An Algorithm to Simulate VMA Processes Having a Spectrum with Fixed Condition Number

Abstract

This article proposes an algorithm to generate vector moving average (VMA) processes with a variable spectrum having a fixed condition number across frequencies. This method is based on the theory of multivariate linear spectrum for VMA processes, and is developed in a two-step procedure. Specific examples are provided, and the precision of generated time series is discussed. Such an algorithm is a useful tool to assess the performance of selected multivariate spectral estimators, and it turns out to be particularly appropriated in the Kolmogorov asymptotic estimation framework.

Keywords:

• Data simulation
• Multivariate spectrum
• Multivariate time series
• Well-conditioning

Mathematics Subject Classification:

• 15A12
• 37M05
• 37M10
• 58C40