# Factorization of a spectral density with smooth eigenvalues of a multidimensional stationary time series

## TL;DR

This paper extends the classical spectral density factorization to multidimensional stationary time series, enabling explicit decomposition and improved prediction of such processes.

## Contribution

It introduces a multidimensional approach to factorize smooth spectral densities, facilitating the analysis and prediction of vector-valued stationary time series.

## Key findings

- Provides a method for explicit spectral density factorization in multiple dimensions
- Enables computation of Wold components for multidimensional series
- Improves linear prediction accuracy for multivariate time series

## Abstract

The aim of this paper to give a multidimensional version of the classical one-dimensional case of smooth spectral density. A smooth spectral density gives an explicit method to factorize the spectral density and compute the constituents of the Wold representation of a regular weakly stationary time series. These constituents are important to give the best linear predictions of the time series.