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Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity

Author

Listed:
  • Isao Ishida

    () (Faculty of Economics, Konan University, 8-9-1 Okamoto, Higashinada-Ku, Kobe 658-8501, Japan)

  • Virmantas Kvedaras

    () (Department of Econometric Analysis, Faculty of Mathematics and Informatics, Vilnius University, Naugarduko 24, Vilnius LT-03225, Lithuania)

Abstract

We introduce and investigate some properties of a class of nonlinear time series models based on the moving sample quantiles in the autoregressive data generating process. We derive a test fit to detect this type of nonlinearity. Using the daily realized volatility data of Standard & Poor’s 500 (S&P 500) and several other indices, we obtained good performance using these models in an out-of-sample forecasting exercise compared with the forecasts obtained based on the usual linear heterogeneous autoregressive and other models of realized volatility.

Suggested Citation

  • Isao Ishida & Virmantas Kvedaras, 2015. "Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity," Econometrics, MDPI, Open Access Journal, vol. 3(1), pages 1-53, January.
  • Handle: RePEc:gam:jecnmx:v:3:y:2015:i:1:p:2-54:d:44835
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    References listed on IDEAS

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    1. Mika Meitz & Pentti Saikkonen, 2008. "Stability of nonlinear AR-GARCH models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(3), pages 453-475, May.
    2. Todd E. Clark & Michael W. McCracken, 2009. "Improving Forecast Accuracy By Combining Recursive And Rolling Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 50(2), pages 363-395, May.
    3. Amado, Cristina & Teräsvirta, Timo, 2014. "Modelling changes in the unconditional variance of long stock return series," Journal of Empirical Finance, Elsevier, vol. 25(C), pages 15-35.
    4. Clark, Todd E. & McCracken, Michael W., 2001. "Tests of equal forecast accuracy and encompassing for nested models," Journal of Econometrics, Elsevier, vol. 105(1), pages 85-110, November.
    5. Fulvio Corsi & Stefan Mittnik & Christian Pigorsch & Uta Pigorsch, 2008. "The Volatility of Realized Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 46-78.
    6. Beaudry, Paul & Koop, Gary, 1993. "Do recessions permanently change output?," Journal of Monetary Economics, Elsevier, vol. 31(2), pages 149-163, April.
    7. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    8. Granger, Clive W. J. & Hyung, Namwon, 2004. "Occasional structural breaks and long memory with an application to the S&P 500 absolute stock returns," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 399-421, June.
    9. Michael McAleer & Marcelo Medeiros, 2008. "Realized Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 10-45.
    10. Scharth, Marcel & Medeiros, Marcelo C., 2009. "Asymmetric effects and long memory in the volatility of Dow Jones stocks," International Journal of Forecasting, Elsevier, vol. 25(2), pages 304-327.
    11. Hall, Peter & Peng, Liang & Yao, Qiwei, 2002. "Moving-maximum models for extrema of time series," LSE Research Online Documents on Economics 6084, London School of Economics and Political Science, LSE Library.
    12. Granger, Clive W. J. & Terasvirta, Timo, 1999. "A simple nonlinear time series model with misleading linear properties," Economics Letters, Elsevier, vol. 62(2), pages 161-165, February.
    13. Diebold, Francis X. & Inoue, Atsushi, 2001. "Long memory and regime switching," Journal of Econometrics, Elsevier, vol. 105(1), pages 131-159, November.
    14. Perron, Pierre & Qu, Zhongjun, 2010. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 275-290.
    15. Meitz, Mika & Saikkonen, Pentti, 2010. "A note on the geometric ergodicity of a nonlinear AR-ARCH model," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 631-638, April.
    16. Hyndman, Rob J. & Koehler, Anne B., 2006. "Another look at measures of forecast accuracy," International Journal of Forecasting, Elsevier, vol. 22(4), pages 679-688.
    17. Kvedaras, Virmantas & Zemlys, Vaidotas, 2012. "Testing the functional constraints on parameters in regressions with variables of different frequency," Economics Letters, Elsevier, vol. 116(2), pages 250-254.
    18. Todd E. Clark & Michael W. Mccracken, 2014. "Tests Of Equal Forecast Accuracy For Overlapping Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 29(3), pages 415-430, April.
    19. Andrew P. Blake & George Kapetanios, 2003. "A radial basis function artificial neural network test for neglected nonlinearity," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 357-373, December.
    20. Clark, Todd E. & West, Kenneth D., 2007. "Approximately normal tests for equal predictive accuracy in nested models," Journal of Econometrics, Elsevier, vol. 138(1), pages 291-311, May.
    21. Ghysels, Eric & Santa-Clara, Pedro & Valkanov, Rossen, 2006. "Predicting volatility: getting the most out of return data sampled at different frequencies," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 59-95.
    22. Deheuvels, Paul, 1983. "Point processes and multivariate extreme values," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 257-272, June.
    23. Hubrich, Kirstin & D’Agostino, Antonello & Cervená, Marianna & Ciccarelli, Matteo & Guarda, Paolo & Haavio, Markus & Jeanfils, Philippe & Mendicino, Caterina & Ortega, Eva & Valderrama, Maria Teresa &, 2013. "Financial shocks and the macroeconomy: heterogeneity and non-linearities," Occasional Paper Series 143, European Central Bank.
    24. Ohanissian, Arek & Russell, Jeffrey R. & Tsay, Ruey S., 2008. "True or Spurious Long Memory? A New Test," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 161-175, April.
    25. Bhattacharya, Rabi & Lee, Chanho, 1995. "On geometric ergodicity of nonlinear autoregressive models," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 311-315, March.
    26. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
    27. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
    28. Xue-Zhong He & Youwei Li, 2008. "Heterogeneity, convergence, and autocorrelations," Quantitative Finance, Taylor & Francis Journals, vol. 8(1), pages 59-79.
    29. Douglas G. Santos & Flavio A. Ziegelmann, 2014. "Volatility Forecasting via MIDAS, HAR and their Combination: An Empirical Comparative Study for IBOVESPA," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 33(4), pages 284-299, July.
    30. Eckhard Liebscher, 2005. "Towards a Unified Approach for Proving Geometric Ergodicity and Mixing Properties of Nonlinear Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(5), pages 669-689, September.
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    More about this item

    Keywords

    forecasting; moving quantiles; non-linearity; realized volatility; test;

    JEL classification:

    • B23 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Econometrics; Quantitative and Mathematical Studies
    • C - Mathematical and Quantitative Methods
    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C3 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs

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