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 (Formula presented.) test, the R-squared, and the Durbin-Watson is also misleading. Finite sample evidence supports our findings.
| Original language | English |
|---|---|
| Pages (from-to) | 2034-2056 |
| Number of pages | 23 |
| Journal | Communications in Statistics - Theory and Methods |
| Volume | 51 |
| Issue number | 7 |
| Early online date | 7 May 2020 |
| DOIs | |
| Publication status | Published - 2022 |
Bibliographical note
Funding Information:The authors would like to thank the anonymous referee, as well as Niels Haldrup, Ignacio Lobato, Michael Massmann, and the participants of the Long Memory Conference 2018 for their valuables comments. All remaining errors are ours.
Publisher Copyright:
© 2020 Taylor & Francis Group, LLC.
Funding
The authors would like to thank the anonymous referee, as well as Niels Haldrup, Ignacio Lobato, Michael Massmann, and the participants of the Long Memory Conference 2018 for their valuables comments. All remaining errors are ours.
Keywords
- Fractional integration
- long memory
- multivariate regression
- spurious regression
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