Evidence of spurious regression driven by heavy-tailed observations with structural changes

ABSTRACT

This article extends the theoretical analysis of spurious relationship and considers the situation where the deterministic components of the processes generating individual series are independent heavy-tailed with structural changes. It shows when those sequences are used in ordinary least-square regression, the convenient t-statistic procedures wrongly indicate that (i) the spurious significance is established when regressing mean-stationary and trend-stationary series with structural changes, (ii) the spurious relationship occurs under broken mean-stationary and difference-stationary sequences, and (iii) the extent of spurious regression becomes stronger between difference-stationary and trend-stationary series in the presence of breaks. The spurious phenomenon is present regardless of the sample size and structural breaks taking place at the same points or not. Simulation experiments confirm our asymptotic results and reveal that the spurious effects are not only sensitive to the relative location of structural changes with the sample, but seriously depend on the stable indexes.

KEYWORDS:

• Heavy-tailed observations
• Spurious regression
• Structural changes
• t-statistic

Mathematics Subject Classification:

• 62J05
• 62E20

Funding

Financial support from NNSF (Nos. 71103143, 71273206, 71473194), SNSF (Nos. 2011JQ1016, 2013KJXX-40), and SESF (Nos. 12JZ018, 12JK0858) are gratefully acknowledged.