STATISTICAL ESTIMATION OF OPTIMAL PORTFOLIOS FOR LOCALLY STATIONARY RETURNS OF ASSETS

2007 ◽  
Vol 10 (01) ◽  
pp. 129-154 ◽  
Author(s):  
HIROSHI SHIRAISHI ◽  
MASANOBU TANIGUCHI
Keyword(s):  
Kernel Method ◽  
Parametric Models ◽  
Stationary Processes ◽  
Optimal Portfolios ◽  
Numerical Studies ◽  
Locally Stationary Processes ◽  
Quasi Maximum Likelihood ◽  
Non Gaussian ◽  
Asymptotically Efficient ◽  
Vector Valued

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.

scholarly journals Estimation for Non-Gaussian Locally Stationary Processes with Empirical Likelihood Method

2012 ◽  
Vol 2012 ◽  
pp. 1-22 ◽  
Author(s):  
Hiroaki Ogata
Keyword(s):  
Empirical Likelihood ◽  
Numerical Study ◽  
Asymptotic Distributions ◽  
Likelihood Method ◽  
Stationary Processes ◽  
Finite Sample ◽  
Empirical Likelihood Method ◽  
Locally Stationary Processes ◽  
Non Gaussian ◽  
Maximum Empirical Likelihood Estimator

An application of the empirical likelihood method to non-Gaussian locally stationary processes is presented. Based on the central limit theorem for locally stationary processes, we give the asymptotic distributions of the maximum empirical likelihood estimator and the empirical likelihood ratio statistics, respectively. It is shown that the empirical likelihood method enables us to make inferences on various important indices in a time series analysis. Furthermore, we give a numerical study and investigate a finite sample property.

Estimation and Forecasting of Locally Stationary Processes

2011 ◽  
Vol 32 (1) ◽  
pp. 86-96 ◽  
Author(s):  
Wilfredo Palma ◽  
Ricardo Olea ◽  
Guillermo Ferreira
Keyword(s):  
Stationary Processes ◽  
Locally Stationary Processes

scholarly journals Reproducing Kernel Method for Solving Nonlinear Fractional Fredholm Integrodifferential Equation

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Bothayna S. H. Kashkari ◽  
Muhammed I. Syam
Keyword(s):  
Exact Solution ◽  
Approximate Solution ◽  
Integrodifferential Equation ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Integrodifferential Equations ◽  
Reproducing Kernel Method ◽  
Numerical Studies ◽  
Uniformly Convergence ◽  
Present Algorithm

This article is devoted to both theoretical and numerical studies of nonlinear fractional Fredholm integrodifferential equations. In this paper, we implement the reproducing kernel method (RKM) to approximate the solution of nonlinear fractional Fredholm integrodifferential equations. Numerical results demonstrate the accuracy of the present algorithm. In addition, we prove the existence of the solution of the nonlinear fractional Fredholm integrodifferential equation. Uniformly convergence of the approximate solution produced by the RKM to the exact solution is proven.

Sign in / Sign up

Export Citation Format

Share Document