The Fourier estimation method with positive semi-definite estimators

2014/10/01 by Jir o Akahori, Jirô Akahori, Nien-Lin Liu +6
Economics, Econometrics and Finance · Mathematics · #FOS: Economics and business #FOS: Mathematics #Financial Risk and Volatility Modeling #Mathematical Dynamics and Fractals #Statistical Finance (q-fin.ST) #Statistics Theory (math.ST) #Stochastic processes and financial applications #math.ST #q-fin.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1410.0112

arxiv created 2014/10/01 · openalex publication_date 2014/10/01 · arxiv updated 2014/10/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we present a slight modification of the Fourier estimation method of the spot volatility (matrix) process of a continuous Itô semimartingale where the estimators are always non-negative definite. Since the estimators are factorized, computational cost will be saved a lot.

Related

• Symmetric positive semi-definite Fourier estimator of instantaneous variance-covariance matrix
• Inference for Volatility Functionals of Multivariate It ^o\n Semimartingales Observed with Jump and Noise
• Estimation of volatility functionals: the case of a square root n window
• Approximation of eigenvalues of spot cross volatility matrix with a view toward principal component analysis
• Estimation of Integrated Volatility Functionals with Kernel Spot Volatility Estimators