Long memory processes and fractional integration in econometrics

https://doi.org/10.1016/0304-4076(95)01732-1Get rights and content

Abstract

This paper provides a survey and review of the major econometric work on long memory processes, fractional integration, and their applications in economics and finance. Some of the definitions of long memory are reviewed, together with previous work in other disciplines. Section 3 describes the population characteristics of various long memory processes in the mean, including ARFIMA. Section 4 is concerned with estimation and examines semiparametric procedures in both the frequency and time domain, and also the properties of various regression based and maximum likelihood techniques. Long memory volatility processes are discussed in Section 5, while Section 6 discusses applications in economics and finance. The paper also has a concluding section.

References (175)

  • N. Crato et al.

    Fractional integration analysis of long-run behavior for US macroeconomic time series

    Economics Letters

    (1994)
  • M.M. Dacorogna et al.

    A geographical model for the daily and weekly seasonal volatility in the foreign exchange market

    Journal of International Money and Finance

    (1993)
  • F.X. Diebold et al.

    Long memory and persistence in aggregate output

    Journal of Monetary Economics

    (1989)
  • F.X. Diebold et al.

    On the power of Dickey Fuller tests against fractional alternatives

    Economics Letters

    (1991)
  • Z. Ding et al.

    A long memory property of stock returns and a new model

    Journal of Empirical Finance

    (1993)
  • E.F. Fama

    Spot and forward exchange rates

    Journal of Monetary Economics

    (1984)
  • C.W.J. Granger

    Long memory relationships and the aggregation of dynamic models

    Journal of Econometrics

    (1980)
  • C.W.J. Granger

    Some properties of time series data and their use in econometric model specification

    Journal of Econometrics

    (1981)
  • C.W.J. Granger et al.

    On the invertibility of time series models

    Stochastic Process Applications

    (1978)
  • M. Greene et al.

    Long-term dependence in common stock returns

    Journal of Financial Economics

    (1977)
  • C.S. Hakkio et al.

    Cointegration: How short is the long run?

    Journal of International Money and Finance

    (1991)
  • U. Hassler et al.

    On the power of unit roots against fractionally integrated alternatives

    Economics Letters

    (1994)
  • I. Adelman

    Long cycles: Fact or artefact?

    American Economic Review

    (1965)
  • R.K. Adenstedt

    On large sample estimation for the mean of a stationary random sequence

    Annals of Mathematical Statistics

    (1974)
  • C. Agiakloglou et al.

    Lagrange multiplier tests for fractional difference

    Journal of Time Series Analysis

    (1994)
  • C. Agiakloglou et al.

    Bias in an estimator of the fractional difference parameter

    Journal of Time Series Analysis

    (1992)
  • A.A. Anis et al.

    The expected value of the adjusted rescaled Hurst range of independent normal summands

    Biometrika

    (1976)
  • F. Avram et al.

    Noncentral limit theorems and Appell polynomials

    Annals of Probability

    (1987)
  • K. Aydogan et al.

    Are there long cycles in common stock returns?

    Southern Economic Journal

    (1988)
  • D.K. Backus et al.

    Long-memory inflation uncertainty: Evidence from the term structure of interest rates

    Journal of Money, Credit and Banking

    (1993)
  • R.T. Baillie

    Tests of rational expectations and market efficiency

    Econometric Reviews

    (1989)
  • R.T. Baillie et al.

    Common stochastic trends in a system of exchange rates

    Journal of Finance

    (1989)
  • R.T. Baillie et al.

    Cointegration, fractional cointegration and exchange rate dynamics

    Journal of Finance

    (1994)
  • R.T. Baillie et al.

    Fractionally integrated generalized autoregressive conditional heteroskedasticity

    Journal of Econometrics

    (1996)
  • R.T. Baillie et al.

    Analyzing inflation by the fractionally integrated ARFIMA-GARCH model

    Journal of Applied Econometrics

    (1995)
  • J.A. Beran

    A test of location for data with slowly decaying serial correlations

    Biometrika

    (1989)
  • J.A. Beran

    A goodness of fit test for time series with long range dependence

    Journal of the Royal Statistical Society B

    (1992)
  • J.A. Beran

    Statistical methods for data with long-range dependence

    Statistical Science

    (1992)
  • J.A. Beran et al.

    Estimation of the long-memory parameter, based on a multivariate central limit theorem

    Journal of Time Series Analysis

    (1994)
  • Beveridge

    Weather and harvest cycles

    Economic Journal

    (1925)
  • S.R. Blough

    The relationship between power and level for generic unit root tests in finite samples

    Journal of Applied Econometrics

    (1992)
  • D.C. Boes et al.

    Parameter estimation in low order fractionally differenced ARMA models

    Stochastic Hydrology and Hydrolics

    (1989)
  • T. Bollerslev et al.

    Modeling and pricing long-memory in stock market volatility

    Journal of Econometrics

    (1996)
  • F.J. Breidt et al.

    Modeling long-memory stochastic volatility

    (1993)
  • P.J. Brockwell et al.

    Time series: Theory and methods

    (1987)
  • J.Y. Campbell et al.

    Are output fluctuations transitory?

    Quarterly Journal of Economics

    (1987)
  • J.Y. Campbell et al.

    Cointegration and tests of present value models

    Journal of Political Economy

    (1987)
  • J.B. Carlin et al.

    Sensitivity analysis of seasonal adjustments: Empirical case studies

    Journal of the American Statistical Association

    (1989)
  • G. Chen et al.

    Lag window estimation of the degree of differencing in fractionally integrated time series models

    Journal of Time Series Analysis

    (1994)
  • Y.-W. Cheung

    Long memory in foreign-exchange rates

    Journal of Business and Economic Statistics

    (1993)
  • Cited by (1254)

    View all citing articles on Scopus
    1

    I am greatly indebted to the editor, Max King, and to three anonymous referees for their very helpful comments on an earlier version of this paper. I also wish to acknowledge several useful discussions with Clive Granger and particularly helpful comments from Tim Bollerslev, Ching-Fan Chung, David Dickey, Frank Diebold, Hans-Ole Mikkelsen, Franz Palm, Peter Robinson, John Rogers, Philip Rothman, Peter Schmidt, and Casper de Vries. This article has also benefited from comments made by seminar participants at Duke University, Federal Reserve Bank of St. Louis, University of California-San Diego, University of California-Santa Barbara, University of California-Riverside, University of Southern California, and University of Washington.

    View full text