume that the true generating mechanism is unknown to the econometrician and he is therefore forced to use some approximating functions. I show that the usual 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 L2-distance between the nonlinear component and approximating function. Optimal forecasts are available for a given class of approximants.

Suggested Citation

  • Vadim Marmer, 2005. "Nonlinearity, Nonstationarity and Spurious Forecasts," Econometrics 0503002, University Library of Munich, Germany, revised 15 Dec 2005.
  • Handle: RePEc:wpa:wuwpem:0503002
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    References listed on IDEAS

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    Cited by:

    1. Kasparis, Ioannis & Andreou, Elena & Phillips, Peter C.B., 2015. "Nonparametric predictive regression," Journal of Econometrics, Elsevier, vol. 185(2), pages 468-494.
    2. Chen, Haiqiang, 2015. "Robust Estimation And Inference For Threshold Models With Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 31(04), pages 778-810, August.
    3. Dong, Chaohua & Gao, Jiti & Tjøstheim, Dag & Yin, Jiying, 2017. "Specification testing for nonlinear multivariate cointegrating regressions," Journal of Econometrics, Elsevier, vol. 200(1), pages 104-117.
    4. Maynard, Alex & Shimotsu, Katsumi, 2009. "Covariance-Based Orthogonality Tests For Regressors With Unknown Persistence," Econometric Theory, Cambridge University Press, vol. 25(01), pages 63-116, February.
    5. 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.
    6. repec:wyi:journl:002203 is not listed on IDEAS
    7. 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.
    8. 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.
    9. Kasparis, Ioannis, 2010. "The Bierens test for certain nonstationary models," Journal of Econometrics, Elsevier, vol. 158(2), pages 221-230, October.
    10. Kasparis, Ioannis & Phillips, Peter C.B., 2012. "Dynamic misspecification in nonparametric cointegrating regression," Journal of Econometrics, Elsevier, vol. 168(2), pages 270-284.
    11. 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.

    More about this item

    Keywords

    forecasting; integrated time series; misspecified models; nonlinear transformations; stock returns; dividend-price ratio.;

    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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