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Testing for Equal Predictability of Stationary ARMA Processes

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  • Edoardo Otrano
  • Umberto Triacca

Abstract

In this work we use a measure of predictability of a time series following a stationary ARMA process to develop a test of equal predictability of two or more time series. The test is derived by a set of propositions which links the structure of the AR and MA coefficients to the predictability measure. A particular case of this general approach is constituted by time series having a Wold decomposition with weights having the same sign; in this framework the equal predictability is equivalent to parallelism among ARMA models and the null hypothesis of equal predictability is simply a set of linear restrictions. The ARMA representation of the GARCH models presents non-negative weights, so that this test can be extended to verify the equal predictability of squared time series following GARCH structures.

Suggested Citation

  • Edoardo Otrano & Umberto Triacca, 2007. "Testing for Equal Predictability of Stationary ARMA Processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(9), pages 1091-1108.
    • Handle: RePEc:taf:japsta:v:34:y:2007:i:9:p:1091-1108
    DOI: 10.1080/02664760701592158
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    References listed on IDEAS

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    2. Findley, David F, et al, 1998. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 169-177, April.
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    4. Findley, David F, et al, 1998. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 127-152, April.
    5. Galbraith, John W. & KI[#x1e63]Inbay, Turgut, 2005. "Content horizons for conditional variance forecasts," International Journal of Forecasting, Elsevier, vol. 21(2), pages 249-260.
    6. Steece, Bert & Wood, Steven, 1985. "A Test for the Equivalence of k ARMA Models," Empirical Economics, Springer, vol. 1(1), pages 1-11.
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    1. Otranto, Edoardo, 2010. "Identifying financial time series with similar dynamic conditional correlation," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 1-15, January.
    2. Otranto, Edoardo, 2008. "Clustering heteroskedastic time series by model-based procedures," Computational Statistics & Data Analysis, Elsevier, vol. 52(10), pages 4685-4698, June.
    3. Umberto Triacca, 2009. "Volatility Persistence and Predictability of Squared Returns in GARCH(1,1) Models," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 1(3), pages 285-291, November.

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