Splines for financial volatility

Journal of the Royal Statistical Society. Series B: Statistical Methodology

Volumn 71, Issue 3, 2009, Pages 655-670

  Audrino, Francesco ^a   Bühlmann, Peter ^b  

^a UNIVERSITY OF ST GALLEN   (Switzerland)

^b ETH ZURICH   (Switzerland)

Author keywords

B splines; Boosting; Conditional variance; Financial time series; Generalized auto regressive conditional heteroscedasticity model; Volatility

Indexed keywords

EID: 66849106564     PISSN: 13697412     EISSN: 14679868     Source Type: Journal    
DOI: 10.1111/j.1467-9868.2009.00696.x     Document Type: Article

References (40)

1. Andersen, T. G., Bollerslev, T. Diebold, F. X. (2005) Parametric and non-parametric volatility measurement. In Handbook of Financial Econometrics (eds Y. Aït-Sahalia L. P. Hansen). Amsterdam : Elsevier.
2. Andrews, D. W. K. Pollard, D. (1994) An introduction to functional central limit theorems for dependent stochastic processes. Int. Statist. Rev., 62, 119 132.
3. Ango Nze, P. Doukhan, P. (2004) Weak dependence: models and applications to econometrics. Econometr. Theory, 20, 995 1045. (Pubitemid 39594141)
4. Audrino, F. (2005) Local likelihood for non parametric ARCH(1) models. J. Time Ser. Anal., 26, 251 278. (Pubitemid 40322547)
5. Audrino, F. Bühlmann, P. (2001) Tree-structured generalized autoregressive conditional heteroscedastic models. J. R. Statist. Soc. B, 63, 727 744.
6. Audrino, F. Bühlmann, P. (2003) Volatility estimation with functional gradient descent for very high-dimensional financial time series. J. Computnl Finan., 6, 65 89.
7. Baillie, R. T., Bollerslev, T. Mikkelsen, H. O. (1996) Fractionally integrated generalized autoregressive conditional heteroskedasticity. J. Econometr., 74, 3 30. (Pubitemid 126375500)
8. Barron, A., Birgé, L. Massart, P. (1999) Risks bounds for model selection via penalization. Probab. Theory Reltd Flds, 113, 301 413.
9. Berkowitz, J. O'Brien, J. 2002) How accurate are Value-at-Risk models at commercial banks? J. Finan., 57, 1093 1111. (Pubitemid 36932126)
10. Bickel, P. J., Ritov, Y. Zakai, A. (2006) Some theory for generalized boosting algorithms. J. Mach. Learn. Res., 7, 705 732.
11. Birgé, L. Massart, P. (1997) From model selection to adaptive estimation. In Festschrift for Lucien Le Cam (eds D. Pollard, E. Torgensen G. Yangs pp. 55 87. New York : Springer.
12. Birgé, L. Massart, P. (1998) Minimum contrast estimators on sieves: exponential bounds and rates of convergence. Bernoulli, 4, 329 375. (Pubitemid 128774525)
13. Bollerslev, T. (1986) Generalized autoregressive conditional heteroskedasticity. J. Econometr., 31, 307 327.
14. de Boor, C. (2001) A Practical Guide to Splines, revised edn. New York : Springer.
15. Bühlmann, P. (2006) Boosting for high-dimensional linear models. Ann. Statist., 34, 559 583.
16. Bühlmann, P. McNeil, A. J. (2002) An algorithm for nonparametric GARCH modelling. Computnl Statist. Data Anal., 40, 665 683. (Pubitemid 35225172)
17. Carrasco, M. Chen, X. (2002) Mixing and moment properties of various GARCH and stochastic volatility models. Econometr. Theory, 18, 17 39. (Pubitemid 36399965)
18. Comte, F. Rozenholc, Y. (2002) Adaptive estimation of mean and volatility functions in (auto-)regressive models. Stochast. Processes Appl., 97, 111 145. (Pubitemid 40030719)
19. Curci, G. Corsi, F. (2003) A discrete sine transform approach for realized volatility measurement. Working Paper 44. National Centre of Competence in Research ''Financial Valuation and Risk Management'', Zurich. (Available from http://www.nccr-finrisk.uzh.ch/media/pdf/wp/WP044-6.pdf.)
20. Diebold, F. X. Mariano, R. S. (1995) Comparing predictive accuracy. J. Bus. Econ. Statist., 13, 253 263.
21. Efron, B., Hastie, T., Johnstone, I. Tibshirani, R. (2004) Least angle regression (with discussion). Ann. Statist., 32, 407 451.
22. Engle, R. F. (2002) Dynamic conditional correlation - a simple class of multivariate GARCH models. J. Bus. Econ. Statist., 20, 339 350.
23. Engle, R. F. Rangel, J. G. (2005) The spline GARCH model for unconditional variance and its global macroeconomic causes. Working Paper. Stern School of Business, New York University, New York.
24. Francq, C. Zakoian, J.-M. (2006) Mixing properties of a general class of GARCH(1,1) models without moment assumptions on the observed process. Econometr. Theory, 22, 815 834.
25. Friedman, J. H. (2001) Greedy function approximation: a gradient boosting machine. Ann. Statist., 29, 1189 1232. (Pubitemid 33405972)
26. Gourieroux, C. Monfort, A. (1992) Qualitative threshold ARCH models. J. Econometr., 52, 159 199.
27. Hafner, C. (1998) Estimating high-frequency foreign exchange rate volatility with nonparametric ARCH models. J. Statist. Planng Inf., 68, 247 269. (Pubitemid 128180639)
28. Hansen, P. R. Lunde, A. (2006) Consistent ranking of volatility models. J. Econometr., 131, 97 121. (Pubitemid 43295771)
29. Hansen, P. R., Lunde, A. Nason, J. M. (2003) Choosing the best volatility models: the model confidence set approach. Oxf. Bull. Econ. Statist., 65, 839 861. (Pubitemid 38085391)
30. Härdle, W. Tsybakov, A. (1997) Local polynomial estimators of the volatility function in nonparametric autoregression. J. Econometr., 81, 223 242. (Pubitemid 127398241)
31. de Jong, R. M. (1998) Uniform laws of large numbers and stochastic Lipschitz-continuity. J. Econometr., 86, 243 268. (Pubitemid 128413590)
32. Laurent, B. Massart, P. (2000) Adaptive estimation of quadratic functionals via model selection. Ann. Statist., 28, 1302 1338. (Pubitemid 33244915)
33. Lin, Y. (2000) Tensor product space ANOVA models. Ann. Statist., 28, 734 755.
34. Lunde, A. Hansen, P. R. (2005) A forecast comparison of volatility models: does anything beat a GARCH(1,1) J. Appl. Econometr., 20, 873 889. (Pubitemid 43097870)
35. Patton, A. J. (2006) Volatility forecast evaluation and comparison using imperfect volatility proxies. Working Paper. London School of Economics and Political Science, London.
36. Rosset, S. Zhu, J. (2007) Piecewise linear regularized solution paths. Ann. Statist., 35, 1012 1030.
37. Tibshirani, R. (1996) Regression shrinkage and selection via the lasso. J. R. Statist. Soc. B, 58, 267 288.
38. Yang, L., Härdle, W. Nielsen, J. (1999) Nonparametric autoregression with multiplicative volatility and additive mean. J. Time Ser. Anal., 20, 579 604.
39. Zhang, L., Aït-Sahalia, Y. Mykland, P. A. (2005) A tale of two time scales: determining integrated volatility with noisy high frequency data. J. Am. Statist. Ass., 100, 1394 1411. (Pubitemid 41801284)
40. Zhao, P. Yu, B. (2007) Stagewise Lasso. J. Mach. Learn. Res., 8, 2701 2726.