A multiple regime smooth transition Heterogeneous Autoregressive model for long memory and asymmetries

Journal of Econometrics

Volumn 147, Issue 1, 2008, Pages 104-119

  McAleer, Michael ^a   Medeiros, Marcelo C ^b  

^a UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

^b PONTIFICAL CATHOLIC UNIVERSITY OF RIO DE JANEIRO   (Brazil)

Author keywords

Financial econometrics; Forecasting; Heterogeneous autoregression; Leverage; Model combination; Realized volatility; Risk management; Sign and size asymmetries; Smooth transition

Indexed keywords

FINANCIAL DATA PROCESSING; FORECASTING; MAXIMUM LIKELIHOOD ESTIMATION; MONTE CARLO METHODS; REGRESSION ANALYSIS; RISK ANALYSIS; RISK MANAGEMENT; TIME SERIES ANALYSIS;

FINANCIAL ECONOMETRICS; HETEROGENEOUS AUTOREGRESSION; LEVERAGE; MODEL COMBINATION; REALIZED VOLATILITY; SIGN AND SIZE ASYMMETRIES; SMOOTH TRANSITION;

RISK PERCEPTION;

EID: 55349091307     PISSN: 03044076     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jeconom.2008.09.032     Document Type: Article

References (117)

1. Andersen T., and Bollerslev T. Answering the skeptics: Yes, standard volatility models do provide accurate forecasts. International Economic Review 39 (1998) 885-906
2. Andersen T., Bollerslev T., Christoffersen P., and Diebold F. Practical volatility and correlation modeling for financial market risk management. In: Carey M., and Stulz R. (Eds). Risks of Financial Institutions (2006), University of Chicago Press for NBER 513-548
3. Andersen T., Bollerslev T., and Diebold F. Roughing it up: Including jump components in the measurement, modeling and forecasting of return volatility. Review of Economics and Statistics 89 (2007) 701-720
4. Andersen T., Bollerslev T., Diebold F.X., and Ebens H. The distribution of realized stock return volatility. Journal of Financial Economics 61 (2001) 43-76
5. Andersen T., Bollerslev T., Diebold F.X., and Labys P. Modeling and forecasting realized volatility. Econometrica 71 (2003) 579-625
6. Anderson H.M., Nam K., and Vahid F. Asymmetric nonlinear smooth transition GARCH models. In: Rothman P. (Ed). Nonlinear Time Series Analysis of Economic and Financial Data (1999), Kluwer 191-207
7. Asai M., and McAleer M. Dynamic asymmetric leverage in stochastic volatility models. Econometric Reviews 24 (2005) 317-332
8. Asai M., and McAleer M. Asymmetric multivariate stochastic volatility. Econometric Reviews 25 (2006) 453-473
9. Asai M., and McAleer M. Non-trading day effects in asymmetric conditional and stochastic volatility models. Econometrics Journal 10 (2007) 113-123
10. Asai M., McAleer M., and Yu J. Multivariate stochastic volatility: A review. Econometric Reviews 25 (2006) 145-175
11. Audrino F., and Bühlmann P. Tree-structured GARCH models. Journal of the Royal Statistical Society, Series B 63 (2001) 727-744
12. Aït-Sahalia, Y., Mykland, P., Zhang, L., 2005. Ultra high frequency volatility estimation with dependent microstructure noise, NBER Working Papers 11380, National Bureau of Economic Research
13. Bai J. A note on spurious break. Econometric Theory 14 (1998) 663-669
14. Baillie R., Bollerslev T., and Mikkelsen H. Fractionally integrated generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 74 (1996) 3-30
15. Bandi, F., Russell, J., 2005. Market microstructure noise, integrated variance estimators, and the limitations of asymptotic approximations: A solution, Unpublished manuscript, Graduate School of Business, University of Chicago.
16. Bandi F., and Russell J. Separating market microstructure noise from volatility. Journal of Financial Economics 79 (2006) 655-692
17. Bandi, F., Russell, J., 2008. Microstructure noise, realized volatility, and optimal sampling, Review of Economic Studies (forthcoming)
18. Barndorff-Nielsen, O., Hansen, P., Lunde, A., Shephard, N., 2008. Designing realised kernels to measure the ex-post variation of equity prices in the presence of noise, Econometrica (forthcoming)
19. Barndorff-Nielsen O., and Shephard N. Econometric analysis of realised volatility and its use in estimating stochastic volatility models. Journal of the Royal Statistical Society B 64 (2002) 253-280
20. Biais B., Glosten L., and Spatt C. Market microstructure: A survey of microfoundations, empirical results, and policy implications. Journal of Financial Markets 8 (2005) 217-264
21. Black, F., 1976. Studies in stock price volatility changes, In: Proceedings of The American Statistical Association, Business and Economic Statistics Section, pp. 177-181
22. Blume M., and Goldstein M. Quotes, order flow, and price discovery. Journal of Finance 52 (1997) 221-244
23. Bollerslev T. Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 21 (1986) 307-328
24. Bollerslev T. A conditionally heteroskedastic time series model for speculative prices and rates of return. The Review of Economics and Statistics 69 (1987) 542-547
25. Breidt F., Crato N., and de Lima P. The detection and estimation of long memory in stochastic volatility. Journal of Econometrics 83 (1998) 325-348
26. Cai J. A Markov model of switching-regime ARCH. Journal of Business and Economic Statistics 12 (1994) 309-316
27. Caporin M., and McAleer M. Dynamic asymmetric GARCH. Journal of Financial Econometrics 4 (2006) 385-412
28. Cappuccio N., Lubian D., and Davide R. Investigating asymmetry in US stock market indexes: Evidence from a stochastic volatility model. Applied Financial Economics 16 (2006) 479-490
29. Carnero M.A., Peña D., and Ruiz E. Persistence and kurtosis in GARCH and stochastic volatility models. Journal of Financial Econometrics 2 (2004) 319-342
30. Chan K.S., and Tong H. On estimating thresholds in autoregressive models. Journal of Time Series Analysis 7 (1986) 179-190
31. Chen R., and Tsay R.S. Functional coefficient autoregressive models. Journal of the American Statistical Association 88 (1993) 298-308
32. Corsi, F., 2004. A simple long memory model of realized volatility, Manuscript, University of Southern Switzerland
33. Davidson J., and Sibbertsen P. Generating schemes for long memory processes: Regimes, aggregation and linearity. Journal of Econometrics 128 (2005) 253-282
34. Deo R., Hurvich C., and Lu Y. Forecasting realized volatility using a long-memory stochastic volatility model: Estimation, prediction and seasonal adjustment. Journal of Econometrics 131 (2006) 29-58
35. Diebold F. Modeling the persistence of conditional variances: A comment. Econometric Reviews 5 (1986) 51-56
36. Diebold F., and Inoue A. Long memory and regime switching. Journal of Econometrics 105 (2001) 131-159
37. Diebold F.X., and Mariano R.S. Comparing predictive accuracy. Journal of Business and Economic Statistics 13 (1995) 253-263
38. Ding Z., Granger C.W.J., and Engle R.F. A long memory property of stock market returns and a new model. Journal of Empirical Finance 1 (1993) 83-106
39. Eitrheim O., and Teräsvirta T. Testing the adequacy of smooth transition autoregressive models. Journal of Econometrics 74 (1996) 59-75
40. Engle R.F. Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation. Econometrica 50 (1982) 987-1007
41. Engle R.F., and Ng V.K. Measuring and testing the impact of news on volatility. Journal of Finance 48 (1993) 1749-1778
42. Fornari F., and Mele A. Sign- and volatility-switching ARCH models: Theory and applications to international stock markets. Journal of Applied Econometrics 12 (1997) 49-65
43. Fouque J.P., Papanicolaou G., Sircar R., and Sølna K. Short time-scale in S&P 500 volatility. Journal of Computational Finance 6 (2003) 1-23
44. Geweke J., and Porter-Hudak S. The estimation and application of long memory time series models. Journal of Time Series Analysis 4 (1983) 221-238
45. Giraitis L., Robinson P., and Surgailis D. LARCH, leverage, and long memory. Journal of Financial Econometrics 2 (2004) 177-210
46. Glosten L., Jagannathan R., and Runkle R. On the relationship between the expected value and the volatility of the nominal excess returns on stocks. Journal of Finance 48 (1993) 1779-1801
47. Goetzmann W.N., Ibbotson R.G., and Peng L. A new historical database for the NYSE 1815 to 1925: Performance and predictability. Journal of Financial Markets 4 (2001) 1-32
48. Gonzalez-Rivera G. Smooth transition GARCH models. Studies in Nonlinear Dynamics and Econometrics 3 2 (1998) 61-78
49. Granger C., and Hyung N. Occasional structural breaks and long memory with an application to the S&P500 absolute stock returns. Journal of Empirical Finance 3 (2004) 399-421
50. Granger C.W.J. Long memory relationships and the aggregation of dynamic models. Journal of Econometrics 14 (1980) 227-238
51. Granger C.W.J., and Teräsvirta T. A simple nonlinear time series model with misleading linear properties. Economics Letters 62 (2001) 161-165
52. Gray S. Modeling the conditional distribution of interest rates as a regime-switching process. Journal of Financial Economics 42 (1996) 27-62
53. Hagerud, G.E., 1997. A new non-linear GARCH model, Ph.D. thesis, Stockholm School of Economics
54. Hamilton J.D., and Susmel R. Autoregressive conditional heteroskedasticity and changes in regime. Journal of Econometrics 64 (1994) 307-333
55. Hansen P., Large J., and Lunde A. Moving average-based estimators of integrated variance. Econometric Reviews 27 (2008) 79-111
56. Hansen P.R., and Lunde A. A forecast comparison of volatility models: Does anything beat a GARCH(1,1) Model?. Journal of Applied Econometrics 20 (2005) 873-889
57. Hansen P.R., and Lunde A. Realized variance and market microstructure noise (with discussion). Journal of Business and Economic Statistics 24 (2006) 127-218
58. Harvey A., and Shephard N. Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns. Journal of Business and Economic Statistics 14 (1996) 429-434
59. Harvey D., Leybourne S., and Newbold P. Testing the equality of prediction mean squared errors. International Journal of Forecasting 13 (1997) 281-291
60. Hasbrouck J. One security, many markets: Determining the contributions to price discovery. Journal of Finance 50 (1995) 1175-1198
61. Hillebrand E. Neglecting parameter changes in GARCH models. Journal of Econometrics 129 (2005) 121-138
62. Hillebrand, E., Medeiros, M., 2008a. Estimating and forecasting GARCH models in the presence of structural breaks and regime switches. In: Wohar, M., Rapach, D. (Eds.) Forecasting in The Presence of Structural Breaks and Model Uncertainty. Emerald, pp. 303-327
63. Hillebrand, E., Medeiros, M., 2008b. Asymmetries, breaks, and long-range dependence: An estimation framework for time series of daily realized volatility, discussion paper, Pontifical Catholic University of Rio de Janeiro
64. Hsu C.-C. Change-point estimation in regressions with I(d) variables. Economics Letters 70 (2001) 147-155
65. Hurvich C., and Ray B. The local whittle estimator of long-memory stochastic volatility. Journal of Financial Econometrics 1 (2003) 445-470
66. Hwang J.T.G., and Ding A.A. Prediction intervals for artificial neural networks. Journal of the American Statistical Association 92 (1997) 109-125
67. Hyung, N., Poon, S.-H., Granger, C., 2008. The source of long memory in financial market volatility. In: Wohar, M., Rapach, D., (Eds.) Forecasting in The Presence of Structural Breaks and Model Uncertainty. Emerald, pp. 329-380
68. Jensen M. Semiparametric Bayesian inference of long-memory stochastic volatility models. Journal of Time Series Analysis 25 (2004) 895-922
69. Kalimipalli, M., Susmel, R., 2007. Switching stochastic volatility and the short-term interest rates, Journal of Empirical Finance (forthcoming)
70. Lamoureux C.G., and Lastrapes W.D. Persistence in variance, structural change, and the GARCH model. Journal of Business and Economic Statistics 8 (1990) 225-234
71. LeBaron B. Stochastic volatility as a simple generator of apparent financial power laws and long memory. Quantitative Finance 1 (2001) 621-631
72. Li C.W., and Li W.K. On a double threshold autoregressive heteroskedastic time series model. Journal of Applied Econometrics 11 (1996) 253-274
73. Lieberman O., and Phillips P. Refined inference on long memory in realized volatility. Econometric Reviews 27 (2008) 254-267
74. Ling S., and McAleer M. Necessary and sufficient moment conditions for the GARCH(r,s) and asymmetric power GARCH(r,s) models. Econometric Theory 18 (2002) 722-729
75. Ling S., and McAleer M. Asymptotic theory for a vector ARMA-GARCH model. Econometric Theory 19 (2003) 280-310
76. Liu J., Li W.K., and Li C.W. On a threshold autoregression with conditional heteroskedastic variances. Journal of Statistical Planning and Inference 62 2 (1997) 279-300
77. Lobato I.N., and Savin N.E. Real and spurious long-memory properties of stock-market data. Journal of Business and Economic Statistics 16 (1998) 261-268
78. Lundbergh S., and Teräsvirta T. Evaluating GARCH models. Journal of Econometrics 110 (2002) 417-435
79. Madhavan A. Market microstructure: A survey. Journal of Financial Markets 3 (2000) 205-258
80. Malmsten, H., Teräsvirta, T., 2004. Stylized facts of financial time series and three popular models of volatility, Working Paper Series in Economics and Finance 563, Stockholm School of Economics
81. Martens, M., van Dijk, D., de Pooter, M., 2004. Modeling and forecasting S&P 500 volatility: Long memory, structural breaks and nonlinearity, discussion paper 04-067/4, Tinbergen Institute
82. McAleer M. Automated inference and learning in modeling financial volatility. Econometric Theory 21 (2005) 232-261
83. McAleer M., and Medeiros M. Realized volatility: A review. Econometric Reviews 27 (2008) 10-45
84. Meddahi N. A theoretical comparison between integrated and realized volatility. Journal of Applied Econometrics 17 (2002) 479-508
85. Medeiros M., Teräsvirta T., and Rech G. Building neural network models for time series: A statistical approach. Journal of Forecasting 25 (2006) 49-75
86. Medeiros M., and Veiga A. Diagnostic checking in a flexible nonlinear time series model. Journal of Time Series Analysis 24 (2003) 461-482
87. Medeiros M., and Veiga A. A flexible coefficient smooth transition time series model. IEEE Transactions on Neural Networks 16 (2005) 97-113
88. Medeiros, M., Veiga, A., 2008. Modeling multiple regimes in financial volatility with a flexible coefficient GARCH(1,1) Model, Econometric Theory (forthcoming)
89. Merton R. On estimating the expected return on the market: An exploratory investigation. Journal of Financial Economics 8 (1980) 323-361
90. Mikosch T., and Starica C. nonstationarities in financial time series, the long-range dependence, and the IGARCH effects. Review of Economics and Statistics 86 (2004) 378-390
91. Müller, U., Dacorogna, M., Dav, R., Olsen, R., Pictet, O., Ward, J., 1993. Fractals and Intrinsic Time-A Challenge to Econometricians. In: Proceedings of the XXXIXth International AEA Conference on Real Time Econometrics
92. Nelson D.B. Conditinal heteroskedasticity in asset returns: A new approach. Econometrica 59 (1991) 347-370
93. Nunes L.C., Kuan C.-M., and Newbold P. Spurious break. Econometric Theory 11 (1995) 736-749
94. Omori Y., Chib S., Shephard N., and Nakajima J. Stochastic volatility with leverage: Fast and efficient likelihood inference. Journal of Econometrics 140 (2007) 425-449
95. Patton, A., 2005. Volatility forecast evaluation and comparison using imperfect volatility proxies, Unpublished manuscript, London School of Economics
96. Pitarakis J. Model selection uncertainty and detection of threshold effects. Studies in Nonlinear Dynamics and Econometrics 10 (2006) 1-28
97. Rabemanjara R., and Zakoian J.M. Threshold ARCH models and asymmetries in volatility. Journal of Applied Econometrics 8 1 (1993) 31-49
98. Rech G., Teräsvirta T., and Tschernig R. A simple variable selection technique for nonlinear models. Communications in Statistics, Theory and Methods 30 (2001) 1227-1241
99. Scharth, M., Medeiros, M., 2006. Asymmetric Effects and Long Memory in the Volatility of DJIA Stocks, Discussion paper, Pontifical Catholic University of Rio de Janeiro
100. Schwert G.W. Stock volatility and the crash of '87. Review of Financial Studies 3 (1990) 77-102
101. Smith A. Level shifts and the illusion of long memory in economic time series. Journal mf Business and Economic Statistics 23 (2005) 321-335
102. So M., Lam K., and Li W. A stochastic volatility model with Markov switching. Journal of Business and Economic Statistics 16 (1998) 244-253
103. So M., Li W., and Lam K. A threshold stochastic volatility model. Journal of Forecasting 21 (2002) 473-500
104. Suarez-Fariñas M., Pedreira C.E., and Medeiros M.C. Local global neural networks: A new approach for nonlinear time series modeling. Journal of the American Statistical Association 99 (2004) 1092-1107
105. Taylor S.J. Modelling Financial Time Series (1986), John Wiley, Chichester, UK
106. Teräsvirta T. Specification, estimation, and evaluation of smooth transition autoregressive models. Journal of the American Statistical Association 89 (1994) 208-218
107. van Dijk D., Franses P., and Paap R. A nonlinear long memory model, with an application to US unemployment. Journal of Econometrics 110 (2002) 135-165
108. White H. Consequences and detection of misspecified nonlinear regression models. Journal of the American Statistical Association 76 374 (1981) 419-433
109. White H. Estimation, Inference and Specification Analysis (1994), Cambridge University Press, New York, NY
110. White H., and Domowitz I. Nonlinear regression with dependent observations. Econometrica 52 (1984) 143-162
111. Wooldridge J.M. A unified approach to robust, regression-based specification tests. Econometric Theory 6 (1990) 17-43
112. Wooldridge J.M. Estimation and Inference for Dependent Process. In: Engle R.F., and McFadden D.L. (Eds). Handbook of Econometrics vol. 4 (1994), Elsevier Science 2639-2738
113. Yu J. On leverage in a stochastic volatility model. Journal of Econometrics 127 (2005) 165-178
114. Zakoian J.M. Threshold heteroskedastic models. Journal of Economic Dynamics and Control 18 (1994) 931-955
115. Zhang, L., 2005. Efficient estimation of stochastic volatility using noisy observations: A multi-scale approach, Unpublished manuscript, Department of Mathematical Sciences, Carnegie Mellon University
116. Zhang L., Mykland P., and Aït-Sahalia Y. A tale of two time scales: Determining integrated volatility with noisy high-frequency data. Journal of the American Statistical Association 100 (2005) 1394-1411
117. Zhou B. High frequency data and volatility in foreign-exchange rates. Journal of Business and Economic Statistics 14 (1996) 45-52