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Inference on transformed stationary time series

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  • Hosoya, Yuzo
  • Terasaka, Takahiro

Abstract

The paper is about an approach for parametric inference on instantaneously transformed stationary processes. The paper discusses the asymptotics of the Whittle estimator of the parameters involved and also provides the explicit expression of the asymptotic covariance matrix which does not necessarily require the innovation Gaussianity assumption. As a specific instantaneous transformation, the paper introduces a new version of the Box-Cox transformation and investigates in detail the vector ARMA processes implemented by that transformation, proposing a computation-intensive procedure for parametric estimation and testing. As a computationally feasible test not relying upon the knowledge of the explicit analytic form of the asymptotic covariance matrix or on the information equality, the paper proposes a Monte Carlo Wald test, providing illustrative simulation and real-data examples.

Suggested Citation

  • Hosoya, Yuzo & Terasaka, Takahiro, 2009. "Inference on transformed stationary time series," Journal of Econometrics, Elsevier, vol. 151(2), pages 129-139, August.
  • Handle: RePEc:eee:econom:v:151:y:2009:i:2:p:129-139
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    References listed on IDEAS

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    1. MacKinnon, James G & Magee, Lonnie, 1990. "Transforming the Dependent Variable in Regression Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(2), pages 315-339, May.
    2. Davidson, Russell & MacKinnon, James G, 1984. "Model Specification Tests Based on Artificial Linear Regressions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(2), pages 485-502, June.
    3. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    4. Amemiya, Takeshi, 1977. "The Maximum Likelihood and the Nonlinear Three-Stage Least Squares Estimator in the General Nonlinear Simultaneous Equation Model," Econometrica, Econometric Society, vol. 45(4), pages 955-968, May.
    5. Robinson, P M, 1991. "Best Nonlinear Three-Stage Least Squares Estimation of Certain Econometric Models," Econometrica, Econometric Society, vol. 59(3), pages 755-786, May.
    6. Yang, Zhenlin, 2006. "A modified family of power transformations," Economics Letters, Elsevier, vol. 92(1), pages 14-19, July.
    7. de Jong, Robert M., 2003. "Logarithmic spurious regressions," Economics Letters, Elsevier, vol. 81(1), pages 13-21, October.
    8. Pollard, David, 1985. "New Ways to Prove Central Limit Theorems," Econometric Theory, Cambridge University Press, vol. 1(03), pages 295-313, December.
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    Cited by:

    1. Hector Manuel Zárate Solano & Angélica Rengifo Gómez, 2013. "Forecasting annual inflation with power transformations: the case of inflation targeting countries," Borradores de Economia 756, Banco de la Republica de Colombia.

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