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Optimal Statistical Inference in Financial Engineering

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The field of financial engineering has developed as a huge integration of economics, mathematics, probability theory, statistics, time series analysis, operation research etc. We describe financial assets as stochastic processes. Using stochastic differential equations, probabilists developed a highly sophisticated mathematical theory in this field. On the other hand empirical people in financial econometrics studied various numerical aspects of financial data by means of statistical methods.

Black (1973) provided the modern option pricing theory assuming that the price process of an underlying asset follows a geometric Brownian motion (see Brownian Motion and Diffusions). But, a lot of empirical studies for the price processes of assets show that they do not follow the geometric Brownian motion. Concretely, we often observe that the sample autocorrelation function

$$\hat{{\rho }}_{{X}_{t}}(l) ={ {\sum \nolimits }_{t=1}^{n-\vert l\vert }({X}_{t+l} -{\overline{X}}_{n})({X}_{t}...

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References and Further Reading

  • Black F, Scholes M (1973) The pricing of options and corporate liabilities. J Polit Econ 81:637–654

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  • Dahlhaus R (1997) Fitting time series models to nonstationary processes. Ann Stat 25:1–37

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  • LeCam L (1986) Asymptotic methods in statistical decision theory. Springer, New York

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  • Shiraishi H, Taniguchi M (2007) Statistical estimation of optimal portfolios for locally stationary returns of assets. Int J Theor Appl Finance 10:129–154

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  • Shiraishi H, Taniguchi M (2008) Statistical estimation of optimal portfolios for non-Gaussian dependent returns of assets. J Forecast 27:193–215

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  • Taniguchi M, Kakizawa Y (2000) Asymptotic theory of statistical inference for time series. Springer, New York

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  • Taniguchi M, Hirukawa J, Tamaki K (2008) Optimal statistical inference in financial engineering. Chapman and Hall/CRC, New York

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© 2011 Springer-Verlag Berlin Heidelberg

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Taniguchi, M. (2011). Optimal Statistical Inference in Financial Engineering. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_432

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