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Parameter Estimation for multi-mixed Fractional Ornstein--Uhlenbeck Processes by Generalized Method of Moments

Hamidreza Maleki Almani, Tommi Sottinen

Abstract

We develop the generalized method of moments (GMM) estimation for the parameters of the finitely mixed multi-mixed fractional Ornstein--Uhlenbeck (mmfOU) processes, and analyze the consistency and asymptotic normality of this estimator. We also include some simulations and provide numerical observations considering different statistical errors.

Parameter Estimation for multi-mixed Fractional Ornstein--Uhlenbeck Processes by Generalized Method of Moments

Abstract

We develop the generalized method of moments (GMM) estimation for the parameters of the finitely mixed multi-mixed fractional Ornstein--Uhlenbeck (mmfOU) processes, and analyze the consistency and asymptotic normality of this estimator. We also include some simulations and provide numerical observations considering different statistical errors.
Paper Structure (5 sections, 5 theorems, 48 equations, 1 figure, 1 table)

This paper contains 5 sections, 5 theorems, 48 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction and Preliminaries
  2. Generalized Methdod of Moments Estimation
  3. Consistency
  4. Asymptotic Normality
  5. Simulation

Key Result

Lemma 1

In the closed rectangle where $\Psi(\cdot)$ is the so called digamma function for $\rho_\theta(t) = \sigma^2\rho_{\lambda,H}(t)$, the matrix is a P-matrix for sufficiently small $\alpha$.

Figures (1)

  • Figure 1: Estimations of $\theta =(\lambda ;\mathbf{H} ;\bm{\sigma})$ for $m=500$ replications.

Theorems & Definitions (11)

  • Definition 1
  • Lemma 1
  • proof
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Remark 1
  • Lemma 2
  • Theorem 3
  • ...and 1 more