Spectral estimation for mixed causal-noncausal autoregressive models

TL;DR

This paper introduces a novel spectral estimation method for mixed causal-noncausal autoregressive models that leverages higher-order cumulants and bispectrum, enabling identification without assuming Gaussian errors.

Contribution

It develops a nonparametric estimation approach combining spectrum and bispectrum, and proposes a simple criterion for model identification in mixed causal-noncausal AR models.

Findings

Unbiased parameter estimates obtained in simulations.

Correct model identification as data deviate from normality.

Application to commodity prices reveals noncausal dynamics.

Abstract

This paper investigates new ways of estimating and identifying causal, noncausal, and mixed causal-noncausal autoregressive models driven by a non-Gaussian error sequence. We do not assume any parametric distribution function for the innovations. Instead, we use the information of higher-order cumulants, combining the spectrum and the bispectrum in a minimum distance estimation. We show how to circumvent the nonlinearity of the parameters and the multimodality in the noncausal and mixed models by selecting the appropriate initial values in the estimation. In addition, we propose a method of identification using a simple comparison criterion based on the global minimum of the estimation function. By means of a Monte Carlo study, we find unbiased estimated parameters and a correct identification as the data depart from normality. We propose an empirical application on eight monthly commodity prices, finding noncausal and mixed causal-noncausal dynamics.