The modified R a robust measure of association for time series


Since times of Yule (1926), it is known that correlation between two time series can produce spurious results. Granger and Newbold (1974) see the roots of spurious correlation in non-stationarity of the time series. However the study of Granger, Hyung and Jeon (2001) prove that spurious correlation also exists in stationary time series. These facts make the correlation coefficient an unreliable measure of association. This paper proposes ‘Modified R’ as an alternate measure of association for the time series. The Modified R is robust to the type of stationarity and type of deterministic part in the time series. The performance Modified R is illustrated via extensive Monte Carlo Experiments.


DOI Code: 10.1285/i20705948v7n1p1

Keywords: Correlation Coefficient; Spurious Regression; Stationary Series


Aldrich, J. (2001). Correlation Spurious and Genuine in Pearson and Yule. Statistical Science , 10 (4), 364-376.

Elderton, W. P. (1907). Frequency Curves and Correlation. London: Institute of Actuaries.

Enders, W. (1995). Applied econometric times series. New York: Willey.

Granger, C. W., & Newbold, P. (1974). Spurious Regression in Econometrics. Journal of Econometrics , 2 (2), 111-120.

Granger, C. W., Hyung, N., & Jeon, Y. (2001). Spurious regressions with stationary series. Applied Economics , 33 (7), 899-904.

Greene, W. H. (2005). Econometric Analysis. New York: Prentice Hall.

Gujarati, D. (1999). Essentials of Econometrics. Irwin: McGraw Hill .

Nelson, C., & Plossor, C. (1982). Trends and Random Walks in Macroeconomic Time Series: Some Evidence and Implications. Journal of Monetary Economics , 10 (2), 139-162.

Pearson, K. (1894). Contributions to the Mathematical Theory of Evolution. Philosophical Transactions of the Royal Society of London , 185, 71-110.

Pearson, K., Lee, A., & Bramley-Moore, L. (1899). Mathematical Contributions to the Theory of Evolution. VI. Genetic (Reproductive) Selection: Inheritance of Fertility in Man, and of Fecundity in Thoroughbred Racehorses,. Philosophical Transactions of the Royal Society of London. Series A , 192, 252-330.

Phillips, P. C. (1987). Time series regression with a unit root. Econometrica , 55 (2), 277-301.

Simon, H. A. (1954). Spurious Correlation: A Causal Interpretation,. Journal of the American Statistical Association, Vol. 49, No. 267 (1954), pp. 467-479 , 49 (267), 467-479.

Yule, G. U. (1910). On the Distribution of Deaths with Age when the Causes of Death Act Cumulatively, and Similar Frequency Distributions,. Journal of the Royal Statistical Society , 73 (1), 26-38.

Yule, G. U. (1897). On the Theory of Correlation. Journal of the Royal Statistical Society .

Yule, G. U. (1926). Why do we sometimes get nonsense-correlations between Time-Series?--a study in sampling and the nature of time-series. Journal of the Royal Statistical Society, , 89 (1), 1-64.

Full Text: pdf

Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.