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2016 | OriginalPaper | Buchkapitel

15. Trends, Integration Tests and Nonsense Regressions

verfasst von : Uwe Hassler

Erschienen in: Stochastic Processes and Calculus

Verlag: Springer International Publishing

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Abstract

Now we consider some applications of the propositions from the previous chapter. In particular, {e _t} and {x _t} are integrated of order 0 and integrated of order 1, respectively, cf. the definitions above Proposition 14.2. It turns out that the regression of a time series on a linear trend leads to asymptotically Gaussian estimators.

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Vorheriges Kapitel Asymptotics of Integrated Processes

Nächstes Kapitel Cointegration Analysis

Many more procedures have been developed over the last decades, notably the test by Elliott et al. (1996) with certain optimality properties.

Through numerous works by Peter Phillips the functional central limit theory has found its way into econometrics. This kind of limiting distributions was then celebrated as “non-standard asymptotics”; meanwhile it has of course become standard.

Equivalently, one might feed detrended data into the ADF regression above.

For the following calculation of s ² we divide by n without correcting for degrees of freedom, which does not matter asymptotically (\(n \rightarrow \infty )\).

“Uncentered”, as the regression is calculated without intercept.

Anderson, T. W., & Darling, D. A. (1952). Asymptotic theory of certain “Goodness of Fit” criteria based on stochastic processes. Annals of Mathematical Statistics, 23, 193–212.CrossRef

Andrews, D. W. K. (1991). Heteroskedasticity and autocorrelation consistent covariance matrix estimation. Econometrica, 59, 817–858.CrossRef

Chang, Y., & Park, J. (2002). On the asymptotics of ADF tests for unit roots. Econometric Reviews, 21, 431–447.CrossRef

Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74, 427–431.

Durlauf, S. N., & Phillips, P. C. B. (1988). Trends versus random walks in time series analysis. Econometrica, 56, 1333–1354.CrossRef

Elliott, G., Rothenberg, T. J., & Stock, J. H. (1996). Efficient tests for an autoregressive unit root. Econometrica, 64, 813–836.CrossRef

Engle, R. F., & Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55, 251–276.CrossRef

Granger, C. W. J. (1981). Some properties of time series data and their use in econometric model specification. Journal of Econometrics, 16, 121–130.CrossRef

Granger, C. W. J., & Newbold P. (1974). Spurious regressions in econometrics. Journal of Econometrics, 2, 111–120.CrossRef

Hamilton, J. (1994). Time series analysis. Princeton: Princeton University Press.

Hassler, U. (2000). Simple regressions with linear time trends. Journal of Time Series Analysis, 21, 27–32.CrossRef

Hendry, D. F. (1980). Econometrics – alchemy or science? Economica, 47, 387–406.CrossRef

Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., & Shin Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54, 159–178.CrossRef

Newey, W. K., & West, K. D. (1987). A Simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica, 55, 703–708.CrossRef

Park, J. Y., & Phillips, P. C. B. (1988). Statistical inference in regressions with integrated processes: Part I. Econometric Theory, 4, 468–497.CrossRef

Phillips, P. C. B. (1986). Understanding spurious regressions in econometrics. Journal of Econometrics, 33, 311–340.CrossRef

Phillips, P. C. B. (1987). Time series regression with a unit root. Econometrica, 55, 277–301.CrossRef

Phillips, P. C. B, & Perron, P. (1988). Testing for a unit root in time series regression. Biometrika, 75, 335–346.CrossRef

Said, S. E., & Dickey, D. A. (1984). Testing for unit roots in autoregressive-moving average models of unknown order. Biometrika, 71, 599–607.CrossRef

Titel: Trends, Integration Tests and Nonsense Regressions
verfasst von: Uwe Hassler
Verlag: Springer International Publishing
Buch: Stochastic Processes and Calculus
Print ISBN: 978-3-319-23427-4

Electronic ISBN: 978-3-319-23428-1

Copyright-Jahr: 2016
DOI: https://doi.org/10.1007/978-3-319-23428-1_15

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