Skip to main content
Log in

The Stochastic Permanent Break Model and the Fractional Integration Hypothesis

  • Published:
Computational Economics Aims and scope Submit manuscript

Abstract

In this article we show via simulations how the stochastic permanent break (STOPBREAK) model proposed by Engle and Smith (1999) is related with the fractionally integrated hypotheses. This connection was established by Diebold and Inoue (2001), showing, theoretically and analytically that stochastic regime switching is easily confused with long memory. In this paper, we use a version of the tests of Robinson (1994) for testing I(d) statistical models in the context of stochastic permanent break models, and give further evidence that both types of processes are easily confused.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Adenstedt, R.K. (1974). On large sample estimation for the mean of a stationary random sequence. Annals of Statistics, 2, 259–272.

    Google Scholar 

  • Beran, J. (1994). Statistics for Long Memory Processes. Clapman and Hall, New York.

    Google Scholar 

  • Chambers, M. (1998). Long memory and aggregation in macroeconomic time series. International Economic Review, 39, 1053–1072.

    Google Scholar 

  • Croczek-Georges, R. and Mandelbrot, B.B. (1995). A class of micropulses and anti-persistent fractional Brownian motion. Stochastic Processes and Their Applications, 60, 1–18.

    Google Scholar 

  • Diebold, F.X. and Inoue, A. (2001). Long memory and regime switching. Journal of Econometrics, 105, 131–159.

    Google Scholar 

  • Diebold, F.X. and Rudebusch, G.D. (1989). Long memory and persistence in the aggregate output. Journal of Monetary Economics, 24, 189–209.

    Google Scholar 

  • Ding, Z., Engle, R.F. and Granger, C.W.J. (1993). A long memory process of stock market returns and a new model. Journal of Empirical Finance, 1, 83–106.

    Google Scholar 

  • Engle, R.F. and Smith, A.D. (1999). Stochastic permanent breaks. Review of Economics and Statistics, 81, 553–574.

    Google Scholar 

  • Geweke, J. and Porter-Hudak, S. (1983). The estimation and application of long memory time series models. Journal of Time Series Analysis, 4, 221–238.

    Google Scholar 

  • Gil-Alana, L.A. (1999). Testing of fractional integration with monthly data. Economic Modelling, 16, 613–629.

    Google Scholar 

  • Gil-Alana, L.A. (2000). Mean reversion in the real exchange rates. Economics Letters, 16, 285–288.

    Google Scholar 

  • Gil-Alana, L.A. (2001). Testing of stochastic cycles in macroeconomic time series. Journal of Time Series Analysis, 22, 411–430.

    Google Scholar 

  • Gil-Alana, L.A. and Robinson, P.M. (1997). Testing of unit roots and other nonstationary hypotheses in macroeconomic time series. Journal of Econometrics, 80, 241–268.

    Google Scholar 

  • Gil-Alana, L.A. and Robinson, P.M. (2001). Testing of seasonal fractional integration in the U.K. and Japanese consumption and income. Journal of Applied Econometrics, 16, 95–114.

    Google Scholar 

  • Granger, C.W.J. (1980). Long memory relationships and the aggregation of dynamic models. Journal of Econometrics, 14, 227–238.

    Google Scholar 

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

    Google Scholar 

  • Granger, C.W.J. and Hyung, J. (1999). Occasional structural breaks and long memory. Discussion Paper 99-14, University of California, San Diego.

    Google Scholar 

  • Granger, C.W.J. and Joyeux, R. (1980). An introduction to long memory time series and fractionally differencing. Journal of Time Series Analysis, 1, 15–29.

    Google Scholar 

  • Hosking, J.R.M. (1981). Modelling persistence in hydrological time series using fractional differencing. Water Resources Research, 20, 1898–1908.

    Google Scholar 

  • Lippi, M. and Zaffaroni, P. (1999). Contemporaneous aggregation of linear dynamic models in large economies. Manuscript, Research Department, Bank of Italy.

  • Parke, W.R. (1999). What is fractional integration? The Review of Economics and Statistics, 81, 632–638.

    Google Scholar 

  • Press, W.H., Flannery, B.P., Teukolsky, S.A. and Vetterling, W.T. (1986). Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, Cambridge.

    Google Scholar 

  • Robinson, P.M. (1978). Statistical inference for a random coefficient autoregressive model. Scandinavian Journal of Statistics, 5, 163–168.

    Google Scholar 

  • Robinson, P.M. (1994). Efficient tests of nonstationary hypotheses. Journal of the American Statistical Association, 89, 1420–1437.

    Google Scholar 

  • Taqqu, M.S. (1975). Weak convergence to fractional motion and to the Rosenblatt process. Z. Wahrscheinlichkeitstheorie verw. Geb., 31, 287–302.

    Google Scholar 

  • Taqqu, M.S., Willinger, W. and Sherman, R. (1997). Proof of a fundamental result in self-similar traffic modelling. Computer Communication Review, 27, 5–23.

    Google Scholar 

  • Yong, C.H. (1974). Asymptotic Behaviour of Trigonometric Series. Hong Kong Chinese University of Hong Kong.

  • Zygmund, A. (1995). Trigonometric Series. Cambridge University Press, Cambridge.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gil-Alana, L.A. The Stochastic Permanent Break Model and the Fractional Integration Hypothesis. Computational Economics 23, 315–324 (2004). https://doi.org/10.1023/B:CSEM.0000026794.43145.fc

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:CSEM.0000026794.43145.fc

Navigation