International Science Index


10007933

Forecasting the Volatility of Geophysical Time Series with Stochastic Volatility Models

Abstract:This work is devoted to the study of modeling geophysical time series. A stochastic technique with time-varying parameters is used to forecast the volatility of data arising in geophysics. In this study, the volatility is defined as a logarithmic first-order autoregressive process. We observe that the inclusion of log-volatility into the time-varying parameter estimation significantly improves forecasting which is facilitated via maximum likelihood estimation. This allows us to conclude that the estimation algorithm for the corresponding one-step-ahead suggested volatility (with ±2 standard prediction errors) is very feasible since it possesses good convergence properties.
References:
[1] S. J. Fong and Z. Nannan (2011), Towards an Adaptive Forecasting of Earthquake Time Series from Decomposable and Salient Characteristics, The Third International Conferences on Pervasive Patterns and Applications - ISBN: 978-1-61208-158-8, 53-60.
[2] R. F. Engle (1982), Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation, Econometrica, 50(4), 987-1007.
[3] T. Bollerslev (1986), Generalized Autoregressive Conditional Heteroskedasticity, J. Econometrics, 31, 307-327.
[4] M. C. Mariani and O. K. Tweneboah (2016), Stochastic differential equations applied to the study of geophysical and financial time series, Physica A, 443, 170-178.
[5] Y. Hamiel, R. Amit, Z. B. Begin, S. Marco, O. Katz, A. Salamon, E. Zilberman, and N. Porat (2009), The seismicity along the Dead Sea fault during the last 60,000 years. Bulletin of Seismological Society of America, 99(3), 2020-2026.
[6] P. Brockman and M. Chowdhury (1997), Deterministic versus stochastic volatility: implications for option pricing models, Applied Financial Economics, 7, 499-505.
[7] F. J. Rubio and A. M. Johansen (2013), A simple approach to maximum intractable likelihood estimation, Electronic Journal of Statistics, 7, 1632-1654.
[8] A. Janssen and H. Drees (2016), A stochastic volatility model with flexible extremal dependence structure, Bernoulli, 22(3), 1448-1490.
[9] S. J. Taylor (1982), Financial returns modeled by the product of two stochastic processes, A study of daily sugar prices, 1961-79. Time Series Analysis: Theory and Practice, ZDB-ID 7214716, 1, 203-226.
[10] J. F. Commandeur and S. J. Koopman (2007), An Introduction to State Space Time Series Analysis, Oxford University press, 107-121.
[11] S. R. Eliason (1993), Maximum Likelihood Estimation-Logic and Practice, Quantitative applications in the social sciences, 96, 1-10.
[12] N. K. Gupta and R. K. Mehra (1974), Computational aspects of maximum likelihood estimation and reduction in sensitivity function calculations, IEEE Transactions on Automatic Control, 19(6), 774-783.
[13] R. H. Jones (1980), Maximum likelihood fitting of ARMA models to time series with missing observations, Technometrics, 22(3), 389-395.
[14] T. Cipra and R. Romera (1991), Robust Kalman Filter and Its Application in Time Series Analysis, Kybernetika, 27(6), 481-494.
[15] M. P. Beccar-Varela, H. Gonzalez-Huizar, M. C. Mariani, and O. K. Tweneboah (2016), Use of wavelets techniques to discriminate between explosions and natural earthquakes, Physica A: Statistical Mechanics and its Applications, 457, 42-51.
[16] S. E. Said and D. A. Dickey (1984), Testing for Unit Roots in Autoregressive Moving-Average Models with Unknown Order, Biometrika, 71, 599-607.