Spurious Multivariate Regressions Under Fractionally Integrated Processes

Daniel Ventosa-Santaulària, J. Eduardo Vera-Valdés, Katarzyna Lasak, Ricardo Ramírez-Vargas

Research output: Contribution to journalJournal articleResearchpeer-review

60 Downloads (Pure)

Abstract

This article studies spurious regression in the multivariate case for any finite number of fractionally integrated variables, stationary or not. We prove that the asymptotic behavior of the estimated coefficients and their t-statistics depend on the degrees of persistence of the regressors and the regressand. Nonsense inference could therefore be drawn when the sum of the degrees of persistence of the regressor and regressand is greater or equal than 1/2. Moreover, the asymptotic behavior from the most persistent regressor spreads to correlated regressors. Thus, the risk of uncovering spurious results increases as more regressors are included. Inference drawn from other test statistics such as the joint F test, the R-squared, and the Durbin-Watson is also misleading. Finite sample evidence supports our findings.

Original languageEnglish
JournalCommunications in Statistics: Theory and Methods
ISSN0361-0926
DOIs
Publication statusE-pub ahead of print - 7 May 2020

Keywords

  • Fractional integration
  • long memory
  • multivariate regression
  • spurious regression

Fingerprint Dive into the research topics of 'Spurious Multivariate Regressions Under Fractionally Integrated Processes'. Together they form a unique fingerprint.

Cite this