Unbalanced Regressions and Spurious Inference

Author(s)
Daniel Ventosa-Santaularia

ABSTRACT

Spurious regression has been extensively studied in time series econometrics since Granger and Newbold’s seminal paper. Recently, it has been advanced that this phenomenon is due to a mistreatment of short-range autocorrelation in the residuals of the regression when at least one of the variables in a bivariate regression is stationary. HAC errors, feasible GLS and Cochrane-Orcutt-type procedures are then proposed to draw correct inference. Such a proposal should be cautiously considered, since nonsense inference might also be due to deterministic trend mechanisms, structural breaks, and long range dependence. In these cases, standard autocorrelation correction procedures would not solve the problem of spurious regression. We aim to make the later argument clear.

Spurious regression has been extensively studied in time series econometrics since Granger and Newbold’s seminal paper. Recently, it has been advanced that this phenomenon is due to a mistreatment of short-range autocorrelation in the residuals of the regression when at least one of the variables in a bivariate regression is stationary. HAC errors, feasible GLS and Cochrane-Orcutt-type procedures are then proposed to draw correct inference. Such a proposal should be cautiously considered, since nonsense inference might also be due to deterministic trend mechanisms, structural breaks, and long range dependence. In these cases, standard autocorrelation correction procedures would not solve the problem of spurious regression. We aim to make the later argument clear.

Cite this paper

D. Ventosa-Santaularia, "Unbalanced Regressions and Spurious Inference,"*Open Journal of Statistics*, Vol. 2 No. 3, 2012, pp. 297-299. doi: 10.4236/ojs.2012.23035.

D. Ventosa-Santaularia, "Unbalanced Regressions and Spurious Inference,"

References

[1] C. W. J. Granger and P. Newbold, “Spurious Regressions in Econometrics,” Journal of Econometrics, Vol. 2 No. 2, 1974, pp. 111-120. doi:10.1016/0304-4076(74)90034-7

[2] P. C. B. Phillips, “Understanding Spurious Regressions in Econometrics,” Journal of Econometrics, Vol. 33, No. 3, 1986, pp. 311-340. doi:10.1016/0304-4076(86)90001-1

[3] D. Ventosa-Santaulària, “Spurious Regression,” Journal of Probability and Statistics, Vol. 2009, No. 1, 2009, pp. 155-182. doi:10.1155/2009/802975

[4] A. E. Noriega and D. Ventosa-Santaulària, “Spurious Regression and Trending Variables,” Oxford Bulletin of Economics and Statistics, Vol. 69, No. 3, 2007, pp. 439- 444. doi:10.1111/j.1468-0084.2007.00481.x

[5] C. Stewart, “A Note on Spurious Significance in Regressions Involving I(0) and I(1) Variables,” Empirical Economics, Vol. 41, No. 3, 2011, pp. 565-571. doi:10.1007/s00181-010-0404-5

[6] C. W. J. Granger IV, N. Hyung and Y. Jeon, “Spurious Regressions with Stationary Series,” Applied Economics, Vol. 33, No. 7, 2001, pp. 899-904.

[7] T. Mikosch and C. G. Vries, “Tail Probabilities for Regression Estimators,” Tinbergen Institute Discussion Papers, TI 2006-085/2, 2006.

[8] P. Perron, “The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis,” Econometrica, Vol. 57, No. 6, 1989, pp. 1631-1401. doi:10.2307/1913712

[9] W. J. Tsay and C. F. Chung, “The Spurious Regression of Fractionally Integrated Processes,” Journal of Econometrics, Vol. 96, No. 1, 2000, pp. 155-182. doi:10.1016/S0304-4076(99)00056-1

[10] B. T. McCallum, “Is the Spurious Regression Problem Spurious?” Economics Letters, Vol. 107, No. 3, 2010, pp. 321-323. doi:10.1016/j.econlet.2010.02.004

[11] Y. Sun, “A Convergent T-Statistic in Spurious Regressions,” Econometric Theory, Vol. 20, No. 5, 2004, pp. 943-962. doi:10.1017/S0266466604205072

[12] G. I. Kolev, “The ‘Spurious Regression Problem’ in the Classical Regression Model Framework,” Economics Bulletin, Vol. 31, No. 1, 2011, pp. 925-937.

[13] B. Martínez-Rivera and D. Ventosa-Santaulària, “A Comment on ‘Is the Spurious Regression Problem Spurious?’” Economics Letters, Vol. 115, No. 2, 2012, pp. 229-231.

[14] D. Davidson and J. G. MacKinnon, “Econometric Theory and Methods,” Oxford University Press, New York, 2004.

[1] C. W. J. Granger and P. Newbold, “Spurious Regressions in Econometrics,” Journal of Econometrics, Vol. 2 No. 2, 1974, pp. 111-120. doi:10.1016/0304-4076(74)90034-7

[2] P. C. B. Phillips, “Understanding Spurious Regressions in Econometrics,” Journal of Econometrics, Vol. 33, No. 3, 1986, pp. 311-340. doi:10.1016/0304-4076(86)90001-1

[3] D. Ventosa-Santaulària, “Spurious Regression,” Journal of Probability and Statistics, Vol. 2009, No. 1, 2009, pp. 155-182. doi:10.1155/2009/802975

[4] A. E. Noriega and D. Ventosa-Santaulària, “Spurious Regression and Trending Variables,” Oxford Bulletin of Economics and Statistics, Vol. 69, No. 3, 2007, pp. 439- 444. doi:10.1111/j.1468-0084.2007.00481.x

[5] C. Stewart, “A Note on Spurious Significance in Regressions Involving I(0) and I(1) Variables,” Empirical Economics, Vol. 41, No. 3, 2011, pp. 565-571. doi:10.1007/s00181-010-0404-5

[6] C. W. J. Granger IV, N. Hyung and Y. Jeon, “Spurious Regressions with Stationary Series,” Applied Economics, Vol. 33, No. 7, 2001, pp. 899-904.

[7] T. Mikosch and C. G. Vries, “Tail Probabilities for Regression Estimators,” Tinbergen Institute Discussion Papers, TI 2006-085/2, 2006.

[8] P. Perron, “The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis,” Econometrica, Vol. 57, No. 6, 1989, pp. 1631-1401. doi:10.2307/1913712

[9] W. J. Tsay and C. F. Chung, “The Spurious Regression of Fractionally Integrated Processes,” Journal of Econometrics, Vol. 96, No. 1, 2000, pp. 155-182. doi:10.1016/S0304-4076(99)00056-1

[10] B. T. McCallum, “Is the Spurious Regression Problem Spurious?” Economics Letters, Vol. 107, No. 3, 2010, pp. 321-323. doi:10.1016/j.econlet.2010.02.004

[11] Y. Sun, “A Convergent T-Statistic in Spurious Regressions,” Econometric Theory, Vol. 20, No. 5, 2004, pp. 943-962. doi:10.1017/S0266466604205072

[12] G. I. Kolev, “The ‘Spurious Regression Problem’ in the Classical Regression Model Framework,” Economics Bulletin, Vol. 31, No. 1, 2011, pp. 925-937.

[13] B. Martínez-Rivera and D. Ventosa-Santaulària, “A Comment on ‘Is the Spurious Regression Problem Spurious?’” Economics Letters, Vol. 115, No. 2, 2012, pp. 229-231.

[14] D. Davidson and J. G. MacKinnon, “Econometric Theory and Methods,” Oxford University Press, New York, 2004.