Nonsense regressions due to neglected time-varying means. (English) Zbl 1017.62077

Hassler, Uwe

Stat. Pap. 44, No. 2, 169-182 (2003).

Summary: Regressions of two independent time series are considered. The variables are covariance stationary but display time-varying although not trending means. Two prominent examples are level shifts due to structural breaks and seasonally varying means. If the variation of the means is not taken into account, this induced nonsense correlations. The asymptotic treatment is supplemented by experimental evidence.

MSC:

62M10

Time series, auto-correlation, regression, etc. in statistics (GARCH)

Keywords:

level shifts; deterministic seasonality; spurious correlations

References:

[1]	Abeysinghe, T., Inappropriate use of seasonal dummies in regressions, Economics Letters, 36, 175-179 (1991)
[2]	Abeysinghe, T., Deterministic seasonal models and spurious regressions, Journal of Econometrics, 61, 259-272 (1994)
[3]	Banerjee, A., J.J. Dolado, J.W. Galbraith, and D.F. Hendry (1993): Cointegration, error-correction, and the econometric analysis of non-stationary data; Oxford University Press. · Zbl 0937.62650
[4]	Cappuccio, N.; Lubian, D., Spurious regressions between I(1) one processes with long memory errors, Journal of Time Series Analysis, 18, 341-354 (1997) · Zbl 0904.62099
[5]	Choi, I., Spurious regressions and residual-based tests for cointegration when regressors are cointegrated, Journal of Econometrics, 60, 313-320 (1994) · Zbl 0789.62094
[6]	Engle, R. F.; Kozicki, S., Testing for common features, Journal of Business & Economic Statistics, 11, 369-380 (1993)
[7]	Granger, C. W.J.; Newbold, P., Spurious regressions in econometrics, Journal of Econometrics, 2, 111-120 (1974) · Zbl 0319.62072
[8]	Haldrup, N., The asymptotics of single-equation cointegration regressions with I(1) and I(2) variables, Journal of Econometrics, 63, 153-181 (1994) · Zbl 0814.62075
[9]	Hassler, U., Spurious regressions when stationary regressors are included, Economics Letters, 50, 25-31 (1996) · Zbl 0875.62594
[10]	Hassler, U., Nonsense correlation between time series with linear trends, Allgemeines Statistisches Archiv, 80, 227-235 (1996)
[11]	Hendry, D. F., Econometrics — Alchemy or Science?, Economica, 47, 387-406. (1980)
[12]	Maddala, G.S., and I.-M. Kim (1998): Unit roots, cointegration, and structural breaks; Cambridge University Press.
[13]	Marmol, F., Nonsense regressions between integrated processes of different orders, Oxford Bulletin of Economics and Statistics, 58, 525-536 (1996)
[14]	Marmol, F., Spurious regression theory with nonstationary fractionally integrated processes, Journal of Econometrics, 84, 233-250 (1998) · Zbl 1041.62529
[15]	Montanes, A.; Reyes, M., Effect of shift in the trend function on Dickey-Fuller unit root tests, Econometric Theory, 14, 355-363 (1998)
[16]	Montanes, A.; Reyes, M., The Asymptotic behaviour of the Dickey-Fuller test under the crash hypothesis, Statistics and Probability Letters, 42, 81-89 (1999) · Zbl 1087.62511
[17]	Perron, P., The great crash, the oil price shock, and the unit root hypothesis, Econometrica, 57, 1361-1401 (1989) · Zbl 0683.62066
[18]	Perron, P., Testing for a unit root in a time series with a changing mean, Journal of Business & Economic Statistics, 8, 153-162 (1990)
[19]	Phillips, P. C.B., Understanding spurious regressions in econometrics, Journal of Econometrics, 33, 311-340 (1986) · Zbl 0602.62098
[20]	Tsay, W.-J.; Chung, C.-F., The spurious regression of fractionally integrated processes, Journal of Econometrics, 96, 155-182 (2000) · Zbl 1054.62586
[21]	Wooldridge, J. M., A note on computing r-squared and adjusted r-squared for trending and seasonal data, Economics Letters, 36, 49-54 (1991) · Zbl 0729.90631
[22]	Yule, G. U., Why do we sometimes get nonsense correlation between time series? A study in sampling and the nature of time series, Journal of the Royal Statistical Society, 89, 1-64 (1926) · JFM 52.0532.04