An Autoregressive Model for Time Series of Random Objects: Model and Stationary Solution

Table of Links

Abstract and 1. Introduction

2. Preliminaries

3. The GAR(1) Model

3.1. Model and Stationary Solution

3.2. Identifability

4. Estimation of model parameters and 4.1. Fréchet mean

4.2. Concentration parameter

5. Testing for the absence of serial dependence

6. Numerical experiments

6.1. R with multiplicative noise

6.2. Univariate distributions with a density

6.3. SPD Matrices

7. Application

8. Acknowledgement

Appendix A. General results in Hadamard spaces

Appendix B. Proofs

Reference

3. The GAR(1) Model

3.1. Model and Stationary Solution

Unfortunately, this condition does not hold in every Hadamard space. Thus, we will assume the following.

Furthermore, if the condition holds for a Hadamard space (Ω, d), then it also holds for a Hadamard space constructed by taking the image of a bijection ω as described in the second part of Example 2.3.