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Extracting a common stochastic trend: Theory with some applications

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  • Chang, Yoosoon
  • Isaac Miller, J.
  • Park, Joon Y.

Abstract

This paper investigates the statistical properties of estimators of the parameters and unobserved series for state space models with integrated time series. In particular, we derive the full asymptotic results for maximum likelihood estimation using the Kalman filter for a prototypical class of such models--those 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 we explicitly consider comprise a special-yet useful-class of models that may be employed to extract the common stochastic trend from multiple integrated time series. Such 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 this class of models extracting a common stochastic trend from three sets of time series involving short- and long-term interest rates, stock return volatility and trading volume, and Dow Jones stock prices.

Suggested Citation

  • Chang, Yoosoon & Isaac Miller, J. & Park, Joon Y., 2009. "Extracting a common stochastic trend: Theory with some applications," Journal of Econometrics, Elsevier, vol. 150(2), pages 231-247, June.
  • Handle: RePEc:eee:econom:v:150:y:2009:i:2:p:231-247
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    References listed on IDEAS

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    Cited by:

    1. Li, Yong & Yu, Jun, 2012. "Bayesian hypothesis testing in latent variable models," Journal of Econometrics, Elsevier, pages 237-246.
    2. Miller, J. Isaac & Park, Joon Y., 2010. "Nonlinearity, nonstationarity, and thick tails: How they interact to generate persistence in memory," Journal of Econometrics, Elsevier, pages 83-89.
    3. Bretó, Carles, 2014. "On idiosyncratic stochasticity of financial leverage effects," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 20-26.
    4. Ledenyov, Dimitri O. & Ledenyov, Viktor O., 2015. "Wave function method to forecast foreign currencies exchange rates at ultra high frequency electronic trading in foreign currencies exchange markets," MPRA Paper 67470, University Library of Munich, Germany.
    5. Miller, J. Isaac, 2011. "Testing the bounds: Empirical behavior of target zone fundamentals," Economic Modelling, Elsevier, vol. 28(4), pages 1782-1792, July.
    6. Durdyev, Ruslan & Peresetsky, Anatoly, 2014. "Autocorrelation in the global stochastic trend," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 35(3), pages 39-58.
    7. Berger, Tino & Everaert, Gerdie, 2010. "Labour taxes and unemployment evidence from a panel unobserved component model," Journal of Economic Dynamics and Control, Elsevier, vol. 34(3), pages 354-364, March.
    8. Chen, Xiaoshan & MacDonald, Ronald, 2015. "Measuring the dollar–euro permanent equilibrium exchange rate using the unobserved components model," Journal of International Money and Finance, Elsevier, vol. 53(C), pages 20-35.

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