Abstract

AbstractThis paper introduces the notion of common non‐causal features and proposes tools to detect them in multivariate time series models. We argue that the existence of co‐movements might not be detected using the conventional stationary vector autoregressive (VAR) model as the common dynamics are present in the non‐causal (i.e. forward‐looking) component of the series. We show that the presence of a reduced rank structure allows to identify purely causal and non‐causal VAR processes of order P>1 even in the Gaussian likelihood framework. Hence, usual test statistics and canonical correlation analysis can be applied, where either lags or leads are used as instruments to determine whether the common features are present in either the backward‐ or forward‐looking dynamics of the series. The proposed definitions of co‐movements are also valid for the mixed causal—non‐causal VAR, with the exception that a non‐Gaussian maximum likelihood estimator is necessary. This means however that one loses the benefits of the simple tools proposed. An empirical analysis on Brent and West Texas Intermediate oil prices illustrates the findings. No short run co‐movements are found in a conventional causal VAR, but they are detected when considering a purely non‐causal VAR.

Highlights

  • MotivationThis paper studies the existence of common cyclical features in economic and financial variables by considering both causal and noncausal vector autoregressive (VAR) models

  • This paper provides a novel explanation for the inability of detecting common features in a vector autoregressive (VAR) framework

  • We show that common features that cannot be detected in the causal representation might be revealed in the noncausal dynamics of the series

Read more

Summary

Motivation

This paper studies the existence of common cyclical features in economic and financial variables by considering both causal and noncausal vector autoregressive (VAR) models. Using either lags or leads within a canonical correlation analysis or a Generalized Method of Moments (GMM) approach, the reduced rank restrictions help to identify the correct model This result stems from the fact that, except for VARs with either one lag or one lead only, the existence of SCCF implies that the autocorrelation matrices of series Yt have a common left null space for either any lag or any lead different from zero. This important observation does not extend to mixed causal-noncausal models.

Causal and noncausal models
Univariate models
Multivariate models with common features
Co-movements in purely causal or noncausal models
Co-movements in mixed models
Test statistics
LR tests
GMM tests
Monte Carlo results
Testing for common cyclical features
Price indicators
Commodity prices co-movements
Conclusion
Full Text
Published version (Free)

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call