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Extracting a Common Stochastic Trend: Theories with Some Applications

Author

Listed:
  • Chang, Yoosoon

    (Rice U)

  • Miller, J. Isaac

    (University of Missouri)

  • Park, Joon Y.

    (Rice University and Sungkyunkwan University)

Abstract
This paper investigates the statistical properties of the Kalman filter for state space models including integrated time series. In particular, we derive the full asymptotics of maximum likelihood estimation for some prototypical class of such models, i.e., the models with a single latent common stochastic trend. Indeed, we establish the consistency and asymptotic mixed normality of the maximum likelihood estimator and show that the conventional method of inference is valid for this class of models. The models considered explicitly in the paper comprise a special, yet useful, class of models that we may use to extract the common stochastic trend from multiple integrated time series. As we show in the paper, the models can be very useful to obtain indices that represent fluctuations of various markets or common latent factors that affect a set of economic and financial variables simultaneously. Moreover, our derivation of the asymptotics of this class makes it clear that the asymptotic Gaussianity and the validity of the conventional inference for the maximum likelihood procedure extends to a larger class of more general state space models involving integrated time series. Finally, we demonstrate the utility of the state space model by extracting a common stochastic trend in three empirical analyses: interest rates, return volatility and trading volume, and Dow Jones stock prices.

Suggested Citation

  • Chang, Yoosoon & Miller, J. Isaac & Park, Joon Y., 2005. "Extracting a Common Stochastic Trend: Theories with Some Applications," Working Papers 2005-06, Rice University, Department of Economics.
    • Handle: RePEc:ecl:riceco:2005-06
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    File URL: http://www.ruf.rice.edu/~econ/papers/2005papers/chang06.pdf
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    References listed on IDEAS

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    Cited by:

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    3. Mitra, Sinchan & Sinclair, Tara M., 2012. "Output Fluctuations In The G-7: An Unobserved Components Approach," Macroeconomic Dynamics, Cambridge University Press, vol. 16(3), pages 396-422, June.

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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