Models of asset returns: changes of pattern from high to low event frequency

References

• Akgiray , V and Booth , G . 1987 . Compound distribution models of stock returns: an empirical comparison . J. Financial Res. , 10 : 269 – 80 .
   Web of Science ®Google Scholar
• Ariel , R A . 1987 . A monthly effect in stock returns . J. Financial Economics , 18 : 161 – 74 .
   Web of Science ®Google Scholar
• Bachelier , L . 1900 . Theorie de la Speculation , Paris : Gauthier-Villars .
   Google Scholar
• Bingham , N H and Kiesel , R . 2002 . Semi-parametric modelling in finance: theoretical foundations . Quant. Finance , 2 : 241 – 50 .
   Google Scholar
• Blattberg , R and Gonedes , N . 1974 . A comparison of stable and student distributions as statistical models for stock prices . J. Business , 47 : 244 – 80 .
   Web of Science ®Google Scholar
• Bollerslev , T . 1986 . Generalized autoregressive conditional heteroscedasticity . J. Econometrics , 31 : 307 – 27 .
   Web of Science ®Google Scholar
• Bollerslev , T . 1987 . A conditional heteroscedastic model for speculative prices and rates of return . Rev. Economics Statistics , 69 : 542 – 7 .
   Web of Science ®Google Scholar
• Bouchaud , J-P and Potters , M . 1997 . Théorie des Risques Financiers Commissariat al'Eńergie Atomique
   Google Scholar
• Box , G E P and Tiao , G C . 1973 . Bayesian Inference in Statistical Analysis , Reading , MA : Addison-Wesley .
   Google Scholar
• Cont , R . 2001 . Empirical properties of asset returns: stylized facts and statistical issues . Quant. Finance , 1 : 223 – 36 .
   Web of Science ®Google Scholar
• Cont , R , Potters , M and Bouchaud , J-P . Scaling in stock market data: stable laws and beyond . Proc. CNRS Workshop on Scale Invariance, Les Houses . 1997 . Scale Invariance and Beyond , Edited by: Dubrulle , B , Graner , F and Sornette , D . Berlin : Springer .
   Google Scholar
• Engle , R F . 1982 . Autoregressive conditional heteroscedasticity with estimates of the variance of UK . Econometrica , 50 : 987 – 1007 .
   Web of Science ®Google Scholar
• Erbelein , E . 2001 . “ Applications of generalized hyperpolic Lévy motions to finance ” . In Lévy Processes: Theory and Applications , Edited by: Barndorff-Nielsen , O E , Mikosch , T and Resnick , S I . Boston , MA : Birkhäuser .
   Google Scholar
• Fama , E . 1965 . The behaviour of stock market prices . J. Business , 38 : 34 – 105 .
   Web of Science ®Google Scholar
• Fama , E . 1970 . Multiperiod consumption-investment decisions . Am. Econ. Rev. , 60 : 163 – 74 .
   Web of Science ®Google Scholar
• Fama , E F and Roll , R . 1968 . Some properties of symmetric stable distributions . J. Am. Stat. Assoc , 63 : 817 – 36 .
   Web of Science ®Google Scholar
• Fama , E F and Roll , R . 1971 . Parameter estimates for symmetric stable distributions . J. Am. Stat. Assoc. , 66 : 331 – 8 .
   Web of Science ®Google Scholar
• Gillemot , L , Töyli , J and Kaski , K . 2000 . Time-independent models of asset returns revisited . Physica A , 282 : 304 – 24 .
   Web of Science ®Google Scholar
• Gnedenko , B V and Kolmogorov , A N . 1954 . Limit Distributions for Sums of Independent Random Variables , Reading , MA : Addison-Wesley . chapter 7
   Google Scholar
• Hagerman , R L . 1978 . More evidence on the distribution of security returns . J. Finance , 33 : 1213 – 21 .
   Web of Science ®Google Scholar
• Hsieh , D A . 1991 . Chaos and nonlinear dynamics: application to financial markets . J. Finance , 46 : 1839 – 77 .
   Web of Science ®Google Scholar
• Hsu , D A . 1982 . A Bayesian robust detection of shift in the risk structure of stock market returns . J. Am. Stat. Assoc. , 77 : 29 – 39 .
   Web of Science ®Google Scholar
• Jacquier , E , Polson , N G and Rossi , P E . 1994 . Bayesian analysis of stochastic volatility models . J. Business Econ. Statistics , 12 : 371 – 89 .
   Web of Science ®Google Scholar
• Janicki , A and Weron , A . 1994 . Can one see α-stable variables and processes? . Stat. Sci. , 9 : 109 – 26 .
   Web of Science ®Google Scholar
• Kon , S J . 1984 . Models of stock returns—a comparison . J. Finance , 39 : 147 – 65 .
   Web of Science ®Google Scholar
• Koponen , I . 1995 . Analytic approach to the problem of convergence of truncated Lévy flights towards the Gaussian stochastic process . Phys. Rev. E , 52 : 1197 – 9 .
   PubMed Web of Science ®Google Scholar
• Kullman , L , Töyli , J , Kertesz , J , Kanto , A and Kaski , K . 1999 . Characteristic times in stock market indices . Physica A , 269 : 98 – 110 .
   Web of Science ®Google Scholar
• Kullman , L , Töyli , J , Kertesz , J , Kanto , A and Kaski , K . 2000 . Break-down of scaling and convergence to Gaussian . Int. J. Theor. Appl. Finance , 3 : 371 – 3 .
   Google Scholar
• Lévy , P . 1925 . Calcul des Probabilities, Part II , Paris : Gauthier-Villars . chapter 6
   Google Scholar
• Mandelbrot , B . 1963 . The variation of certain speculative prices . J. Business , 36 : 394 – 419 .
   Web of Science ®Google Scholar
• Mandelbrot , B . 1972 . Correction of an error in ‘The variation of certain speculative prices’ . J. Business , 45 : 542 – 3 .
   Google Scholar
• Mandelbrot , B . 1999 . A multifractal walk down wall street . Sci. Am. , 280 : 50 – 3 .
   Web of Science ®Google Scholar
• Mantegna , R N and Stanley , E H . 1994 . Stochastic process with ultraslow convergence to a Gaussian: the truncated Lévy flight . Phys. Rev. Lett. , 73 : 2946 – 9 .
   PubMed Web of Science ®Google Scholar
• Mantegna , R N and Stanley , E H . 1995 . Scaling behaviour in the dynamics of an economic index . Nature , 376 : 46 – 9 .
   Web of Science ®Google Scholar
• Mantegna , R N and Stanley , E H . 2000 . An Introduction to Econophysics Correlations and Complexity in Finance , Cambridge : Cambridge University Press .
   Google Scholar
• Merton , R C . 1976 . Option pricing when underlying stock returns are discontinuous . J. Financial Economics , 3 : 125 – 44 .
   Web of Science ®Google Scholar
• Osborne , M F M . 1959 . Brownian motion in the stock market . Operations Res. , 7 : 145 – 73 .
   Web of Science ®Google Scholar
• Schwarz , G . 1978 . Estimating the dimension of a model . Ann. Statistics , 6 : 461 – 4 .
   Web of Science ®Google Scholar
• Silverman , B W . 1986 . Density Estimation for Statistics and Data Analysis , London : Chapman and Hall .
   Google Scholar
• Taylor , S J . 1986 . Modelling Financial Series , Chichester : Wiley .
   Google Scholar
• Taylor , S J . 1994 . Modeling stochastic volatility: a review and comparative study . Math. Finance , 4 : 183 – 204 .
   Google Scholar
• Tucker , A L . 1992 . A reexamination of finite- and infinite-variance distributions of daily stock returns . J. Business Econ. Statistics , 10 : 73 – 81 .
   Web of Science ®Google Scholar
• Töyli , J , Kaski , K and Kanto , A . 2002a . Variability of Hex return distribution . Finnish J. Business Economics , 51 : 64 – 89 .
   Google Scholar
• Töyli , J , Kaski , K and Kanto , A . 2002b . On the shape of asset return distribution . Commun. Statistics—Simul. Comput. , 31 : 489 – 521 .
   Web of Science ®Google Scholar