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Costationarity of Locally Stationary Time Series


  • Cardinali Alessandro

    (University of Bristol)

  • Nason Guy P

    (University of Bristol)


Given more than one locally stationary (LS) time series, this article describes a method to discover time-varying linear combinations of the LS series that are stationary. Systems for which this can occur are called costationary, and the associated time-varying linear combinations are called costationary vectors. Costationary systems are interesting for a number of reasons. The costationary vectors shed light on the nature and strength of a potentially interesting relationship between the LS series. The derived stationary series, which is the time-varying combination of the LS series, is often of independent interest and use. The article discusses why a spectral approach is often preferred to the time-domain and why costationary vectors need to be complexity constrained, and it also demonstrates an interesting error-correction formulae which shows how costationary systems must evolve to maintain stationarity in response to system shocks. We illustrate our methodology with two examples: one from asset allocation in financial portfolio construction and the other which mitigates intermittency in wind power management. In the former, a stationary synthetic asset is constructed using market index data and is shown to have superior Sharpe ratios to two established portfolio selectors. In the latter, power outputs from separate wind series are dynamically combined to provide a power output which has smaller intermittency than the individual inputs.

Suggested Citation

  • Cardinali Alessandro & Nason Guy P, 2011. "Costationarity of Locally Stationary Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 2(2), pages 1-35, January.
  • Handle: RePEc:bpj:jtsmet:v:2:y:2011:i:2:n:1

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    References listed on IDEAS

    1. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    2. Sébastien Van Bellegem & Rainer Dahlhaus, 2006. "Semiparametric estimation by model selection for locally stationary processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(5), pages 721-746.
    3. Granger Clive W.J., 2008. "Non-Linear Models: Where Do We Go Next - Time Varying Parameter Models?," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(3), pages 1-11, September.
    4. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    5. Richard A. Davis & Thomas C. M. Lee & Gabriel A. Rodriguez-Yam, 2008. "Break Detection for a Class of Nonlinear Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(5), pages 834-867, September.
    6. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    7. Ahamada, Ibrahim, 2002. "Tests for covariance stationarity and white noise, with an application to Euro/US dollar exchange rate: An approach based on the evolutionary spectral density," Economics Letters, Elsevier, vol. 77(2), pages 177-186, October.
    8. Bierens, Herman J. & Martins, Luis F., 2010. "Time-Varying Cointegration," Econometric Theory, Cambridge University Press, vol. 26(05), pages 1453-1490, October.
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    Cited by:

    1. Cardinali, Alessandro & Nason, Guy P., 2013. "Costationarity of Locally Stationary Time Series Using costat," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 55(i01).
    2. Schnurr Alexander & Woerner Jeannette H. C., 2011. "Well-balanced Lévy driven Ornstein–Uhlenbeck processes," Statistics & Risk Modeling, De Gruyter, vol. 28(4), pages 343-357, December.

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