Testing for Non-Linear Dependence in Univariate Time Series An Empirical Investigation of the Austrian Unemployment Rate

Koller, Wolfgang and Fischer, Manfred M. (2001): Testing for Non-Linear Dependence in Univariate Time Series An Empirical Investigation of the Austrian Unemployment Rate. Published in: Networks and Spatial Economics , Vol. 2, No. 2 (2002): pp. 191-209.

Abstract

In recent years interest has been growing in testing for stochastic non-linearity in macroeconomic time series. There are several inference procedures available. But not much is known about their behaviour on real world small-sized settings. This paper surveys some of these tests. Their performance is compared using monthly Austrian unemployment data that cover the period January 1960 to December 1997. It is found that the test procedures surveyed are complementary rather than competing. Several useful guidelines are provided for applying the increasingly complex test procedures in practice.

• Item Type: MPRA Paper
• Language: English
• Keywords: n.a.
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes

References

Barnett, W. A., Gallant, A. R., Hinich, M. J., Jungeilges, J. A., Kaplan, D. T., and Jensen, M. J. (1997). A single-blind controlled competition among tests for nonlinearity and chaos. Journal of Econometrics, 82, 157–192.

Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31(3), 307–327.

Box, G. E. and Jenkins, G. M. (1970). Time Series Analysis: Forecasting and Control. San Francisco: Holden-Day.

Brock, W. A., Dechert, W. D., and Scheinkman, J. A. (1987). A Test for Independence Based on the Correlation Dimension. Work. pap., Department of Economics, University of Wisconsin at Madison, University of Houston, and University of Chicago.

Brock, W. A., Dechert, W. D., Scheinkman, J. A., and LeBaron, B. (1996). A test for independence based on the correlation dimension. Econometric Reviews, 15(3), 197–235.

Brock, W. A., Hsieh, D. A., and LeBaron, B. (1991). Nonlinear dynamics, chaos, and instability: Statistical theory and economic evidence. Cambridge, Mass. and London: MIT Press.

Brock, W. A. and Sayers, C. L. (1988). Is the business cycle characterized by deterministic chaos? Journal of Monetary Economics, 22(1), 71–90. Brockwell, P. J. and Davis, R. A. (1991). Time Series: Theory and Methods. New York: Springer.

Burgess, S. M. (1992). Asymmetric employment cycles in Britain: Evidence and an explanation. Economic Journal, 102, 279–290.

Craig, S. G., Kohlhase, J. E., and Papell, D. H. (1991). Chaos theory and microeconomics: An application to model specification and hedonic estimation. Review of Economics and Statistics, 73(2), 208–215.

Cromwell, J. B., Labys, W. C., and Terraza, M. (1994). Univariate Tests for Time Series Models. Thousand Oaks, CA: SAGE Publications.

Engle, R. F. (1982). Autoregressive conditional heteroskedasticity with estimates of the variance of U.K. inflation. Econometrica, 50(4), 987–1007.

Engle, R. F., Lilien, D. M., and Robins, R. P. (1987). Estimating time varying risk premia in the term structure: The ARCH-M model. Econometrica, 55(2), 391–407.

Granger, C. W. (1991). Developments in the nonlinear analysis of economic series. Scandinavian Journal of Economics, 93(2), 263–276.

Granger, C. W. and Andersen, A. (1978). An Introduction to Bilinear Time Series Models. Göttingen: Vandenhoeck & Ruprecht.

Grassberger, P. and Procaccia, I. (1983). Measuring the strangeness of strange attractors. Physica D, 9, 189–208.

Hsieh, D. A. (1989). Testing for nonlinear dependence in daily foreign exchange rates. Journal of Business, 62(3), 339–368.

Lee, T.-H., White, H., and Granger, C. W. (1993). Testing for neglected nonlinearity in time series models. Journal of Econometrics, 56, 269–290.

Lumsdaine, R. L. and Ng, S. (1999). Testing for ARCH in the presence of a possibly misspecified mean. Journal of Econometrics, 93(2), 257–279.

McLeod, A. and Li, W. (1983). Diagnostic checking of ARMA time series models using squared residuals autocorrelations. Journal of Time Series Analysis, 4, 269–273.

Ozaki, T. (1980). Non-linear time series models for non-linear random vibrations. Journal of Applied Probability, 17, 84–93.

Peel, D. A. and Speight, A. E. H. (1998). The non-linear time series properties of unemployment rates. Applied Economics, 30, 287–294.

Sentana, E. (1995). Quadratic ARCH models. Review of Economic Studies, 62(4), 639–661.

Skalin, J. and Teräsvirta, T. (1999). Modelling asymmetries and moving equilibria in unemployment rates. Work. Pap. Working Paper No. 262, Stockholm School of Economics.

Teräsvirta, T., Lin, C.-F., and Granger, C. (1993). Power of the neural network linearity test. Journal of Time Series Analysis, 14(2), 209–220.

Tong, H. and Lim, K. S. (1980). Threshold autoregression, limit cycles and cyclical data. Journal of the Royal Statistical Society, B42, 245–292.

Wallis, K. F. (1987). Time series analysis of bounded economic variables. Journal of Time Series Analysis, 8(1), 115–123.

White, H. (1989). An additional hidden unit test for neglected non-linearity in multilayer feedforward networks. In Proceedings of the International Joint Conference on Neural Networks, Washington, DC, vol. I, pp. 451–455, San Diego, CA. SOS Printing.