Abstract
In this paper we use a statistical procedure which is appropriate to test for deterministic and stochastic (stationary and nonstationary) cycles in macroeconomic time series. These tests have standard null and local limit distributions and are easy to apply to raw time series. Monte Carlo evidence shows that they perform relatively well in the case of functional misspecification in the cyclical structure of the series. As an example, we use this approach to test for the presence of cycles in US real GDP.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ahtola J, Tiao GC (1987) Distributions of least squares estimators of autoregressive parameters for a process with complex roots on the unit circle. J Time Ser Anal 8:1–14
Andel J (1986) Long memory time series models. Kybernetika 22:105–123
Arteche J, Robinson PM (2000a) Seasonal and cyclical long memory, In: Ghosh S. (eds) Asymptotics, nonparametrics and time series. Marcel Dekker Inc., New York, pp 115–148
Arteche J, Robinson PM (2000b) Semiparametric inference in seasonal and cyclical long memory processes. J Time Ser Anal 21:1–25
Bierens HJ (2001) Complex unit roots and business cycles, Are they real? Economet Theory 17:962–983
Chan Y, Wei CZ (1988) Limiting distributions of least squares estimates of unstable autoregressive process. Ann Stat 16:367–401
Dalla V, Hidalgo J (2005) A parametric bootstrap test for cycles. J Economet 129:219–261
Dickey DA, Fuller WA (1979) Distribution of the estimators for autoregressive time series with a unit root. J Am Statist Assoc 74:427–431
Gil-Alana LA (2001) Testing of nonstationary cycles in macroeconomic time series. J Time Ser Anal 22:411–430
Gil-Alana LA (2004) Testing of unit root cycles in the Swedish economy. Empirica 31:333–344
Gil-Alana LA, Robinson PM (1997) Testing of unit roots and other nonstationary hypotheses in macroeconomic time series. J Economet 80:241–268
Gray HL, Yhang N, Woodward WA (1989) On generalized fractional processes. J Time Ser Anal 10:233–257
Gray HL, Yhang N, Woodward WA (1994) On generalized fractional processes. A correction. J Time Ser Anal 15:561–562
Gregoir S (1999a) Multivariate time series with various hidden unit roots. Part I. Integral operator algebra and representation theory. Economet Theory 15:435–468
Gregoir S (1999b) Multivariate time series with various hidden unit roots. Part II. Estimation and testing. Economet Theory 15:469–518
Harvey A (1985) Trends and cycles in macroeconomic time series. J Business Econ Statistics 3:216–227
Kwiatkowski D, Phillips PCB, Schmidt P, Shin Y (1992) Testing the null hypothesis of stationarity against the alternative of a unit root. J Economet 54:159–178
Lobato I, Robinson PM (1998) A non-parametric test for I(0). Rev Econ Stat 65:475–495
Magnus W, Oberhettinger F, Soni RP (1966) Formulas and theorema for the special functions of mathematical physics. Springer, Berlin
Press WH, Flannery BP, Teukolsky SA, Vetterling WT (1986) Numerical recipes: the art of scientific computing. Cambridge University Press, Cambridge
Rainville ED (1960) Special functions. MacMillan, New York
Robinson PM (1994) Efficient tests of nonstationary hypotheses. J Am Statistical Assoc 89:1420–1437
Acknowledgements
The second named author gratefully acknowledges financial support from the Ministerio de Ciencia y Tecnologia (SEJ2005-07657/ECON, Spain). Comments of an anonymous referee are also gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Caporale, G.M., Gil-Alana, L.A. Testing for deterministic and stochastic cycles in macroeconomic time series. Empirica 34, 155–169 (2007). https://doi.org/10.1007/s10663-007-9033-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10663-007-9033-4