An Autoregressive Model for Time Series of Random Objects: SPD Matrices

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

6.3. SPD Matrices

Here, Figure 5 shows similar results as in the other two experimental settings. The convergence rate proved in Theorem 4.2 is confirmed in panel (a). We observe that in this setting, the stability of the error curves seems to indicate an early attainment of the asymptotic regime. Similarly, we observe in panels (c) and (d) that the test exposes the right level and high power, already at small sample sizes for all tested values of φ.