×

zbMATH — the first resource for mathematics

Local scale models. State space alternative to integraded GARCH processes. (English) Zbl 0800.62807

MSC:
62P20 Applications of statistics to economics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Abramowitz, M.; Stegun, I. A.: Handbook of mathematical functions. (1970) · Zbl 0171.38503
[2] Anderson, B. D. O.; Moore, J. B.: Optimal filtering. (1979) · Zbl 0688.93058
[3] Baillie, R. T.; Bollerslev, T.: The message in daily exchange rates: A conditional variance tale. Journal of business and economic statistics 7, 297-305 (1989)
[4] Baillie, R. T.; Degennaro, R. P.: Stock returns and volatility. Journal of financial and quantitative analysis 25, 203-214 (1990)
[5] Bather, J. A.: Invariant conditional distributions. Annals of mathematical statistics 36, 829-846 (1965) · Zbl 0143.19602
[6] Bollerslev, T.: Generalised autoregressive conditional heteroskedasticity. Journal of econometrics 51, 307-327 (1986) · Zbl 0616.62119
[7] Bollerslev, T.: A conditionally heteroskedastic time series model for speculative prices and the rates of return. Review of economics and statistics 69, 542-547 (1987)
[8] Bollerslev, T.; Engle, R. F.: Common persistence in conditional variance. Econometrica 61, 167-186 (1993) · Zbl 0782.62102
[9] Box, G. E. P.; Tiao, G. C.: Bayesian inference in statistical analysis. (1973) · Zbl 0271.62044
[10] Chesney, M.; Scott, L. O.: Pricing European currency options: A comparison of the modified black–Scholes model and a random variance model. Journal of financial and quantitative analysis 24, 267-284 (1989)
[11] De Jong, P.: Smoothing and interpolation with the state space model. Journal of the American statistical association 84, 1085-1088 (1989) · Zbl 0702.62093
[12] Engle, R. F.: Autoregressive conditional heteroskedasticity with estimates of the variance of the united kingdom inflation. Econometrica 50, 987-1007 (1982) · Zbl 0491.62099
[13] Engle, R. F.; Bollerslev, T.: Modelling the persistence of conditional variances. Econometric reviews 5, 1-50 (1986) · Zbl 0619.62105
[14] Engle, R. F.; Bollerslev, T.: Modelling the persistence of conditional variances. Econometric reviews 5, 81-87 (1986) · Zbl 0619.62105
[15] Engle, R. F.; Lilien, D. M.; Robins, R. P.: Estimating time varying risk premia in the term structure: the ARCH-M model. Econometrica 55, 391-407 (1987)
[16] Harvey, A. C.: Forecasting, structural time series models and the Kalman filter. (1989)
[17] Harvey, A. C.; Fernandes, C.: Time series models for count or qualitative observations (with discussion). Journal of business and economic statistics 7, 407-422 (1989)
[18] Harvey, A. C.; Fernandes, C.: Time series models for insurance claims. Journal of the institute of actuaries 116, 513-528 (1989)
[19] Harvey, A. C.; Ruiz, E.; Shephard, N.: Multivariate stochastic variance models. Financial markets group discussion paper (1992)
[20] Hull, J.; White, A.: Hedging the risk from writing foreign currency options. Journal of international money and finance 6, 131-152 (1987)
[21] Kitagawa, G.: Non-Gaussian state-space modelling of nonstationary time series. Journal of the American statistical association 82, 1032-1041 (1987) · Zbl 0644.62088
[22] Lewis, P. A. W.; Mckenzie, E.; Hugus, D. K.: Gamma processes. Communications in statistics–stochastic models 5, 1-30 (1989) · Zbl 0665.62090
[23] Lipster, R. S.; Shiryayev, A. N.: Statistics of random processes II: Applications. (1978) · Zbl 0369.60001
[24] Melino, A.; Turnbull, S. M.: Pricing foreign options with stochastic volatility. Journal of econometrics 45, 239-265 (1990) · Zbl 1126.91374
[25] Muth, J. F.: Optimal properties of exponentially weighted forecasts. Journal of the American statistical association 55, 299-305 (1960) · Zbl 0100.14602
[26] Nelson, D. B.: Stationarity and persistence in the \(GARCH(1, 1)\) model. Econometric theory 6, 318-334 (1990)
[27] Nelson, D. B.: ARCH models as diffusion approximations. Journal of econometrics 45, 7-39 (1990) · Zbl 0719.60089
[28] Nelson, D. B.: Conditional heteroskedasticity in asset returns: A new approach. Econometrica 59, 347-370 (1991) · Zbl 0722.62069
[29] Nelson, D. B.: Filtering and forecasting with misspecified ARCH models I: Getting the right variance with the wrong model. Journal of econometrics 52, 61-90 (1992) · Zbl 0761.62169
[30] Scott, L. O.: Option pricing when the variance changes randomly: theory, estimation and an application. Journal of financial and quantitative analysis 22, 417-438 (1987)
[31] Shephard, N.: A local scale model: an unobserved component alternative to integrated GARCH processes. STICERD discussion paper EM/90/220 (1990)
[32] Smith, R. L.; Miller, J. E.: A non-Gaussian state space model and application to prediction of records. Journal of the royal statistical society 48, 79-88 (1986) · Zbl 0593.62099
[33] Taylor, S. J.: Modelling financial time series. (1986) · Zbl 1130.91345
[34] Taylor, S. J.: Modelling stochastic volatility. (1991)
[35] Taylor, S. J.; Kingsman, B. G.: An analysis of the variance and distribution of commodity price-changes. Australian journal of management 4, 135-149 (1989)
[36] Tong, H.: Non-linear time series. (1990) · Zbl 0716.62085
[37] West, M.; Harrison, P. J.: Bayesian forecasting and dynamic models. Springer series in statistics (1989) · Zbl 0697.62029
[38] Whittle, P.: Likelihood as path integrals (with discussion). Journal of the royal statistical society 53, 505-538 (1991) · Zbl 0800.62539
[39] Wiggins, J. B.: Option values under stochastic volatility: theory and empirical estimates. Journal of financial economics 19, 351-372 (1987)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.