Statistical Estimation for Portfolios
This is a special joint DEM-DF Seminar in honor of Prof. Masanobu Taniguchi, Waseda University, Japan. Prof. Taniguchi is currently visiting the University of Luxembourg on an Institute of Advanced Studies (IAS) Distinguished Grant.
Abstract:
The field of financial engineering has developed as a huge integration of economics, probability theory, statistics etc. for these decades. The composition of portfolio is one of the most fundamental and important methods of financial engineering to control the risk of investments. This talk provides a comprehensive development of statistical inference for portfolios and its applications. Historically, Morkowitz contributed to the advancement of modern portfolio theory laying the foundation for the diversification of investment portfolio. His approach is called the mean-variance portfolio, which maximizes the mean of portfolio return with reducing its variance ( risk of portfolio ). Actually, the mean-variance portfolio coefficients are expressed as a function of the mean and variance matrix of the return process. Optimal portfolio coefficients based on the mean and variance matrix have been derived by various criteria. Assuming that the return process is i.i.d. Gaussian, Jobson and Korkie(1980) proposed a portfolio coefficient estimator of optimal portfolio by making the sample version of the mean-variance portfolio. However, emplical studies show that observed stretches of financial return are often non-Gaussian dependent. In this situation, it is shown that portfolio estimators of the mean-variance type are not asymptotically efficient generally even if the process is Gaussian, which gives a strong warning for use of the usual portfolio estimators. We also provide a necessary and sufficient condition for the estimators to be asymptotically efficient in terms of the spectral density matrix of the return. This motivates the fundamental important issue of the talk. Hence we will provide modern statistical techniques for the problems of portfolio estimation, grasping them as optimal statistical inference for various return processes. We will introduce a variety of stochastic processes, e.g., non-Gaussian stationary processes, non-linear processes, non-stationary processes etc.. For them we will develop a modern statistical inference by use of local asymototic normality(LAN), which is due to LeCam. The approach is a unified and very general one. Based on this we address a lot of important problems for portfolio.
Cowork with Shiraishi H.
About Masanobu Taniguchi:
Masanobu Taniguchi received his Ph.D. degree in mathematical science from Osaka University in 1981. He held positions in mathematics at Hiroshima and Osaka universities, then joined Tokyo and Waseda University where he created the research group that put this university on the map of time series analysis and mathematical statistics worldwide. While focused on the statistical analysis of time series and more general stochastic processes, Masanobu Taniguchi’s research is spanning an exceptionally broad spectrum of statistical methods and subjects—spectral analysis, asymptotics and the notoriously difficult area of higher-order asymptotics, curved stochastic models, time-series discriminant analysis, causal inference, long-memory processes, empirical likelihood methods, Bartlett adjustments and Box-Cox transformations, shrinkage and James-Stein estimators, portfolio optimization, circular data and data on manifolds, time-series analysis of variance, infinite variance and stable processes, quantile regression, information geometry, … all in connection with time series and inference for stochastic processes. He is the author or coauthor of several books, among which the influential “Asymptotic Theory of Statistical Inference for Time Series” (Springer 2000).
He received the Ogawa Prize in 1989, the Econometric Theory Award in 2000, the Japan Statistical Society Prize in 2004, the Analysis Award of the Mathematical Society of Japan in 2013, and in 2022 the Commendation for Science and Technology Prize by the Japanese Minister of Education, Culture, Sports, Science and Technology. He is a Fellow of the Institute of Mathematical Statistics and acted as the Editor-in-Chief for the Journal of the Japan Statistical Society from 2006 to 2009. An indefatigable traveller, he has been the worldwide ambassador-at-large of Japanese research excellence, building long-lasting relationships with a number of European teams among which Belgium, Italy, Germany, and Norway.
Language: English
This is a free seminar. Registration is mandatory.
Cold lunches are provided to registered participants.
TIMEDATA project team acknowledges financial support of the Institute for Advanced Studies of the University of Luxembourg through a “Distinguished” grant (TIMEDATA – 2023).
