IDEAS home Printed from https://ideas.repec.org/a/rjr/romjef/vy2014i3p108-135.html
   My bibliography  Save this article

Nonlinearity, Volatility and Fractional Integration in Daily Oil Prices: Smooth Transition Autoregressive ST-FI(AP)GARCH Models

Author

Listed:
  • Melike Bildirici

    (Yıldız Technical University, Department of Economics, Istanbul, Turkey, Corresponding author,)

  • Özgür Ömer Ersin

    (Beykent University, Department of Economics, Istanbul, Turkey)

Abstract

The study aims to extend the GARCH type volatility models to their nonlinear TAR (Tong, 1990) and STAR-based (Terasvirta, 1994) counter parts where both the conditional mean and the conditional variance processes follow TAR and STAR nonlinearity. The paper further investigates the models under their fractional integration and asymmetric power variants. The STAR-based models are LSTARLST- GARCH, LSTAR-LST-FIGARCH, LSTAR-LST-FIPGARCH and LSTAR-LSTFIAPGARCH models, which may be easily applied to model and forecast various financial time series. In the empirical section, an application is provided to model the daily returns in WTI crude oil prices considering the regime shifts the crude oil prices were subject to during history. Models are evaluated in terms of their out-of-sample forecasting capabilities with equal forecast accuracy tests and also in terms of various error criteria. The results suggest that volatility clustering, asymmetry and nonlinearity characteristics are modeled more efficiently as compared to their single regime variants, such as the GARCH, FIGARCH and FIAPGARCH models. Further, the outof- sample results suggest that the LSTAR-LST-FIAPGARCH model provides the best forecasting accuracy in terms of RMSE and MSE error criteria.

Suggested Citation

  • Melike Bildirici & Özgür Ömer Ersin, 2014. "Nonlinearity, Volatility and Fractional Integration in Daily Oil Prices: Smooth Transition Autoregressive ST-FI(AP)GARCH Models," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(3), pages 108-135, October.
  • Handle: RePEc:rjr:romjef:v::y:2014:i:3:p:108-135
    as

    Download full text from publisher

    File URL: http://www.ipe.ro/rjef/rjef3_14/rjef3_2014p108-135.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hagerud, Gustaf E., 1997. "A Smooth Transition ARCH Model for Asset Returns," SSE/EFI Working Paper Series in Economics and Finance 162, Stockholm School of Economics.
    2. Christian Conrad & Berthold R. Haag, 2006. "Inequality Constraints in the Fractionally Integrated GARCH Model," Journal of Financial Econometrics, Oxford University Press, vol. 4(3), pages 413-449.
    3. Andrew Ang & Geert Bekaert, 2002. "International Asset Allocation With Regime Shifts," The Review of Financial Studies, Society for Financial Studies, vol. 15(4), pages 1137-1187.
    4. Ralf Ostermark & Jaana Aaltonen & Henrik Saxen & Kenneth Soderlund, 2004. "Nonlinear modelling of the Finnish Banking and Finance branch index," The European Journal of Finance, Taylor & Francis Journals, vol. 10(4), pages 277-289.
    5. Terasvirta, T & Anderson, H M, 1992. "Characterizing Nonlinearities in Business Cycles Using Smooth Transition Autoregressive Models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 7(S), pages 119-136, Suppl. De.
    6. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    7. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    8. Clements, M.C. & Krolzig, H.-M., 2001. "Modelling Business Cycle Features Using Switching Regime Models," Economics Series Working Papers 9958, University of Oxford, Department of Economics.
    9. Hans-Martin Krolzig & Michael P. Clements, 2002. "Can oil shocks explain asymmetries in the US Business Cycle?," Empirical Economics, Springer, vol. 27(2), pages 185-204.
    10. Andreas Röthig & Carl Chiarella, 2007. "Investigating nonlinear speculation in cattle, corn, and hog futures markets using logistic smooth transition regression models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 27(8), pages 719-737, August.
    11. Giraitis, Liudas & Leipus, Remigijus & Robinson, Peter M. & Surgailis, Donatas, 2004. "LARCH, leverage, and long memory," LSE Research Online Documents on Economics 294, London School of Economics and Political Science, LSE Library.
    12. Lee, Junsoo & Degennaro, Ramon P, 2000. "Smooth Transition ARCH Models: Estimation and Testing," Review of Quantitative Finance and Accounting, Springer, vol. 15(1), pages 5-20, July.
    13. Giorgio Busetti & Matteo Manera, 2003. "STAR-GARCH Models for Stock Market Interactions in the Pacific Basin Region, Japan and US," Working Papers 2003.43, Fondazione Eni Enrico Mattei.
    14. Daniel, Kent & Hirshleifer, David & Teoh, Siew Hong, 2002. "Investor psychology in capital markets: evidence and policy implications," Journal of Monetary Economics, Elsevier, vol. 49(1), pages 139-209, January.
    15. González-Rivera Gloria, 1998. "Smooth-Transition GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 3(2), pages 1-20, July.
    16. Liudas Giraitis, 2004. "LARCH, Leverage, and Long Memory," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 177-210.
    17. Melike Bildirici & Özgür Ersin, 2011. "Fiyat Teorisinin Mali Teorisine Farklý Bir Bakýþ: MLSTAR ve MLP Modelleri," Koç University-TUSIAD Economic Research Forum Working Papers 1115, Koc University-TUSIAD Economic Research Forum.
    18. Adrangi, Bahram & Chatrath, Arjun & Dhanda, Kanwalroop Kathy & Raffiee, Kambiz, 2001. "Chaos in oil prices? Evidence from futures markets," Energy Economics, Elsevier, vol. 23(4), pages 405-425, July.
    19. Barberis, Nicholas & Shleifer, Andrei & Vishny, Robert, 1998. "A model of investor sentiment," Journal of Financial Economics, Elsevier, vol. 49(3), pages 307-343, September.
    20. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    21. Harrison Hong & Jeremy C. Stein, 1999. "A Unified Theory of Underreaction, Momentum Trading, and Overreaction in Asset Markets," Journal of Finance, American Finance Association, vol. 54(6), pages 2143-2184, December.
    22. Shambora, William E. & Rossiter, Rosemary, 2007. "Are there exploitable inefficiencies in the futures market for oil?," Energy Economics, Elsevier, vol. 29(1), pages 18-27, January.
    23. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    24. Raymond, Jennie E & Rich, Robert W, 1997. "Oil and the Macroeconomy: A Markov State-Switching Approach," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(2), pages 193-213, May.
    25. Alvarez-Ramirez, Jose & Alvarez, Jesus & Rodriguez, Eduardo, 2008. "Short-term predictability of crude oil markets: A detrended fluctuation analysis approach," Energy Economics, Elsevier, vol. 30(5), pages 2645-2656, September.
    26. Felix Chan & Michael McAleer, 2003. "Estimating smooth transition autoregressive models with GARCH errors in the presence of extreme observations and outliers," Applied Financial Economics, Taylor & Francis Journals, vol. 13(8), pages 581-592.
    27. Menelaos Karanasos & Zacharias Psaradakis & Martin Sola, 2004. "On the Autocorrelation Properties of Long‐Memory GARCH Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 265-282, March.
    28. Tse, Y. K. & Tsui, Albert K. C., 1997. "Conditional volatility in foreign exchange rates: Evidence from the Malaysian ringgit and Singapore dollar," Pacific-Basin Finance Journal, Elsevier, vol. 5(3), pages 345-356, July.
    29. Nelson, Daniel B., 1992. "Filtering and forecasting with misspecified ARCH models I : Getting the right variance with the wrong model," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 61-90.
    30. Raymond, Jennie E & Rich, Robert W, 1997. "Erratum [Oil and the Macroeconomy: A Markov State-Switching Approach]," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(4), pages 555-555, November.
    31. Mark Holmes & Ping Wang, 2003. "Oil Price Shocks and the Asymmetric Adjustment of UK Output: A Markov-switching approach," International Review of Applied Economics, Taylor & Francis Journals, vol. 17(2), pages 181-192.
    32. Ane, Thierry & Ureche-Rangau, Loredana, 2006. "Stock market dynamics in a regime-switching asymmetric power GARCH model," International Review of Financial Analysis, Elsevier, vol. 15(2), pages 109-129.
    33. Tang, Linghui & Hammoudeh, Shawkat, 2002. "An empirical exploration of the world oil price under the target zone model," Energy Economics, Elsevier, vol. 24(6), pages 577-596, November.
    34. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
    35. Felix Chan & Michael McAleer, 2002. "Maximum likelihood estimation of STAR and STAR-GARCH models: theory and Monte Carlo evidence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 509-534.
    36. Brooks, Robert D. & Faff, Robert W. & McKenzie, Michael D. & Mitchell, Heather, 2000. "A multi-country study of power ARCH models and national stock market returns," Journal of International Money and Finance, Elsevier, vol. 19(3), pages 377-397, June.
    37. Oehler, Andreas & Heilmann, Klaus & Lager, Volker & Oberlander, Michael, 2003. "Coexistence of disposition investors and momentum traders in stock markets: experimental evidence," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 13(5), pages 503-524, December.
    38. T. Ane & L. Ureche-Rangau, 2006. "Stock market dynamics in a regime-switching asymmetric power GARCH model," Post-Print hal-00170841, HAL.
    39. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    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. Melike Bildirici & Nilgun Guler Bayazit & Yasemen Ucan, 2020. "Analyzing Crude Oil Prices under the Impact of COVID-19 by Using LSTARGARCHLSTM," Energies, MDPI, vol. 13(11), pages 1-18, June.
    2. Monge, Manuel & Gil-Alana, Luis A. & Pérez de Gracia, Fernando, 2017. "Crude oil price behaviour before and after military conflicts and geopolitical events," Energy, Elsevier, vol. 120(C), pages 79-91.
    3. Gil-Alana, Luis A. & Gupta, Rangan & Olubusoye, Olusanya E. & Yaya, OlaOluwa S., 2016. "Time series analysis of persistence in crude oil price volatility across bull and bear regimes," Energy, Elsevier, vol. 109(C), pages 29-37.
    4. Murad A. BEIN & Mehmet AGA, 2016. "On the Linkage between the International Crude Oil Price and Stock Markets: Evidence from the Nordic and Other European Oil Importing and Oil Exporting Countries," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(4), pages 115-134, December.

    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. Bildirici, Melike & Ersin, Özgür, 2012. "Nonlinear volatility models in economics: smooth transition and neural network augmented GARCH, APGARCH, FIGARCH and FIAPGARCH models," MPRA Paper 40330, University Library of Munich, Germany, revised May 2012.
    2. Tomasz Wójtowicz & Henryk Gurgul, 2009. "Long memory of volatility measures in time series," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 19(1), pages 37-54.
    3. Adnen Ben Nasr & Ahdi Noomen Ajmi & Rangan Gupta, 2014. "Modelling the volatility of the Dow Jones Islamic Market World Index using a fractionally integrated time-varying GARCH (FITVGARCH) model," Applied Financial Economics, Taylor & Francis Journals, vol. 24(14), pages 993-1004, July.
    4. McAleer, Michael & Medeiros, Marcelo C., 2008. "A multiple regime smooth transition Heterogeneous Autoregressive model for long memory and asymmetries," Journal of Econometrics, Elsevier, vol. 147(1), pages 104-119, November.
    5. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654.
    6. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    7. Conrad, Christian & Karanasos, Menelaos & Zeng, Ning, 2011. "Multivariate fractionally integrated APARCH modeling of stock market volatility: A multi-country study," Journal of Empirical Finance, Elsevier, vol. 18(1), pages 147-159, January.
    8. Carl Lönnbark, 2016. "Asymmetry with respect to the memory in stock market volatilities," Empirical Economics, Springer, vol. 50(4), pages 1409-1419, June.
    9. Melike Bildirici & Nilgun Guler Bayazit & Yasemen Ucan, 2020. "Analyzing Crude Oil Prices under the Impact of COVID-19 by Using LSTARGARCHLSTM," Energies, MDPI, vol. 13(11), pages 1-18, June.
    10. Thomas Chuffart, 2015. "Selection Criteria in Regime Switching Conditional Volatility Models," Econometrics, MDPI, vol. 3(2), pages 1-28, May.
    11. Ho, Kin-Yip & Shi, Yanlin & Zhang, Zhaoyong, 2013. "How does news sentiment impact asset volatility? Evidence from long memory and regime-switching approaches," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 436-456.
    12. Yanlin Shi & Yang Yang, 2018. "Modeling High Frequency Data with Long Memory and Structural Change: A-HYEGARCH Model," Risks, MDPI, vol. 6(2), pages 1-28, March.
    13. Adnen Ben Nasr & Mohamed Boutahar & Abdelwahed Trabelsi, 2010. "Fractionally integrated time varying GARCH model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(3), pages 399-430, August.
    14. Brooks, Robert, 2007. "Power arch modelling of the volatility of emerging equity markets," Emerging Markets Review, Elsevier, vol. 8(2), pages 124-133, May.
    15. Wang, Yudong & Wu, Chongfeng & Wei, Yu, 2011. "Can GARCH-class models capture long memory in WTI crude oil markets?," Economic Modelling, Elsevier, vol. 28(3), pages 921-927, May.
    16. repec:wyi:journl:002190 is not listed on IDEAS
    17. Lang, Korbinian & Auer, Benjamin R., 2020. "The economic and financial properties of crude oil: A review," The North American Journal of Economics and Finance, Elsevier, vol. 52(C).
    18. Li, Gang & Li, Yong, 2015. "Forecasting copper futures volatility under model uncertainty," Resources Policy, Elsevier, vol. 46(P2), pages 167-176.
    19. Michael McKenzie & Heather Mitchell & Robert Brooks & Robert Faff, 2001. "Power ARCH modelling of commodity futures data on the London Metal Exchange," The European Journal of Finance, Taylor & Francis Journals, vol. 7(1), pages 22-38.
    20. Klein, Tony & Walther, Thomas, 2017. "Fast fractional differencing in modeling long memory of conditional variance for high-frequency data," Finance Research Letters, Elsevier, vol. 22(C), pages 274-279.
    21. Tarek Bouazizi & Zouhaier Hadhek & Fatma Mrad & Mosbah Lafi, 2021. "Changes in Demand for Crude Oil and its Correlation with Crude Oil and Stock Market Returns Volatilities: Evidence from Three Asian Oil Importing Countries," International Journal of Energy Economics and Policy, Econjournals, vol. 11(3), pages 27-43.

    More about this item

    Keywords

    volatility; oil prices; LSTAR-LST-GARCH; LSTAR-LST-FIGARCH and LSTAR-LST-FIAPGARCH models;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

    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:rjr:romjef:v::y:2014:i:3:p:108-135. 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: Corina Saman (email available below). General contact details of provider: https://edirc.repec.org/data/ipacaro.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.