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Various Methods for Financial Engineering

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Statistical Inference for Financial Engineering

Part of the book series: SpringerBriefs in Statistics ((BRIEFSSTATIST))

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Abstract

Various statistical methods have been introduced to many application fields. Such methods are often designed for standard settings, i.e., i.i.d. cases, regular model etc. However, financial data are usually dependent and have complicated features (see Chap. 1). In this chapter, we state various methods which are suitable for financial data. In Sect. 3.2, the control variate method is applied to time series models. Control variate method is the one to reduce the variance of estimators. However, this method has been developed mainly in i.i.d. cases. Because financial data are usually dependent, we extend this method to dependent case. In Sect. 3.3, we apply an instrumental variable method to a stochastic regression model. In stochastic regression models, a natural estimator for the regression coefficients is the ordinary least squares estimator (OLS). However, if the explanatory variable and the stochastic disturbance are correlated, this estimator is inconsistent. To overcome this difficulty, the instrumental variable method is used. In the CAPM model, it will be shown that the explanatory variable and the disturbance are fractionally cointegrated. Hence, we use the instrumental variable method to estimate the regression coefficients.

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Waseda University, Tokyo, Japan

    Masanobu Taniguchi

  2. Faculty of Economics, Wakayama University, Wakayama, Japan

    Tomoyuki Amano

  3. School of Business Administration, Faculty of Urban Liberal Arts, Tokyo Metropolitan University, Tokyo, Japan

    Hiroaki Ogata

  4. School of International Liberal Studies, Waseda University, Tokyo, Japan

    Hiroyuki Taniai

Authors
  1. Masanobu Taniguchi
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  2. Tomoyuki Amano
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  3. Hiroaki Ogata
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  4. Hiroyuki Taniai
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Correspondence to Masanobu Taniguchi .

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Taniguchi, M., Amano, T., Ogata, H., Taniai, H. (2014). Various Methods for Financial Engineering. In: Statistical Inference for Financial Engineering. SpringerBriefs in Statistics. Springer, Cham. https://doi.org/10.1007/978-3-319-03497-3_3

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