Quantile-Based Spectral Analysis in an Object-Oriented Framework and a Reference Implementation in R: The quantspec Package

Abstract

Quantile-based approaches to the spectral analysis of time series have recently attracted a lot of attention. Several methods for estimation have been proposed in the literature and their statistical properties were analyzed. Yet, so far, neither a systematic method for computation nor a comprehensive software implementation are available to date. This paper contains two main contributions. First, an extensible framework for quantile-based spectral analysis of time series is developed and documented using object-oriented models. A comprehensive, open source reference implementation of this framework is provided in the R package quantspec, which is available from the Comprehensive R Archive Network. The second contribution of the present paper is to provide a detailed tutorial, with worked examples, for this R package. A reader who is already familiar with quantile-based spectral analysis and whose primary interest is not the design of the quantspec package, but how to use it, can read the tutorial and worked examples (Sections 3 and 4) independently.

Keywords

• time series
• spectral analysis
• periodogram
• quantile regression
• copulas
• ranks
• R
• quantspec
• framework
• object-oriented design