േ⊛✢ᒻࡕ࠺࡞ߦၮߠߊࡈࠔ࠶࠻࡮࠹࡯࡞ಽᏓߩ⏕₸᷹ᐲᄌ឵The Probability Measure Transformation of a Fat-Tailed Distribution Using Dynamic Linear Model

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The Probability Measure Transformation of a Fat-Tailed Distribution Using Dynamic Linear Model

_* _** Eiji Minemura Tadashi Imaizumi

The measure-transformation method to convert a long- or heavy-tailed distribution into the easier-to-handle standard normal distribution is much needed not only in financial engineering but also in the wider fields of economics, business administration, and systems engineering. In this paper, the author proposes a new method of probability measure transformation, while utilizing dynamic linear models.

Keywords: hierarchical modeling approaches, dynamic linear model, probability measure transformation

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[1] Bollerslev, T. (1986). "Generalised Autoregressive Conditional Heteroskedasticity," Journal of Econometrics, 31, 307-327. ª [2] Borland, L., Bouchaud, J, P., Muzy, J, F., & Zumbach, G. (2005). The Dynamics of Financial Markets - Mandelbrot s

Multifractal Cascades, and Beyond, Wilmott magazine, Issue 16:86-96. ª

[3] Carlin, B.P. & Louis, T.A. (2000). Bayes and Empirical Bayes Methods for Data Analysis, 2

^nd

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Hall/CRC. ª

[4] Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of United Kingdom inflation, Econometrica, 50 987-1008. ª

[5] Gelman, A., Carlin, J. B., Stern, H. S. & Rubin, D. B. (2004). Bayesian Data Analysis, 2

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Hall/CRC. ª

[6] Mandelbrot, B. B (1963a). The Variation of Certain Speculative Prices, Journal of Business, 36 394-419. ª [7] Mandelbrot, B. B (1963b). New Methods in Statistical Economics, Journal of Political Economy, 71 421-440. ª

[8] Mandelbrot, B. B (1972). Possible Refinement of the Lognormal Hypothesis Concerning the Distribution of Energy Dissipation in Intermittent Turbulence, Statistical Models & Turbulence, New York, Springer, 333-351. ª

[9] Mandelbrot, B. B, Calvet, L, & Fisher, A. (1997a). A Multifractal Model of Asset Returns, Discussion Papers of the Cowles Foundation for Economics at Yale University: Paper #1164 ª

[10] Mandelbrot, B. B, Calvet, L, & Fisher, A. (1997b) .A Multifractality of the Deutschmark/US Dollar Exchange Rate, Discussion Papers of the Cowles Foundation for Economics at Yale University: Paper #1165 ª

[11] Mandelbrot, B. B (2001a) .Scaling in Financial Prices: . Cartoon Brownian Motions in Multifractal Time , Quantitative Finance, 1 427-440. ª

[12] Mandelbrot, B. B (2001b). Scaling in Financial Prices: . Multifractal Concentration , Quantitative Finance, 1 641-649. ª

[13] Mandelbrot, B. B & Hudson, R. L . (2004). THE (MIS) BEHAVIOR OF MARKETS: A Fractal View of Risk, Ruin, and

(26)

Reward, Cambridge, MA : Perseus Books.

[14] Minemura, E. (2006). An Interest-Rate Model Analysis Based on Data Augmentation Bayesian Forecasting, Journal of Applied Statistics, 33 1085-1104.

[15] Øksendal, B. (1998). Stochastic Differential Equations; An Introduction with Applications,5

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[16] West, M. & Harrison, J. (1997). Bayesian Forecasting and Dynamic Models, 2

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