Hiroshi Shiraishi

Preliminary test estimation for regression models with long-memory disturbance

For a class of time series regression models with long-memory disturbance, we are interested in estimation of a subset of the regression coefficient vector and spectral parameter of the residual process when the complementary subset is suspected to be close to 0. In this situation, we evaluate the mean square errors of the restricted and unrestricted MLE and a preliminary test estimator when the complementary parameters are contiguous to zero vector. The results are expressed in terms of the regression spectra and the residual spectra. Since we assume long-memory dependence for the disturbance, the asymptotics are much different from the case of i.i.d. disturbance. Numerical studies elucidate some interesting features of regression and long-memory structures.

Statistical estimation of optimal portfolios for locally stationary returns of assets

This paper discusses the asymptotic property of estimators for optimal portfolios when the returns are vector-valued locally stationary processes. First, we derive the asymptotic distribution of a nonparametric portfolio estimator based on the kernel method. Optimal bandwidth and kernel function are given by minimizing the mean squares error of it. Next, assuming parametric models for non-Gaussian locally stationary processes, we prove the LAN theorem, and propose a parametric portfolio estimator ĝ based on a quasi-maximum likelihood estimator. Then it is shown that ĝ is asymptotically efficient based on the LAN. Numerical studies are provided to investigate the accuracy of the portfolio estimators parametrically and nonparametrically. They illuminate some interesting features of them.

A Simulation Approach to Statistical Estimation of Multiperiod Optimal Portfolios

This paper discusses a simulation-based method for solving discrete-time multiperiod portfolio choice problems under AR(1) process. The method is applicable even if the distributions of return processes are unknown. We first generate simulation sample paths of the random returns by using AR bootstrap. Then, for each sample path and each investment time, we obtain an optimal portfolio estimator, which optimizes a constant relative risk aversion (CRRA) utility function. When an investor considers an optimal investment strategy with portfolio rebalancing, it is convenient to introduce a value function. The most important difference between single-period portfolio choice problems and multiperiod ones is that the value function is time dependent. Our method takes care of the time dependency by using bootstrapped sample paths. Numerical studies are provided to examine the validity of our method. The result shows the necessity to take care of the time dependency of the value function.

Cluster analysis for stable processes

It is known that various financial time series, e.g., daily log returns on a share price, foreign exchange rates, excess bond returns, etc., exhibit heavy-tailed behavior. Recently, discriminant analysis has been applied to financial time series, such as, the problem of credit rating for companies. In this article, we investigate the problem of classifying an α-stable linear process into one of two categories with indices α1 and α2, respectively. We propose some discriminant criteria. It is shown that our discriminant statistics are consistent. The misclassification probabilities are also evaluated under contiguous hypotheses. Some numerical studies for an (AR(1)) process are given.

Improved estimation for the autocovariances of a Gaussian stationary process

For a Gaussian stationary process with mean μ and autocovariance function γ(·), we consider to improve the usual sample autocovariances with respect to the mean squares error (MSE) loss. For the cases μ=0 and μ≠0, we propose sort of empirical Bayes type estimators Γˆ and Γ˜, respectively. Then their MSE improvements upon the usual sample autocovariances are evaluated in terms of the spectral density of the process. Concrete examples for them are provided. We observe that if the process is near to a unit root process the improvement becomes quite large. Thus, consideration for estimators of this type seems important in many fields, e.g., econometrics.

Optimal Portfolios with End-of-Period Target

We study the estimation of optimal portfolios for a Reserve Fund with an end-of-period target and when the returns of the assets that constitute the Reserve Fund portfolio follow two specifications. In the first one, assets are split into short memory (bonds) and long memory (equity), and the optimality of the portfolio is based on maximizing the Sharpe ratio. In the second, returns follow a conditional heteroskedasticity autoregressive nonlinear model, and we study when the distribution of the innovation vector is heavy-tailed stable. For this specification, we consider appropriate estimation methods, which include bootstrap and empirical likelihood.

Statistical Estimation of Portfolios for Dependent Financial Returns

1 Department of Applied Mathematics, Waseda University, Tokyo 169-8555, Japan 2 Department of Statistics/Graduate Institute of Statistics & Actuarial Science, Feng Chia University Taichung 407, Taiwan 3 Department of Mathematics, Faculty of Science, Niigata University, Niigata 950-2181, Japan 4 The Jikei University School of Medicine, Tokyo 105-8461, Japan 5 ECARES-Solvay Brussels School of Economics and Management, Universite Libre de Bruxelles, 1050 Brussels, Belgium