The past and future of empirical finance: some personal comments

Granger, Clive W. J.

doi:10.1016/j.jeconom.2004.09.002

Cited by 23 publications

(11 citation statements)

References 8 publications

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“…The upper and lower bounds in the figure correspond to the levels of ±2/ √ N and are based on the asymptotics of the sample autocorrelations under GBM. This empirical evidence matches the findings in Heyde and Liu (2001) and Cont (2001), and supports the "stylized facts" outlined in Granger (2005).…”

Section: Testing the Independence Assumption Of The Returns Processsupporting

confidence: 88%

The Student Subordinator Model with Dependence for Risky Asset Returns

Leonenko

Petherick

Sikorskii

2011

Communications in Statistics - Theory and Methods

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A new, tractable model of the stock price due to Heyde (1999) (see also Heyde and Leonenko, 2005) is elaborated here and used for asset price movement. The model is driven by a Brownian motion, which has a "fractal clock" rather than a calendar clock. We incorporate the Student's t-distribution, and a special dependence structure is introduced through the construction of this fractal time. The Student model described has desired features supported by real financial data.

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Section: Testing the Independence Assumption Of The Returns Processsupporting

confidence: 88%

The Student Subordinator Model with Dependence for Risky Asset Returns

Leonenko

Petherick

Sikorskii

2011

Communications in Statistics - Theory and Methods

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“…This model generalizes classical geometric Brownian motion (GBM) model according to which the log returns are independent Gaussian. The FATGBM model has some similarities with stochastic volatility model of Barndorff-Nielsen and Shephard [3] (for the discussion of pricing formulae, see [31]), and supports the desired "stylized features" of log returns (log price increments) discussed in [17,19,21]. We provide the empirical evidence that supports the violation of the assumption of independent Gaussian returns.…”

Section: Introductionsupporting

confidence: 69%

Fractal Activity Time Models for Risky Asset with Dependence and Generalized Hyperbolic Distributions

Leonenko

Petherick

Sikorskii

2012

Stochastic Analysis and Applications

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Risky asset models with the dependence through fractal activity time are described. The construction of the fractal activity time is implemented via superpositions of Ornstein-Uhlenbeck type processes driven by Lévy noise. The model features both tractable dependence structure and desired marginal distributions of the returns from the generalized hyperbolic class: the Variance Gamma and normal inverseGaussian. These distributions provide good fit to real financial data. Pricing formulae for the proposed models are derived.

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“…Uncorrelated returns, non-constant volatility through time and fat tailed return distributions are probably the most prominent, listed, for example, in Cont (2001) and Granger (2005). In addition, there are several asymmetry properties, for example, the skewness of the return distribution and the asymmetric impact of good and bad news to future volatility.…”

Section: Introductionmentioning

confidence: 99%