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Journal of Time Series Econometrics

Editor-in-Chief: Hidalgo, Javier

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CiteScore 2017: 0.25

SCImago Journal Rank (SJR) 2017: 0.236
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1941-1928
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A Generalized ARFIMA Model with Smooth Transition Fractional Integration Parameter

Heni Boubaker
  • Corresponding author
  • IHEC of Sousse, B.P. 40, Route de la ceinture-Sahloul III, 4054, Sousse, Tunisia.
  • IPAG LAB, IPAG Business School, 184 boulevard Saint-Germain Paris, France
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Published Online: 2017-07-19 | DOI: https://doi.org/10.1515/jtse-2015-0001

Abstract

This paper proposes a model of time-varying fractional integration where the long-memory parameter, d, in an ARFIMA model is allowed to depend on t and evolve according to a Smooth Transition Regressive (STR) model advanced by Teräsvirta (1994, 1998) . To estimate the time-varying fractional integration parameter, we suggest a new multi-step estimation method based on the wavelet approach using the instantaneous least squares estimator (ILSE). We conduct some simulation experiments and we find that our estimation iterative procedure performs better than that proposed by Boutahar, Dufrénot, and Péguin-Feissolle (2008). An empirical application of this methodology to the volatility of some financial time series is used for illustration purposes. Finally, it is shown that the model proposed offers an interesting framework to describe long-range dependence in the volatility with heterogeneous persistence.

Keywords: time-varying long memory; local-stationarity; STR model; wavelet; ILSE; financial time series

JEL Classification: C13; C22; C32; G15

References

  • Abry, P., and D. Veitch. 1998. “Wavelet Analysis of Long-Range Dependent Traffic.” IEEE Transactions on Information Theory 44 (1): 2–15.CrossrefGoogle Scholar

  • Alfarano, S., and T. Lux. (2002). A Minimal Noise Trader Model with Realistic Time Series Properties Working paper.Google Scholar

  • Aloy, M., G. Dufrénot, C.L. Tong, and A. Péguin-Feissolle. 2013. “A Smooth Transition Long-Memory Model Studies in Nonlinear.” Dynamics and Econometrics 17 (13): 281–296.Google Scholar

  • Alvarez-Ramirez, J., J. Alvarez, and R. Solis. 2010. “Crude Oil Market Efficiency and Modeling: Insights from the Multiscaling Autocorrelation Pattern.” Energy Economics 32 (5): 993–1000.CrossrefGoogle Scholar

  • Andersen, T.G., and T. Bollerslev. 1997. “Heterogeneous Information Arrivals and Return Volatility Dynamics: Uncovering the Long-Run in High Frequency Returns.” The Journal of Finance 52 (3): 975–1005.CrossrefGoogle Scholar

  • Bai, J., and P. Perron. 2003. “Computation and Analysis of Multiple Structural Change Models.” Journal of Applied Econometrics 18 (1): 1–22.CrossrefGoogle Scholar

  • Baillie, R.T., and T. Bollerslev. 1994. “Cointegration, Fractional Cointegration and Exchange Rate Dynamics.” The Journal of Finance 49 (2): 737–745.CrossrefGoogle Scholar

  • Beine, M., and S. Laurent. Structural Changes and Long Memory in Olatility: Newevidence from Daily Exchange Rates. In: Dunis C., Timmerman A., and Moody J., editors. Developments in Forecast Combination and Portfolio Choice 145-157. Wiley series in quantitative analysis (chap. 6, 2001.

  • Beran, J. 2009. “On Parameter Estimation for Locally Stationary Long-Memory Processes.” Journal of Statistical Planning and Inference 143 (1): 201–220.Google Scholar

  • Bollerslev, T., and H.O. Mikkelsen. 1996. “Modelling and Pricing Long Memory in Stock Market Volatility.” Journal of Econometrics 73 (1): 151–184.CrossrefGoogle Scholar

  • Boutahar, M., G. Dufrénot, and A. Péguin-Feissolle. 2008. “A Simple Fractionally Integrated Model with a Time varying Long Memory Parameter dt .” Computational Economics 31 (3): 225–231.CrossrefGoogle Scholar

  • Chandler, G., and W. Polonik. 2006. “Discrimination of Locally Stationary Time Series Based on the Excess Mass Functional.” Journal of the American Statistical Association 101 (473): 240–253.CrossrefGoogle Scholar

  • Cheung, Y.W. 1993. “Long Memory in Foreign-Exchanges Rates.” Journal of business and Economic Statistics 11 (1): 93–101.Google Scholar

  • Dahlhaus, R. 1996. “Maximum Likelihood Estimation Method Selection for Nonstationary Process.” Journal Nonparametric Statistics 6 (2-3): 171–191.CrossrefGoogle Scholar

  • Daubechies, I. (1992).Ten Lectures on Wavelets."Volume 61 of CBMS-NSF Regional Conference Series in Applied Mathematics," Philadelphia: Society for Industrial and Applied Mathematics (SIAM).Google Scholar

  • Davidson, J. 2004. “Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model.” Journal of Business and Economics Statistics 22 (1): 16–29.CrossrefGoogle Scholar

  • Diebold, F.X., S. Husted, and M. Rush. 1991. “Real Exchange Rates under the Gold Standard.” Journal of Political Economy 99 (6): 1252–1271.CrossrefGoogle Scholar

  • Dufrénot, Gilles, et al. D. Guegan and A. Peguin-Feissolle. 2005a. “Modelling squared returns using a SETAR model with long-memory dynamics.” Economics Letters 86 (2): 237–243. DOI:.CrossrefGoogle Scholar

  • Dufrénot, Gilles, et al. D. Guegan and A. Peguin-Feissolle. 2005b. “Long-memorydynamics in a SETAR model-applications to stock markets.” Journal of International Financial Markets, Institutions and Money 15 (5): 391–406. DOI:.CrossrefGoogle Scholar

  • Dufrénot, Gilles, et al. D. Guegan and A. Peguin-Feissolle. 2008. “Changing-regime volatility: a fractionally integrated SETAR model.” Applied Financial Economics 18 (7): 519–526. 2008. DOI:.CrossrefGoogle Scholar

  • Engelen, S., P. Norouzzadeh, W. Dullaert, and C. Rahmani. 2011. “Multifractal Features of Spot Rates in the Liquid Petroleum Gas Shipping Market.” Energy Economics 33 (1): 88–98.CrossrefGoogle Scholar

  • Gaunersdorfer, A. 2001. “Adaptive Beliefs and the Volatility of Asset Prices.” Central European Journal of Operations Research 9: 5–30.Google Scholar

  • Genton, M., and O. Perrin. 2004. “On a Time Deformation Reducing Nonstationary Stochastic Processes to Local Stationarity.” Journal of Applied Probability 41: 236–249.CrossrefGoogle Scholar

  • Geweke, J., and S. Porter-Hudak. 1983. “The Estimation and Application of Long Memory Time Series Models.” Journal of Time Series Analysis 4 (4): 221–238.CrossrefGoogle Scholar

  • Granger, C.W.J., and R. Joyeux. 1980. “An Introduction to Long Memory Time Series and Fractional Differencing.” Journal of Times Series Analysis 1 (1): 15–29.CrossrefGoogle Scholar

  • Guo, W., M. Dai, H. C. Ombao, and R. von Sachs. 2003. “Smoothing Spline ANOVA for Time-Dependent Spectral Analysis.” Journal of the American Statistical Association 98 (463): 643–652.CrossrefGoogle Scholar

  • Hosking, J.R.M. 1981. “Fractional Differencing.” Biometrika 68 (1): 165–176.CrossrefGoogle Scholar

  • Hurvich, C.M., R.S. Deo, and J. Brodsky. 1998. “The Mean Squared Error of Geweke and Porter-Hudak’s Estimator of the Memory Parameter of a Long-Memory Time Series.” Journal of Time Series Analysis 19 (1): 19–46.CrossrefGoogle Scholar

  • Jensen, M.J. 1999a. “An Approximate Wavelet MLE of Short and Long Memory Parameters.” Studies in Nonlinear Dynamics and Economics 3:4.Google Scholar

  • Jensen, M.J. 1999b. “Using Wavelets to Obtain a Consistent Ordinary Least Squares Estimator of the Long-Memory Parameter.” Journal of Forecasting 18 (1): 17–32.CrossrefGoogle Scholar

  • Jensen, M.J. 2000. “An Alternative Maximum Likelihood Estimator of Long-Memory Processes Using Compactly Supported Wavelets.” Journal of Economic Dynamics and Control 24 (3): 361–387.CrossrefGoogle Scholar

  • Kirman, A., and G. Teyssière. 2002. “Microeconomic Models for Long Memory in the Volatility of Financial Times Series.” Studies in Nonlinear Dynamics and Economics 5:4.Google Scholar

  • Luukkonen, R., P. Saïkkonen, and T. Teräsvirta. 1988. “Testing Linearity Against Smooth Transition Autoregressive Models.” Biometrika 75 (3): 491–499.CrossrefGoogle Scholar

  • Lux, T., and M. Marchesi. 2000. “Volatility Clustering in Financial Markets: A microsimulation of Interacting Agents.” International Journal of Theoretical and Applied Finance 3 (4): 675–602.CrossrefGoogle Scholar

  • Mallat, S. 1999. A Wavelet Tour of Signal Processing. San Diego: Academic Press.Google Scholar

  • Mallat, S., and W.L. Hwang. 1992. “Singularity Detection and Processing with Wavelets.” IEEE Transactions on Information Theory 38 (2): 617–643.CrossrefGoogle Scholar

  • Mallat, S., and Z. Zhang. 1993. “Matching Pursuits with Time-Frequency Dictionaries.” IEEE Transactions on Signal Processing 41 (12): 3397–3415.CrossrefGoogle Scholar

  • McCoy, E.J., and A.T. Walden. 1996. “Wavelet Analysis and Synthesis of Stationary Long-Memory Processes.” Journal of Computational and Graphical Statistics 5 (1): 26–56.Google Scholar

  • Pagan, A. 1984. “Econometric Issues in the Analysis of Regressions with Generated Regressors.” International Economic Review 25 (1): 221–247.CrossrefGoogle Scholar

  • Palma, W., and R. Olea. 2010. “An Efficient Estimator for Locally Stationary Gaussian Long-Memory Process.” The Annals of Statistics 38 (5): 2958–2997.CrossrefGoogle Scholar

  • Percival, D.B., and A.T. Walden. 2000. Wavelet Methods for Time Series Analysis. Cambridge: Cambridge University Press.Google Scholar

  • Philippe, A., D. Surgailis, and M.-C. Viano. 2008. “Time-Varying Fractionally Integrated Processes with Non-Stationary Long-Memory.” Theory of Probability and Applications 52 (4): 651–673.CrossrefGoogle Scholar

  • Roueff, F., and R. von Sachs. 2011. “Locally Stationary Long Memory Estimation.” Stochastic Processes and their Applications 121 (4): 813–844.CrossrefGoogle Scholar

  • Shimotsu, K., and P.C.B. Phillips. 2005. “Exact Local Whittle Estimation of Fractional Integration.” The Annals of Statistics 33 (4): 1890–1933.CrossrefGoogle Scholar

  • Surgailis, D. 2008. “Non-Homogenous Fractional Integration and Multifractional Processes.” Stochastic Processes and their Applications 118 (2): 171–198.CrossrefGoogle Scholar

  • Taylor, S. 1986. Modelling Financial Time Series. Chichester: Wiley.Google Scholar

  • Teräsvirta, T. 1994. “Specification, Estimation and Evaluation of Smooth Transition Autoregressive Models.” Journal of American Statistical Association 89 (425): 208–218.Google Scholar

  • Teräsvirta, T. 1998. “Modelling Economic Relationship with Smooth Transition Regression.”. In Lütkepohl, H., and M. Krästzig (Eds.), Applied Time Series Econometrics. 222–242. Cambridge University Press.Google Scholar

  • Tsay, W.J., and W.K. Härdle. 2009. “A Generalized ARFIMA Process with Markov-Switching Fractional Differencing Parameter.” Journal of Statistical Computation and Simulation 79 (5): 731–745.CrossrefGoogle Scholar

  • van Dijk, D., T. Teräsvirta, and P.H. Franses. 2002. “Smooth Transition Autoregressive Models-a Survey of Recent Developments.” Econometric Reviews 21 (1): 1–47.CrossrefGoogle Scholar

  • Whitcher, B., and M.K. Jensen. 2000. “Wavelet Estimation of a Local Long Memory Parameter.” Exploration Geophysics 31 (1–2): 94–103.CrossrefGoogle Scholar

About the article

Published Online: 2017-07-19


Citation Information: Journal of Time Series Econometrics, Volume 10, Issue 1, 20150001, ISSN (Online) 1941-1928, DOI: https://doi.org/10.1515/jtse-2015-0001.

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