zbMATH — the first resource for mathematics

Fuzzy coefficient volatility (FCV) models with applications. (English) Zbl 1165.91415
Summary: Recently, C. Carlson and R. Fullér [Fuzzy Sets Syst. 122, 315–326 (2001; Zbl 1016.94047)] have introduced possibilistic mean, variance and covariance of fuzzy numbers and R. Fullér and P. Majlender [Fuzzy Sets Syst. 136, 363–374 (2003; Zbl 1022.94032)] have introduced the notion of crisp weighted possibilistic moments of fuzzy numbers. In this paper, we propose a class of FCV (Fuzzy Coefficient Volatility) models and study the moment properties. The method used here is very similar to the method used by S.S. Appadoo, M. Ghahramani and A. Thavaneswaran [Math. Sci. 30, No. 1, 50–63 (2005; Zbl 1083.62081)]. The proposed models incorporate fuzziness, subjectivity, arbitrariness and uncertainty observed in most financial time series. The usual forecasting method does not incorporate parameter variability. Fuzzy numbers are used to model the parameters to incorporate parameter variability.

91B28 Finance etc. (MSC2000)
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P05 Applications of statistics to actuarial sciences and financial mathematics
03E72 Theory of fuzzy sets, etc.
Full Text: DOI
[1] Carlsson, C.; Fuller, R., On possibilistic Mean value and variance of fuzzy numbers, Fuzzy sets and systems, 122, 315-326, (2001) · Zbl 1016.94047
[2] Fuller, R.; Majlender, P., On weighted possibilistic Mean and variance of fuzzy numbers, Fuzzy sets and systems, 136, 363-374, (2003) · Zbl 1022.94032
[3] Appadoo, S.S.; Ghahramani, M.; Thavaneswaran, A., Moment properties of some time series models, Math. sci., 30, 1, 50-63, (2005) · Zbl 1083.62081
[4] Carlsson, C.; Fuller, R., Fuzzy reasoning in decision making and optimization, (2002), Physica-Verlag · Zbl 1016.68111
[5] Zadeh, L.A., Fuzzy sets, inform. control, 8, 338-353, (1965) · Zbl 0139.24606
[6] Dubois, D.; Prade, H., Fuzzy sets and systems: theory and applications, (1980), Academic Press New York · Zbl 0444.94049
[7] Carlsson, C.; Fuller, R., A fuzzy approach to real option valuation, Fuzzy sets and systems, 139, 297-312, (2003) · Zbl 1055.91019
[8] Goetschel, R.; Voxman, W., Elementary fuzzy calculus, Fuzzy sets and systems, 18, 31-43, (1986) · Zbl 0626.26014
[9] Nicholls, D.F.; Quinn, B.G., ()
[10] Thavaneswaran, A.; Appadoo, S.S.; Samanta, M., Random coefficient GARCH models, Math. comput. modelling, 41, 6-7, 723-733, (2005) · Zbl 1079.62088
[11] C.W.J. Granger, Overview of non-linear time series specification in economics, Berkeley NSF-Symposia, 1998
[12] Abraham, B.; Thavaneswaran, A., A nonlinear time series model and estimation of missing observations, Ann. inst. stat. math., 43, 493-504, (1991) · Zbl 0760.62084
[13] Tsay, R.S., Analysis of financial time series, (2002), John Wiley & Sons · Zbl 1037.91080
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.