Gao, Jiti (2002): Modeling long-range dependent Gaussian processes with application in continuous-time financial models. Published in: Journal of Applied probability , Vol. 46, No. 2 (June 2004): pp. 467-482.
Preview |
PDF
MPRA_paper_11973.pdf Download (342kB) | Preview |
Abstract
This paper considers a class of nonstationary Gaussian processes with possible long-range dependence (LRD) and intermittency.
The author proposes a new estimation method to simultaneously estimate both the LRD and intermittency parameter. An application of the proposed estimation method to a continuous-time financial model is discussed.
Item Type: | MPRA Paper |
---|---|
Original Title: | Modeling long-range dependent Gaussian processes with application in continuous-time financial models |
Language: | English |
Keywords: | continuous-time model; diffusion process; long-range dependent process; parameter estimation; stochastic volatility |
Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General |
Item ID: | 11973 |
Depositing User: | jiti Gao |
Date Deposited: | 09 Dec 2008 00:20 |
Last Modified: | 28 Sep 2019 04:44 |
References: | Anh, V., Angulo, J. and Ruiz-Medina, M. (1999). Possible long-range dependence in fractional random fields. J. Statist. Planning Infer. 80, 95--110. Anh, V. V., Heyde, C. C. and Leonenko, N. N. (2002). Dynamic models of long-memory processes driven by Lévy noise. J. Appl. Prob. 39, 730--747. Baillie, R. T. and King, M. L. (eds) (1996). Special issue of Journal of Econometrics. (Ann. Econom. 73.) Black, F. and Scholes, M. (1973). The pricing of options and corporate liabilities. J. Political Econom. 3, 637--654. Brockwell, P. and Davis, R. (1990). Time Series Theory and Methods. Springer, New York. Comte, F. and Renault, E. (1996). Long memory continuous-time models. J. Econometrics 73, 101--149. Comte, F. and Renault, E. (1998). Long memory in continuous-time stochastic volatility models. Math. Finance 8, 291--323. Dahlhaus, R. (1989). Efficient parameter estimation for self-similar processes. Ann. Statist. 17, 1749--1766. Ding, Z. and Granger, C. W. J. (1996). Modelling volatility persistence of speculative returns: a new approach. J. Econometrics 73, 185--215. Ding, Z., Granger, C. W. J. and Engle, R. F. (1993). A long memory property of stock market returns and a new model. J. Empirical Finance 1, 83--105. Dym, H. and McKean, H. (1976). Gaussian Process, Function Theory and the Inverse Spectral Problem. Academic Press, New York. Fox, R. and Taqqu, M. S. (1986). Large sample properties of parameter estimates for strongly dependent stationary Gaussian time series. Ann. Statist. 14, 517--532. Frisch, U. (1995). Turbulence. Cambridge University Press. Gao, J., Anh, V. and Heyde, C. (2002). Statistical estimation of nonstationary Gaussian processes with long-range dependence and intermittency. Stoch. Process. Appl. 99, 295--321. Gao, J., Anh, V., Heyde, C. and Tieng, Q. (2001). Parameter estimation of stochastic processes with long-range dependence and intermittency. J. Time Ser. Anal. 22, 517--535. Heath, D. and Platen, E. (2002). A variance reduction technique based on integral representations. Quant. Finance 2, 362--369. Heyde, C. (1999). A risky asset model with strong dependence through fractal activity time. J. Appl. Prob. 36, 234--1239. Heyde, C. and Gay, R. (1993). Smoothed periodogram asymptotics and estimation for processes and fields with possible long-range dependence. Stoch. Process. Appl. 45, 169--182. Hurst, S. R., Platen, E. and Rachev, S. R. (1997). Subordinated Markov index models: a comparison. Financial Eng. Japanese Markets 4, 97--124. Kleptsyna, M., Kloeden, P. and Anh, V. (1998). Existence and uniqueness theorems for fBm stochastic differential equations. Problems Inf. Transmission 34, 51--61. Kloeden, P. and Platen, E. (1999). Numerical Solution of Stochastic Differential Equations (Appl. Math. 23). Springer, New York. Mandelbrot, B. and Taylor, H. (1967). On the distribution of stock price differences. Operat. Res. 15, 1057--1062. Mandelbrot, B. and van Ness, J. (1968). Fractional Brownian motion, fractional noises and applications. SIAM Rev. 10, 422--437. Mandelbrot, B., Fisher, A. and Calvet, L. (1997). A multifractal model of asset returns. Cowles Foundation Discussion Paper 1164. Merton, R. C. (1969). Lifetime portfolio selection under uncertainty: the continuous time case. Rev. Econom. Statist. 51, 247--257. Merton, R. C. (1973). The theory of rational option pricing. Bell J. Econom. 4, 141--183. Merton, R. C. (1990). Continuous-Time Finance. Blackwell, Oxford. Platen, E. (1999). An introduction to numerical methods for stochastic differential equations. Acta Numerica 8, 197--246. Podlubny, I. (1999). Fractional Differential Equations. Academic Press, San Diego, CA. Prudnikov, A., Brychkov, Y. and Marichev, O. (1990). Integrals and Series, Vol. 3. Gordon and Breach, New York. Robinson, P. (1994). Time series with strong dependence. In Advances In Econometrics, Sixth World Congress (Econom. Soc. Monogr. 23), Vol. 1, ed. C. A. Sims, Cambridge University Press, pp. 47--96. Robinson, P. (1995). Gaussian semiparametric estimation of long-range dependence. Ann. Statist. 23, 1630--1661. Robinson, P. (1999). The memory of stochastic volatility models. J. Econometrics 101, 195--218. Rockafeller, R. T. (1970). Convex Analysis. Princeton University Press. Shiryaev, A. N. (1999). Essentials of Stochastic Finance. World Scientific, Singapore. Sims, C. A. (1984). Martingale-like behavior of asset prices and interest rates. Discussion Paper 205, Department of Economics, University of Minnesota. Sundaresan, S. (2001). Continuous-time methods in finance: a review and an assessment. J. Finance 55, 1569--1622. Vasicek, O. (1977). An equilibrium characterization of the term structure. J. Financial Econom. 5, 177--188. |
URI: | https://mpra.ub.uni-muenchen.de/id/eprint/11973 |