Skip to main content
SpringerLink
Log in

A monte carlo analysis of two spectral tests of the martingale hypothesis

  • Published:
Journal of the Italian Statistical Society Aims and scope Submit manuscript

Summary

The size, power, and robustness properties of the Kolmogorov-Smirnov and Cramér-von Mises spectral tests of the martingale (difference) hypothesis are investigated by Monte Carlo methods. The results highlight a marked superiority of the Cramér-von Mises with respect to the Kolmogorov-Smirnov test. The paper also shows that the Cramér-von Mises test is simple to compute, more general and more powerful than other converntionally used tests.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Barro, R. J. (1979): On the Determination of Public Debt,Journal of Political Economy, 87, 940–971.

    Article  Google Scholar 

  • Beveridge, S. andNelson, C. R. (1981): A New Approach to Decomposition of Economic Time Series into Permanent and Transitory Components with Particular Attention to Measurement of the ‘Business Cycle’.Journal of Monetary Economics, 7, 151–174.

    Article  Google Scholar 

  • Bizer, D. S. andDurlauf, S. N. (1990): Testing the Positive Theory of Government Finance,Journal of Monetary Economics, 26, 123–141.

    Article  Google Scholar 

  • Bollerslev, T. (1986): Generalized Autoregressive Conditional Heteroskedasticity.Journal of Econometrics, 31, 307–327.

    Article  MATH  MathSciNet  Google Scholar 

  • Box, G. E. P. andPierce, D. A. (1970): The Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models.Journal of the American Statistical Association, 65, 1509–1526.

    Article  MATH  MathSciNet  Google Scholar 

  • Burbin, J. andWatson, G. S. (1950): Testing for Serial Correlation in Least Squares Regression I,Biometrika, 37, 409–428.

    MathSciNet  Google Scholar 

  • Durbin, J. andWatson, G. S. (1951): Testing for Serial Correlation in Least Squares Regression II.Biometrika, 38, 159–178.

    MATH  MathSciNet  Google Scholar 

  • Durlauf, S. N. (1989): Output Persistence, Economic Structure, and the Choice of Stabilization Policy,Brookings Papers on Economic Activity, 69–136.

  • Durlauf, S. N. (1991): Spectral Based Testing of the Martingale Hypothesis.Journal of Econometrics, 50, 355–376.

    Article  MATH  MathSciNet  Google Scholar 

  • Durlauf, S. N. (1993): Time Series Properties of Aggregate Output Fluctuations,Journal of Econometrics, 56, 39–56.

    Article  MATH  MathSciNet  Google Scholar 

  • Engle, R. F. (1982): Autoregressive Conditional Heteroskedasticity With Estimates of the Variance of United Kingdom Inflation.Econometrica, 50, 987–1008.

    Article  MATH  MathSciNet  Google Scholar 

  • Fong, W. M. andOuliaris, S. (1995): Spectral Tests of the Martingale Hypothesis for Exchange Rates.Journal of Applied Econometrics, 10, 255–271.

    Google Scholar 

  • French, K., Schwert, G. andStambaugh, R. (1985): Expected Stock Returns and Volatility,Journal of Financial Economics, 19, 3–30.

    Article  Google Scholar 

  • Hall, R. E. (1978): Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence,Journal of Political Economy, 86, 971–987.

    Article  Google Scholar 

  • Hanan, E. J. andHeyde, C. C. (1972): On limit Theorems for Quadratic Functions of Discrete Time Series.Annals of mathematical Statistics, 43, 2058–2066.

    MathSciNet  Google Scholar 

  • Harvey, A. C. (1993):Time Series Models (2nd Edition). London, Harvester Wheatsheaf.

    MATH  Google Scholar 

  • Johnson, N. L. andKotz, S. (1970):Continuous Univariate Distributions-2. Boston, Houghton Mifflin Company.

    Google Scholar 

  • Ljung, G. M. andBox, G. E. P. (1978): On a Measure of Lack of Fit in Time-Series Models,Biometrika, 65, 297–303.

    Article  MATH  Google Scholar 

  • Lo, A. W. andMacKinley, C. (1989): The Size and Power of the Variance Ratio Test in Finite Samples: A Monte Carlo Investigation,Journal of Econometrics, 40, 203–238.

    Article  MathSciNet  Google Scholar 

  • Lupi, C. andOrdine, P. (1994): Un'analisi non parametrica di occupazione e salari: alcuni fatti stilizzati, in A. Amendola (ed.),Disoccupazione e mercato del lavoro. Napoli, ESI.

    Google Scholar 

  • Lupi, C. andOrdine, P. (1997): Asymmetries in Unemployment Rates: An International Comparison, ISPE, Documenti di lavoro No. 63/97, presented at the 52nd Econometric Society European Meeting, Toulouse.

  • Milhøj, A. (1985): The Moment Structure of ARCH Processes,Scandinavian Journal of Statistics, 12, 281–292.

    Google Scholar 

  • Nelson, D. B. (1990): Stationarity and Persistence in the GARCH(1,1) Model,Econometric Theory, 6, 318–334.

    Article  MathSciNet  Google Scholar 

  • Nelson, D. B. (1991): Conditional Heteroskedasticity in Asset Returns: A New Approach,Econometrica, 59, 347–370.

    Article  MATH  MathSciNet  Google Scholar 

  • Phillips, P. C. B. andSolo, V. (1992): Asymptotics for Linear Processes,Annals of Statistics, 20, 971–1001.

    MATH  MathSciNet  Google Scholar 

  • Poterba, J. andSummers, L. (1986): The Persistence of Volatility and Stock Market Fluctuations,American Economic Review, 76, 1142–1151.

    Google Scholar 

  • Samuelson, P. A. (1965): Proof that Properly Anticipated Prices Fluctuate Randomly,Industrial Management Review, 6, 41–50.

    Google Scholar 

  • Watson, M. W. (1986): Univariate Detrending Methods with Stochastic Trends,Journal of Monetary Economics, 18, 49–75.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. ISPE-Instituto di Studi per la programmazione economica, Corso Vittorio Emanuele, 284, I-00186, Roma, Italy

    Claudio Lupi

Authors
  1. Claudio Lupi
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lupi, C. A monte carlo analysis of two spectral tests of the martingale hypothesis. J. It. Statist. Soc. 5, 335–360 (1996). https://doi.org/10.1007/BF02589095

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02589095

Keywords and phrases

Search

Navigation