A recursive online algorithm for the estimation of time-varying ARCH parameters

Bernoulli

Volumn 13, Issue 2, 2007, Pages 389-422

  Dahlhaus, Rainer ^a   Subba Rao, Suhasini ^a  

^a UNIVERSITY OF HEIDELBERG   (Germany)

Author keywords

Locally stationary; Recursive online algorithms; Time varying ARCH process

Indexed keywords

EID: 37549031844     PISSN: 13507265     EISSN: None     Source Type: Journal    
DOI: 10.3150/07-BEJ5009     Document Type: Article

References (15)

1. Aguech, R., Moulines, E. and Priouret, P. (2000). On a perturbation approach for the analysis of stochastic tracking algorithms. SIAM J. Control Optim. 39 872-899.
2. Chen, X. and White, H. (1998). Nonparametric learning with feedback. J. Economic Theory 82 190-222.
3. Dahlhaus, R. and Subba Rao, S. (2006). A recursive online algorithm for the estimation of time-varying ARCH parameters. Technical report.
4. Dahlhaus, R. and Subba Rao, S. (2006). Statistical inference for time-varying ARCH processes. Ann. Statist. 34 1075-1114.
5. Guo, L. (1994). Stability of recursive stochastic tracking algorithms. SIAM J. Control Optim. 32 1195-1225.
6. Hall, P. and Heyde, C. (1980). Martingale Limit Theory and Its Application. New York: Academic Press.
7. Kushner, H. and Yin, G. (2003). Stochastic Approximation and Recursive Algorithms and Applications. Berlin: Springer-Verlag.
8. Ljung, L. and Söderström, T. (1983). Theory and Practice of Recursive Identification. Cambridge, MA: MIT Press.
9. Mikosch, T. and Stǎricǎ, C. (2000). Is it really long memory we see in financial returns? In P. Embrechts (ed.), Extremes and Integrated Risk Management, pp. 439-459. London: Risk Books.
10. Mikosch, T. and Stiricǎ, C. (2004). Non-stationarities in financial time series, the long-range dependence and the IGARCH effects. Rev. Econometrics Statist. 86 378-390.
11. Moulines, E., Priouret, P. and Roueff, F. (2005). On recursive estimation for locally stationary time varying autoregressive rocesses. Ann. Statist. 33 2610-2654.
12. Solo, V. (1981). T second order properties of a time series recursion. Ann. Statist. 9 307-317.
13. Solo, V. (1989). The limiting behavior of the LMS. IEEE Trans. Acoust. Speech Signal Proc. 37 1909-1922.
14. Subba Rao, S. (2004). On some nonstationary, nonlinear random processes and their stationary approximations. Adv. in Appl. Probab. 38 1155-1172.
15. White, H. (1996). Parametric statistical estimation using artifical neural networks. In P. Smolensky, M. Mozer and D. Rumelhart (eds), Mathematical Perspectives on Neural Networks, pp. 719-775. Hillsdale, NJ: Lawrence Erlbaum Associates.