Asymmetric business cycle co-movements

Abstract

We investigate the presence of common cyclical features at different data points separated by a threshold variable. Our two-step procedure consists of first estimating the unknown threshold in a VAR or a VECM (Tsay, 1998). Next, cofeature test-statistics are carried out on the parts.

Notes

¹ Examples are Vahid and Engle (1997), Cubadda and Hecq (2001) and Hecq et al. (2006).

² For instance, in Hecq et al. (2006) conditions (ii) or (iv) define weak form common features.

³ The DGP (B) illustrates the difference between the model developed in this article and the framework proposed in Anderson and Vahid (1998). For instance (1 : 0) is a common nonlinear feature vector in (B) because the first row of the autoregressive matrix is the same in both regimes.

⁴ We make these response surfaces as simple as possible to save space and to emphasize the main message. For instance nonlinear models with a different set of explanatory variables for every IC improve the estimations but they are more complicated to read. For simplicity of the presentation we do not impose the frequencies to be bounded by 100%. For instance with the HQ, the asymptotic frequency with which m = 1 is found is 100.10% for p = 6. These outcomes are of marginal occurence and are due to the sampling variability.

⁵ In a VAR with p = 1, if such an outlier is detected at observation t in Y _{2, t −1} we also need to drop the line t − 1. In general, in the VAR(p), p + 1 rows will be deleted by outliers using this method. This is why it should be used with parsimony.