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}...
References and Further Reading
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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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Authors and Affiliations
Professor,
Waseda University, Tokyo, Japan
Masanobu Taniguchi
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Editors and Affiliations
Department of Statistics and Informatics, Faculty of Economics, University of Kragujevac, City of Kragujevac, Serbia
Miodrag Lovric
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