Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-26T15:14:21.958Z Has data issue: false hasContentIssue false
  • English
  • Français

APPARENT LONG MEMORY IN TIME SERIES AS AN ARTIFACT OF A TIME-VARYING MEAN: CONSIDERING ALTERNATIVES TO THE FRACTIONALLY INTEGRATED MODEL

Published online by Cambridge University Press:  05 May 2010

Richard A. Ashley  and
Douglas M. Patterson
Richard A. Ashley*
Affiliation:
Virginia Tech
Douglas M. Patterson
Affiliation:
Virginia Tech
*
Address correspondence to: Richard A. Ashley, Economics Department (0316), Virginia Tech, Blacksburg, VA 24061, USA; e-mail: [email protected].
Get access Rights & Permissions [Opens in a new window]

Abstract

Structural breaks and switching processes are known to induce apparent long memory in a time series. Here we show that any significant time variation in the mean renders the sample correlogram (and related spectral estimates) inconsistent. In particular, smooth time variation in the mean—i.e., even a weak trend, either stochastic or deterministic—induces apparent long memory. This apparent long memory can be eliminated by either high-pass filtering or by detrending. Here we demonstrate the effectiveness in this regard of nonlinear detrending via penalized-spline nonparametric regression. A time-varying mean can be of economic interest in its own right. This suggests that isolating out and separately examining both a local mean (i.e., a nonlinear trend or the realization of a stochastic trend) and deviations from it is preferable as a modeling strategy to simply estimating a fractionally integrated model. We illustrate the superiority of this strategy using stock return volatility data.

Keywords

Long MemoryFractional IntegrationDetrendingStock ReturnsVolatility
Type
Articles
Information
Macroeconomic Dynamics , Volume 14 , Supplement S1: Nonlinear Time Series , May 2010 , pp. 59 - 87
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abadir, K.M., Distaso, W., and Giriatis, L. (2005) Semiparametric Estimation and Inference for Trending I(d) and Related Processes. Mimeo, Department of Economics, Imperial College London.Google Scholar
Ashley, R. (2008) On the Origins of Conditional Heteroscedasticity in Time Series. Mimeo, Economics Department, Virginia Tech. http://ashleymac.econ.vt.edu/working_papers/origins_of_conditional_heteroscedasticity.pdf.Google Scholar
Ashley, R. and Patterson, D.M. (2007) Apparent Long Memory in Time Series as an Artifact of a Time-Varying Mean: A “Local Mean” Filtering Alternative to the Fractionally Integrated Model. Mimeo, Economics Department, Virginia Tech.Google Scholar
Baillie, R.T. (1996) Long-memory processes and fractional integration in economics. Journal of Econometrics 73, 5–59.CrossRefGoogle Scholar
Baillie, R.T. and Kapetanios, G. (2005) Testing for Neglected Nonlinearity in Long Memory Models. Unpublished manuscript, Department of Economics, Michigan State University.Google Scholar
Baxter, M. and King, R. (1999) Measuring business cycles: Approximate band-pass filters for economic time series. Review of Economics and Statistics 81, 575–593.CrossRefGoogle Scholar
Beran, J. (1994) Statistics for Long-Memory Processes. New York: Chapman and Hall.Google Scholar
Beran, J. and Ocker, D. (2001) Volatility of stock-market indexes: An analysis based on SEMIFAR models. Journal of Business and Economic Statistics 19, 103–116.CrossRefGoogle Scholar
Bhattacharya, R.N., Gupta, V.K., and Waymire, E. (1983) The Hurst effect under trends. Journal of Applied Probability 20, 649–662.CrossRefGoogle Scholar
Box, G.E.P. and Jenkins, G.M. (1976) Time Series Analysis. San Francisco: Holden-Day.Google Scholar
Charfeddine, L. and Guégan, D. (2007) Which Is Best for the US Inflation Series: A Structural Change Model or a Long Memory Process? CES-AC working paper 01-2007.Google Scholar
Diebold, F.X. and Inoue, A. (2001) Long memory and regime switching. Journal of Econometrics 105, 131–159.CrossRefGoogle 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.CrossRefGoogle Scholar
Gourieroux, C. and Jasiak, J. (2001) Memory and infrequent breaks. Economics Letters 70, 29–41.CrossRefGoogle Scholar
Granger, C.W.J. (1980) Long-memory relationships and the aggregation of dynamic models. Journal of Econometrics 14, 227–238.CrossRefGoogle Scholar
Granger, C.W.J. and Hyung, N. (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 models and fractional differencing. Journal of Time Series Analysis 1, 15–39.CrossRefGoogle Scholar
Granger, C.W.J. and Teräsvirta, T. (1999) A simple nonlinear time series model with misleading linear properties. Economics Letters 62, 161–165.CrossRefGoogle Scholar
Hamilton, James D. (1994) Time Series Analysis. Princeton, NJ: Princeton University Press.CrossRefGoogle Scholar
Hinich, Melvin J., Foster, John, and Wild, Philip (2008) An Investigation of the Cycle Extraction Properties of Several Bandpass Filters Used to Identify Business Cycles. School of Economics Discussion Paper No. 358, School of Economics, The University of Queensland, Australia.Google Scholar
Jensen, M.J. and Liu, M. (2006) Do long swings in the business cycle lead to strong persistence in output? Journal of Monetary Economics 53 (3), 597–611.CrossRefGoogle Scholar
Kauermann, G., Krivobokova, T., and Semmler, W. (2008) Filtering Time Series with Penalized Splines. Unpublished manuscript, New School for Social Research.Google Scholar
Kendall, M., Stuart, A., and Ord, J.K. (1983) The Advanced Theory of Statistics, 4th ed., vol. 3. London: Charles Griffen.Google Scholar
Krivobokova, T. and Kauermann, G. (2007) A note on penalized spline smoothing with correlated errors. Journal of the American Statistical Association 102 (440), 1328–1337.CrossRefGoogle Scholar
Mikosch, T. and Stǎricǎ, Cǎtǎlin (2004) Nonstationarities in financial time series, the long-range dependence, and the IGARCH effects. Review of Economics and Statistics 86 (1), 378–390.CrossRefGoogle Scholar
Patterson, D.M. and Ashley, R. (2000) A Nonlinear Time Series Workshop. Boston: Kluwer Academic.CrossRefGoogle Scholar
Perron, P. and Qu, Z. (2006) An Analytical Evaluation of the Log-Periodogram Estimate in the Presence of Level Shifts and Its Implications for Stock Returns Volatility. Mimeo, Department of Economics, Boston University.Google Scholar
Raymo, M. (1997) The timing of major climate terminations. Paleoceanography 12 (4), 577–585.CrossRefGoogle Scholar
Robinson, P.M. (1995) Log-periodogram regression of time series with long range dependence. Annals of Statistics 23 (3), 1048–1072.CrossRefGoogle Scholar
Wahba, G. (1990) Spline Models for Observational Data. Philadelphia: Society for Industrial and Applied Mathematics.CrossRefGoogle Scholar