# Multivariate Fractional Components Analysis

## TL;DR

This paper introduces a new framework for analyzing multivariate fractional time series with diverse cointegration properties, applicable to high-dimensional data, and demonstrates its effectiveness in modeling realized covariance matrices.

## Contribution

It develops a novel fractional components analysis method that handles nonstationary processes with varying fractional orders and cointegration strengths in high dimensions.

## Key findings

- Orthogonal short- and long-memory components fit realized covariance data well.
- The proposed method shows competitive out-of-sample performance.
- Applicable to high-dimensional time series with diverse fractional properties.

## Abstract

We propose a setup for fractionally cointegrated time series which is formulated in terms of latent integrated and short-memory components. It accommodates nonstationary processes with different fractional orders and cointegration of different strengths and is applicable in high-dimensional settings. In an application to realized covariance matrices, we find that orthogonal short- and long-memory components provide a reasonable fit and competitive out-of-sample performance compared to several competing methods.